This paper presents a novel model predictive control (MPC) formulation for linear hybrid systems. The algorithm relies on a multiple-degree-of-freedom formulation that enables the user to adjust the speed of setpoint tracking, measured disturbance rejection and unmeasured disturbance rejection independently in the closed-loop system. Consequently, controller tuning is more flexible and intuitive than relying on move suppression weights as traditionally used in MPC schemes. The formulation is motivated by the need to achieve robust performance in using the algorithm in emerging applications, for instance, as a decision policy for adaptive, time-varying interventions used in behavioral health. The proposed algorithm is demonstrated on a hypothetical adaptive intervention problem inspired by the Fast Track program, a real-life preventive intervention for improving parental function and reducing conduct disorder in at-risk children. Simulation results in the presence of simultaneous disturbances and significant plant-model mismatch are presented. These demonstrate that a hybrid MPC-based approach for this class of interventions can be tuned for desired performance under demanding conditions that resemble participant variability that is experienced in practice when applying an adaptive intervention to a population.
There is good evidence that naltrexone, an opioid antagonist, has a strong neuroprotective role and may be a potential drug for the treatment of fibromyalgia. In previous work, some of the authors used experimental clinical data to identify input-output linear time invariant models that were used to extract useful information about the effect of this drug on fibromyalgia symptoms. Additional factors such as anxiety, stress, mood, and headache, were considered as additive disturbances. However, it seems reasonable to think that these factors do not affect the drug actuation, but only the way in which a participant perceives how the drug actuates on herself. Under this hypothesis the linear time invariant models can be replaced by State-Space Affine Linear Parameter Varying models where the disturbances are seen as a scheduling signal signal only acting at the parameters of the output equation. In this paper a new algorithm for identifying such a model is proposed. This algorithm minimizes a quadratic criterion of the output error. Since the output error is a linear function of some parameters, the Affine Linear Parameter Varying system identification is formulated as a separable nonlinear least squares problem. Likewise other identification algorithms using gradient optimization methods several parameter derivatives are dynamical systems that must be simulated. In order to increase time efficiency a canonical parametrization that minimizes the number of systems to be simulated is chosen. The effectiveness of the algorithm is assessed in a case study where an Affine Parameter Varying Model is identified from the experimental data used in the previous study and compared with the time-invariant model.
We compared four algorithms for controlling a MEMS deformable mirror of an adaptive optics (AO) scanning laser ophthalmoscope. Interferometer measurements of the static nonlinear response of the deformable mirror were used to form an equivalent linear model of the AO system so that the classic integrator plus wavefront reconstructor type controller can be implemented. The algorithms differ only in the design of the wavefront reconstructor. The comparisons were made for two eyes (two individuals) via a series of imaging sessions. All four controllers performed similarly according to estimated residual wavefront error not reflecting the actual image quality observed. A metric based on mean image intensity did consistently reflect the qualitative observations of retinal image quality. Based on this metric, the controller most effective for suppressing the least significant modes of the deformable mirror performed the best.
Excessive gestational weight gain (GWG) represents a major public health concern. In this paper, we present a dynamical systems model that describes how a behavioral intervention can influence weight gain during pregnancy. The model relies on the integration of a mechanistic energy balance with a dynamical behavioral model. The behavioral model incorporates some well-accepted concepts from psychology: the Theory of Planned Behavior (TPB) and the principle of self-regulation which describes how internal processes within the individual can serve to reinforce the positive outcomes of an intervention. A hypothetical case study is presented to illustrate the basic workings of the model and demonstrate how the proper design of the intervention can counteract natural trends towards declines in healthy eating and reduced physical activity during the course of pregnancy. The model can be used by behavioral scientists to evaluate decision rules for adaptive time-varying behavioral interventions, or as the open-loop model for hybrid model predictive control algorithms acting as decision frameworks for such interventions.
Excessive gestational weight gain (GWG) represents a major public health issue. In this paper, we pursue a control engineering approach to the problem by applying model predictive control (MPC) algorithms to act as decision policies in the intervention for assigning optimal intervention dosages. The intervention components consist of education, behavioral modification and active learning. The categorical nature of the intervention dosage assignment problem dictates the need for hybrid model predictive control (HMPC) schemes, ultimately leading to improved outcomes. The goal is to design a controller that generates an intervention dosage sequence which improves a participant's healthy eating behavior and physical activity to better control GWG. An improved formulation of self-regulation is also presented through the use of Internal Model Control (IMC), allowing greater flexibility in describing self-regulatory behavior. Simulation results illustrate the basic workings of the model and demonstrate the benefits of hybrid predictive control for optimized GWG adaptive interventions.
Data-centric estimation methods such as Model-on-Demand and Direct Weight Optimization form attractive techniques for estimating unknown functions from noisy data. These methods rely on generating a local function approximation from a database of regressors at the current operating point with the process repeated at each new operating point. This paper examines the design of optimal input signals formulated to produce informative data to be used by local modeling procedures. The proposed method specifically addresses the distribution of the regressor vectors. The design is examined for a linear time-invariant system under amplitude constraints on the input. The resulting optimization problem is solved using semidefinite relaxation methods. Numerical examples show the benefits in comparison to a classical PRBS input design.
The chronic, relapsing nature of tobacco use represents a major challenge in smoking cessation treatment. Recently, novel intervention paradigms have emerged that seek to adjust treatments over time in order to meet a patient's changing needs. This article demonstrates that Hybrid Model Predictive Control (HMPC) offers an appealing framework for designing these optimized, time-varying smoking cessation interventions. HMPC is a particularly appropriate approach as it recognizes that intervention doses must be assigned in predetermined, discrete units while retaining receding-horizon, constraint-handling, and combined feedback and feedforward capabilities. Specifically, an intervention algorithm is developed here in which counseling and two pharmacotherapies are manipulated to reduce daily smoking and craving levels. The potential usefulness of such an intervention is illustrated through simulated treatment of a quit attempt in a hypothetical patient, which highlights that prioritizing reduction in craving over total daily smoking levels significantly reduces craving levels, suppresses relapse, and successfully rejects time-varying disturbances such as stress, all while adhering to several practical operational constraints and resource use considerations.
Cigarette smoking remains a major public health issue. Despite a variety of treatment options, existing intervention protocols intended to support attempts to quit smoking have low success rates. An emerging treatment framework, referred to as adaptive interventions in behavioral health, addresses the chronic, relapsing nature of behavioral health disorders by tailoring the composition and dosage of intervention components to an individual's changing needs over time. An important component of a rapid and effective adaptive smoking intervention is an understanding of the behavior change relationships that govern smoking behavior and an understanding of intervention components' dynamic effects on these behavioral relationships. As traditional behavior models are static in nature, they cannot act as an effective basis for adaptive intervention design. In this article, behavioral data collected daily in a smoking cessation clinical trial is used in development of a dynamical systems model that describes smoking behavior change during cessation as a self-regulatory process. Drawing from control engineering principles, empirical models of smoking behavior are constructed to reflect this behavioral mechanism and help elucidate the case for a control-oriented approach to smoking intervention design.
In previous work, we have developed optimal-control based approaches that seek to minimize the risk of subsequent virological failure by "pre-conditioning" the viral load during therapy switches. These techniques result in the transient susceptibility of the total viral load, and rely on finding the minimum of a dip in viral load and switching before viral load rebound. Model uncertainty necessitates a closed-loop approach to minimum-finding. Blood measurements are costly in terms of money, inconvenience and risk. In this paper, we introduce an iterative parameter estimation approach to find the viral load minimum, and measure the degree of optimality of minimum-seeking under conditions of measurement noise. We evaluate the cost-savings of this approach in terms of number of samples saved from a constant measurement rate.
Control engineering offers a systematic and efficient means for optimizing the effectiveness of behavioral interventions. In this paper, we present an approach to develop dynamical models and subsequently, hybrid model predictive control schemes for assigning optimal dosages of naltrexone as treatment for a chronic pain condition known as fibromyalgia. We apply system identification techniques to develop models from daily diary reports completed by participants of a naltrexone intervention trial. The dynamic model serves as the basis for applying model predictive control as a decision algorithm for automated dosage selection of naltrexone in the face of the external disturbances. The categorical/discrete nature of the dosage assignment creates a need for hybrid model predictive control (HMPC) schemes. Simulation results that include conditions of significant plant-model mismatch demonstrate the performance and applicability of hybrid predictive control for optimized adaptive interventions for fibromyalgia treatment involving naltrexone.
This paper develops an optimization method to synthesize trajectories for use in the identification of system parameters. Using widely studied techniques to compute Fisher information based on observations of nonlinear dynamical systems, an infinite-dimensional, projection-based optimization algorithm is formulated to optimize the system trajectory using eigenvalues of the Fisher information matrix as the cost metric. An example of a cart-pendulum simulation demonstrates a significant increase in the Fisher information using the optimized trajectory with decreased parameter variances shown through Monte-Carlo tests and computation of the Cramer-Rao lower bound.
This paper is concerned with the model reduction of positive systems. For a given stable positive system, our attention is focused on the construction of a reduced-order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed H<sub>∞</sub> performance. Based upon a system augmentation approach, a novel characterization on the stability with H<sub>∞</sub> performance of the error system is first obtained in terms of linear matrix inequality (LMI). Then, a necessary and sufficient condition for the existence of a desired reduced-order model is derived accordingly. A significance of the proposed approach is that the reduced-order system matrices can be parametrized by a positive definite matrix with flexible structure, which is fully independent of the Lyapunov matrix; thus, the positivity constraint on the reduced-order system can be readily embedded in the model reduction problem. Finally, a numerical example is provided to show the effectiveness of the proposed techniques.
The reduced structure controller design problem was previously defined in A. Nobakhti and N. Munro (2003). Thereof, a two-stage process for the design of the forementioned controllers were proposed. In this paper, a single-stage, genetic algorithm approach to solving the problem is proposed.
A concept for knowledge-based control systems is presented. The concept integrates conventional control functions with knowledge-based techniques. The basis for the concept is a common object-oriented, multi-view knowledge-base. Operating upon the common knowledge-base are a number of tools for execution of basic control functions, rule-based monitoring and diagnosis, simulation, troubleshooting, etc. The concept is demonstrated on Steritherm, a process for UHT sterilization of liquid food products. A G2 prototype is presented. It contains a dynamic simulation of the process connected to an emulation of the knowledge-based control system including continuous control functions, sequential logic implemented with Grafcet-style sequential flow charts, alarm logics, monitoring rules, model-based fault diagnosis, and troubleshooting fault trees.
The primary mirror diameter of affordable space telescopes is limited by mass and manufacturing cost. Currently planned optical/near-IR space telescopes use a segmented primary mirror with relatively few segments, and make limited use of real-time position control. However, control can be used as an enabler for a fundamentally different, very highly segmented architecture, leading to a significant reduction in areal density, and hence a significant increase in the realistically achievable diameter of a space telescope. Small segments can be thinner, and overall mirror stiffness provided by control rather than a back-support structure. However, the resulting control problem involves thousands of actuators and sensors, and many lightly damped modes within the bandwidth. A local control approach similar to that previously developed for large deformable mirrors can provide robust performance for this problem. This is illustrated here for a 30 m diameter primary mirror composed of 12 000 0.3 m diameter segments. The areal density might be as low as 3-4kg/m<sup>2</sup>, nearly an order of magnitude lower than current designs.
Replicating genetically modified adenoviruses have shown promise as a new treatment approach against cancer. Recombinant adenoviruses replicate only in cancer cells which contain certain mutations, such as the loss of functional p53, as is the case in the virus ONYX-015. The successful entry of the viral particle into target cells is strongly dependent on the presence of the main receptor for adenovirus, the coxsackie- and adeno-virus receptor (CAR). This receptor is frequently down-regulated in highly malignant cells, rendering this population less vulnerable to viral attack. It has been shown that use of MEK inhibitors can up-regulate CAR expression, resulting in enhanced adenovirus entry into the cells. However, inhibition of MEK results in G1 cell cycle arrest, rendering infected cells temporarily unable to produce virus. This forces a tradeoff. While drug mediated up-regulation of CAR enhances virus entry into cancer cells, the consequent cell cycle arrest inhibits production of new virus particles and the replication of the virus. Optimal control-based schedules of MEK inhibitor application should increase the efficacy of this treatment, maximizing the overall tumor toxicity by exploiting the dynamics of CAR expression and viral production. We introduce two mathematical models of these dynamics and show simple optimal control based strategies which motivate this approach
This paper sets forth and illustrates some techniques for
parameter identification (PId) of a nonlinear state model that
approximates the dynamical behavior of the humoral immune response of a
human to Haemophilus influenzae Type-b. The natural physiological
time-separation of the primary, late follicular, and secondary immune
responses of this biological process allows one to divide the PId
problem into a sequence of smaller PId sub-problems. To reduce the
dimension of the PId even further, coupling effects are minimized or
eliminated by temporarily replacing variables and/or certain other
functions of variables by approximate a priori known time functions
called exogenous inputs. This sequence of low dimensional PId problems
entails matching a set of one or two parameters at each step to a
time-attribute pair defined as a maximum or minimum measured
concentration level in a given time window. The identification
sub-problem solution reduces to the inverse of an approximate local
parameter-to-measurement map. The techniques presented are applicable to
other nonlinear systems which exhibit similar time-sequenced properties
This paper presents a scalable control system for synchronized control of complex multi-axis non-linear machines utilizing a communication network based on the IEEE I394b high-speed serial bus standard. The system introduces a unique clustered architecture which allows for a high level of centralization of control algorithms in clusters of remote controllers in selected areas while promoting distribution of control algorithms running on substantially autonomous controllers in other areas. As a result, high performance control can be achieved where necessary without burdening the entire communication network by a heavy time-critical traffic and impairing the overall scalability of the control system. The distributed nature of the control system opens numerous challenges in the areas of implementation of model-based control, synchronization of individual controllers, and handling of events associated with inputs on multiple controllers. The paper proposes practical solutions to these challenges in the framework of the IEEE 1394b standard.
We consider an F-16 fighter aircraft subject to asymmetric actuator failures. To address non-symmetric faults, it is not possible to decouple the longitudinal and lateral dynamics. It is necessary to deal with a full six degree of freedom airframe. Firstly, we outline an automated procedure to assemble the symbolic and simulation models of complex aircraft. The symbolic model can be manipulated in various ways and used for both linear and nonlinear control system design. In the event of actuator failures, the failed surfaces not only cease to function as viable inputs but also impose persistent disturbances on the system. As previously shown, the problem of designing a reconfigured controller can be formulated as a nonlinear disturbance rejection problem. We apply this method to design a controller for the F-16.
A predictive, multiple model control strategy is developed based
on an ensemble of local linear models of the nonlinear system dynamics
for a transonic wind tunnel. The local linear models are estimated
directly from the weights of a self-organizing map (SOM). Multiple
self-organizing maps collectively model the global response of the wind
tunnel to a finite set of representative prototype controls. These
prototype controls partition the control space and incorporate
experiential knowledge gained from decades of operation. Each SOM models
the combination of the tunnel with one of the representative controls,
over the entire range of operation. The SOM based linear models are used
to predict the tunnel response to a larger family of control sequences
which are on the representative prototypes. The control which
corresponds to the prediction that best satisfies the requirements on
the system output is applied as the external driving signal. Each SOM
provides a codebook representation of the tunnel dynamics corresponding
to a prototype control. Different dynamic regimes are organized into
topological neighborhoods where the adjacent entries in the codebook
represent the minimization of a similarity metric which is the essence
of the self organizing feature of the map. Thus, the SOM is additionally
employed to identify the local dynamical regime, and consequently
implements a switching scheme that selects the best available model for
the applied control. Experimental results of controlling the wind
tunnel, with the proposed method, during operational runs where strict
research requirements on the control of the Mach number were met, are
Presents a methodology of blending two linear parameter varying (LPV) controllers over the entire parameter spaces. Optimal blending matrix functions are calculated to preserve each performance level of the LPV controller synthesized over each parameter subspace. The design of an LPV controller for the F-16 longitudinal axes over the entire flight envelope is demonstrated using this blending approach. The nonlinear simulations of the blended LPV controller show that the desired performance and robustness objectives are achieved across all altitude variations.
The application of receding horizon control (RHC) with the linear
parameter varying (LPV) design methodology to a high fidelity, nonlinear
F-16 aircraft model is demonstrated. The highlights of the paper are: i)
use of RHC to improve upon the performance of a LPV regulator; ii)
discussion on details of implementation such as control space
formulation, tuning of RHC parameters, computation time and numerical
properties of the algorithms; and iii) simulated response of nonlinear
RHC and LPV regulator
A discrete time neural network based lateral controller design for an F-16 nonlinear model is presented. The controller is designed using model reference indirect adaptive control and the input output representation and control law for nonlinear model are established using system theory. The input-output representation and control law are approximated using neural networks with linear filters. The design takes into account the multi input multi output nature of the lateral model. Roll rate and side slip commands are used to generate reference signals and the neural networks are trained to follow the reference signals. Nonlinear simulation results are given to prove the effectiveness of the controller.
We consider the application of a conditional integrator based sliding mode control design for robust regulation of minimum-phase nonlinear systems to the control of the longitudinal flight dynamics of an F-16 aircraft. The design exploits the modal decomposition of the linearized dynamics into its short-period and phugoid approximations. The control design is based on linearization, but is implemented on the nonlinear multiple-input multiple-output longitudinal model of the F-16 aircraft. We consider model following for the angle-of- attack, with the regulation of the aircraft velocity (or the Mach- hold autopilot) as a secondary objective. It is shown through extensive simulations that the inherent robustness of the SMC design provides a convenient way to design controllers without gain scheduling, with transient performance that is far superior to that of a conventional gain-scheduled approach with integral control.
A time delay may be defined as the time interval between the start of an event at one point in a system and its resulting action at another point in the system. Delays are also known as transport lags or dead times; they arise in physical, chemical, biological and economic systems, as well as in the process of measurement and computation. Methods for the compensation of time delayed processes may be broadly divided into proportional integral derivative (PID) based controllers, in which the controller parameters are adapted to the controller structure, and structurally optimised controllers, in which the controller structure and parameters are adapted optimally to the structure and parameters of the process model. The purpose of this paper is to extract the essence of the developments in design, tuning and implementation of PID controllers for delayed processes over the five years 1998-2002, concentrating on journal publications. The paper will provide a framework against which the literature may be viewed.
This paper presents a detailed analysis of a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts in an area fire situation. Lanchester linear law attrition model is used to develop the dynamical equations governing the variation in force strength. Here we address a static resource allocation problem namely, Time-Zero-Allocation (TZA) where the resource allocation is done only at the initial time. Numerical examples are given to support the analytical results.
The complexity and cost involved in the design and development of
new vehicles such as energy and price efficient hybrid electric and
electric vehicles is high. Computer modeling and simulation can be used
to reduce the expense and length of the design cycle of these vehicles
by testing configurations and energy management strategies before
prototype construction begins. The HEV research group in Texas A&M
University has developed a computer simulation tool, V-ELPH, to
facilitate the design and analysis of electric and hybrid vehicles. This
paper presents various features of this package and demonstrates its
capabilities while describing the design methodology in developing a
parallel hybrid. In this paper a design example for a parallel hybrid
family sedan is discussed in detail, from design specifications to
complete design, using V-ELPH 2.01 with supporting illustrative graphs
In this paper, we investigate the translational and rotational motion of the end-effector of a robot under visual feedback from a fixed camera. We achieve an exponential stability result for the regulation of the end-effector to a desired location and orientation. Specifically, by utilizing visual information from one fixed camera, we capture the motion of 4 points located in a fictitious plane attached to the end-effector in Cartesian space. By assuming knowledge of the camera intrinsic parameters, we obtain the rotational motion of the end-effector through a homography decomposition while utilizing the pixel motion of one of the four points to obtain the translation information. The stability of the controller is proven through a Lyapunov-based stability analysis.
In this paper, the 3-dimensional (3D) position and orientation of a camera held by the end-effector of a robot manipulator is regulated to a constant desired position and orientation despite (i) the lack of depth information of the actual or desired camera position from a target, (ii) the lack of a geometric model of the target object, and (iii) uncertainty regarding both the angle and axis of rotation of the camera with respect to the robot end-effector (i.e., the orientation extrinsic camera parameters). By fusing 2D image-space and projected 3D task-space information (i.e., 2.5D visual servoing), a robust controller is developed that ensures exponential regulation of the position and orientation of the camera. The stability of the controller is proven through a Lyapunov-based analysis.
This paper presents a hyperbolic tangent model to capture the salient dynamic behavior of large-scale 200 kN magneto-rheological (MR) fluid dampers. The damper model will be used for simulation studies of the effectiveness of semiactive control for seismic protection as well as for controller design and diagnostic tests for large-scale real-time testing of the MR dampers at the University of Colorado at Boulder (CU) fast hybrid test (FHT) facility. A series of sinusoidal tests are conducted at the CU FHT facility for varying frequencies, amplitudes, and constant control current levels to determine the parameters of the hyperbolic tangent model as functions of current. Finally, the simulated damper force from the MR damper model is compared to that of the physical MR dampers subjected to random excitation and random control current. The hyperbolic tangent model is observed to predict closely the experimentally obtained MR damper forces over a wide dynamic range and within the constraints of computation time and fixed integration time step required for real-time diagnostic tests utilizing the CU FHT system.
Presents the design of a reconfigurable linear parameter varying (LPV) controller for the Boeing 747-100/200 longitudinal axis in the up-and-away flight regime. The control objectives are to obtain decoupled flight-path angle and velocity command tracking and achieve good disturbance rejection characteristics during normal operation and in the presence of an elevator fault. The LPV controller is synthesized using a quasi-LPV model of the aircraft longitudinal axis based on the Jacobian linearization approach. The controller schedules on three parameters: flight altitude and velocity and a fault identification signal. During normal flight operations, the LPV controller uses the elevators and thrust for flight maneuvers. The stabilizer is used to trim the aircraft. Two elevator fault scenarios are contemplated-lock and float. The proposed control strategy is to use the stabilizer as the alternative longitudinal control surface. Simulation results with elevator faults present show that the reconfigured controller stabilizes the faulted system at the expense of a factor of a designed one-third reduction in the tracking responsiveness of the longitudinal axis and has good disturbance rejection properties.
The purpose of this tutorial session is to explain how control-theoretic tools and associated mathematical concepts can be used in option trading. No previous knowledge of options will be assumed. After explaining the theory and mechanics of options and introducing the requisite mathematical models, the speakers will present a number of examples to demonstrate application of various trading algorithms, option hedging techniques and the use of both technical and fundamental analysis. The session will also include discussion of new and exciting research problems for the control field. One main theme of this tutorial session is that trading concepts can be explained in the context of a basic feedback loop with the control corresponding to modulation of the amount invested as a function of time.
We describe the design and testing of longitudinal and lateral
controllers for the Bell 205 helicopter. The controllers were designed
using H<sub>∞</sub> optimization in conjunction with low-order
linearization taken from a nonlinear flight mechanic model. During
flight-tests, decoupled responses were obtained, and desired handling
qualities achieved. Tuning the design parameters to bring about desired
changes in performance was straight-forward. The bandwidths achieved in
flight were close to those predicted by linear analysis
Due to the increasing and highly promising use of fuel cells as an important electrical energy source, its modeling has been a major research issue for some years, trying to find mathematical models precise enough to accurately predict how a cell will behave in a real world system, without becoming too complex. Many attempts have been made using different techniques. In this paper, the authors describe a static model for the PEM (proton exchange membrane) fuel cell, developed by means of bond graphs and simulated in 20 sim. The model proves to be simple and accurate, reproducing the characteristic curve of a commercial PEM fuel cell.
The process control course should continue to be a required course for chemical engineering undergraduates because of its fundamental importance and because a large number of graduates are employed in manufacturing or fields connected to manufacturing. Process control technology has changed considerably during the past 15 years, requiring that textbooks to be updated accordingly. In this paper, we discuss some of these changes in the context of revising one of the leading textbooks in process control, "Process Dynamics and Control". Trends that influence how process control will be taught in the future are identified.
This presentation will discuss multiple challenges and opportunities that are presented to young investigators to prepare for careers in science and engineering. How can research and education be integrated? How is interdisciplinary research supported? How do graduate students gain value-added skills while obtaining their degrees? These questions will form the base for this presentation and will use examples from projects supported from various programs at the NSF especially in the Division of Graduate Education.
This paper introduces a phase/gain condition for (marginally) stable systems for characterization of easily controllable systems, and investigates the relationship between the condition and the optimal performance gamma<sub>opt</sub> in H<sub>infin</sub> loop shaping design. More specifically it is shown that there is a close relationship between the condition and a magic number radic(4+2(radic2)), for both continuous-time and discrete-time systems. Furthermore a simple design procedure for robust control based on the obtained knowledge is proposed.
In a previous work, we presented formulae for boundary control laws which stabilized the parabolic profile of an infinite channel flow, linearly unstable for high Reynolds number. Also know as the Poiseuille flow, this problem is frequently cited as a paradigm for transition to turbulence, whose stabilization for arbitrary Reynolds number, without using discretization, had so far been an open problem. L<sub>2</sub> stability was proved for the closed loop system. In this work, we extend the stability result to exponential stability in the H<sub>1</sub> and H <sub>2</sub> norms, and we state and prove some properties of the stabilizing controller, guaranteeing that the control law is well behaved
In this note we consider centralized and decentralized control policies for the detection and containment of a moving source in 2D diffusion-advection PDE, often describing environmental processes. Such a task is enabled by the employment of a network of sensing devices judiciously located within the 2D spatial domain. These devices are assumed to have actuating capabilities aimed at containing the moving source by minimizing its effects on the process concentration. The source-detecting ability of the sensor network is considerably enhanced when the sensing devices are equipped to measure spatial gradients as opposed to only process concentration. The proposed estimation scheme provides estimates of the process state and at the same time provides an estimate of the proximity of the moving source. An added feature of the supervision and monitoring scheme is a power management scheme whereby a subset of the available sensors within the network are kept active over a time interval while the remaining devices are kept dormant. The resulting hybrid infinite dimensional system switches both the actuator, deemed more suitable to contain the source over the duration of a given time interval, and its associated control signal. Additionally, it switches the set of active sensors that are used by the scheme. The control policy examines two different schemes in which both a centralized and a decentralized scheme are considered. In the centralized scheme, information on the status of the active sensors along with the estimate of the state process are transmitted to the supervisor to feed a dynamic output feedback control signal to the actuator closest to the moving source. In the decentralized scheme, a computationally efficient controller is implemented, whereby the outputs from the active sensors are independently fed to the collocated actuators via static output feedback. Simulation studies utilizing at each time 16% of the total sensors and having either a single actuator w-
ith a centralized scheme or 16% of the total actuators with a decentralized scheme and used to minimize the effects of the moving source, are presented.
We present a boundary control law that stabilizes the Hartman profile for low magnetic Reynolds numbers in an infinite magnetohydrodynamic (MHD) channel flow. The proposed control law achieves stability in the L2 norm of the linearized MHD equations, guaranteeing local stability for the fully nonlinear system.
This paper deals with H<sub>∞</sub> state estimation of
two-dimensional (2D) linear discrete time-invariant systems described by
a 2D local state-space Fornasini-Marchesini second model. Several
versions of the bounded real lemma of the 2D discrete systems are
established. The 2D bounded real lemma allows one to solve the finite
horizon H<sub>∞</sub> state estimation problems using a Riccati
difference equation. Further, a solution to the infinite horizon
H<sub>∞</sub> filtering problem based on a linear matrix
inequality approach is developed. Our results extend existing work for
one-dimensional systems to the 2D case and give a state-space solution
to the bounded realness of 2D discrete systems as well as 2D
H<sub>∞</sub> state estimation for the first time
This paper focuses on the development of a technique for tracking
maneuvering target in two dimensions. Since the track of a maneuvering
target in two dimensions can be approximated by an arc of a circle, for
at least some finite distance, it seems obvious to take into account its
movement angularly as well as linearly. The proposed algorithm (the
δ-ε filter) is similar to the α-β filter, except
the filter gains, δ and ε, instead weigh the angular
displacement and angular velocity, respectively. To account for straight
line target trajectories, a linear α-β filter is used in
parallel, and it is at this point a weighted combination of the two
predictions is used to determine final future predicted position
In this paper we give new results on the analysis and control of differential linear repetitive processes, which are a distinct class of 2D linear systems of both systems theoretic and applications interest. The new results relate to stability and control in the presence of uncertainty in the process state space model. The family of control laws used has a well defined physical basis in terms of the underlying process dynamics.
This paper describes a recently proposed algorithm in mapping the unknown obstacle in a stationary environment where the obstacles are represented as curved in nature. The focus is to achieve a guaranteed performance of sensor based navigation and mapping. The guaranteed performance is quantified by explicit bounds of the position estimate of an autonomous aerial vehicle using an extended Kalman filter and to track the obstacle so as to extract the map of the obstacle. This Dubins path planning algorithm is used to provide a flyable and safe path to the vehicle to fly from one location to another. This description takes into account the fact that the vehicle is made to fly around the obstacle and hence will map the shape of the obstacle using the 2D-Splinegon technique. This splinegon technique, the most efficient and a robust way to estimate the boundary of a curved nature obstacles, can provide mathematically provable performance guarantees that are achievable in practice.
For pt.I see Proceedings of 38th. Conf. on Decision and Control (1999). In that part the authors considered boundary control of a viscous incompressible fluid flow in a 2D channel, and globally stabilized the parabolic equilibrium profile by tangential velocity actuation. This feedback is shown to guarantee global stability in at least H<sup>2</sup> norm, which implies continuity in space and time of both the flow field and the control. The theoretical results are limited to low values of Reynolds number, however, we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher
This paper focuses on the H<sub>∞</sub> filtering of
two-dimensional (2D) linear discrete systems with norm-bounded parameter
uncertainty which appears in both the state and output matrices. The
system is described by a 2D local state-space Fornasini-Marchesini
second model. For the finite horizon case, a solution to the
H<sub>∞</sub> filtering is given in terms of two 2D Riccati
difference equations. The infinite horizon 2D H<sub>∞</sub>
filtering is solved via both the algebraic Riccati inequality (ARI) and
the linear matrix inequality approaches. The LMI approach is numerically
more attractive than the ARI approach
This paper uses 2D control systems theory to develop robust iterative learning control laws for linear plants with experimental validation on a gantry robot used for `pick and place' operations commonly found in industries such as food processing. In particular, the stability theory for linear repetitive processes provides the setting for analysis and this allows design to take account of trial-to-trial error convergence, transient response along the trials and robustness. The mechanism for this is the use of a strong form of stability for repetitive processes/2D linear systems known as stability along the pass (or trial) with the added requirement for maintaining this property in the presence of model uncertainty. The resulting design computations are in terms of Linear Matrix Inequalities (LMIs) and the control laws can be implemented without the need to estimate state vector entries.
This paper deals with a class of a nonlinear delay 2D discrete
dynamical systems of the form
<sub>m,n+σi</sub>)=0, (E). We show that if a positive solution
exists, then a related minorant equation has a positive solution as
well. Similar results for a dual equation are also obtained. In fact, we
remark further that equation (E) may also be regarded as a discrete
analog of partial differential equations of the form
<sub>i</sub>))=0. Therefore, qualitative of (E) may yield useful
information for this companion partial differential equation
This work focuses on the application of a multivariable model predictive controller that regulates thin film surface roughness and mean slope to a two-dimensional kinetic Monte-Carlo thin film growth model using both substrate temperature and deposition rate as manipulated inputs. The description of the thin film growth involving both adsorption and surface migration is first given. Surface roughness and surface slope are defined as the root-mean-squares of the surface height profile and the surface slope profile, respectively. The dynamics of the evolution of the thin film surface height profile are assumed to be described by an Edwards-Wilkinson-type equation (a second-order stochastic partial differential equation) in two spatial dimensions. Analytical solutions of the expected surface roughness and surface slope are obtained on the basis of the Edwards-Wilkinson equation and are used in the controller design. The model parameters of the Edwards-Wilkinson equation depend on the substrate temperature and deposition rate. This dependence is used in the formulation of the predictive controller to predict the influence of the control action on the surface roughness and slope at the end of the growth process. The model predictive controller involves constraints on the magnitude and rate of change of the control action and optimizes a cost that involves penalty on both surface roughness and mean slope from the set-point values. The controller is applied to the two-dimensional kinetic Monte-Carlo thin film growth model and is shown to successfully regulate surface roughness and mean slope to set-point values at the end of the deposition.
Differential linear repetitive processes are a distinct class of 2D continuous-discrete linear systems of both applications and systems theoretic interest. In the latter area, they arise, for example, in the analysis of both iterative learning control schemes and iterative algorithms for computing the solutions of nonlinear dynamic optimal control algorithms based on the maximum principle. Repetitive processes cannot be analysed/controlled by direct application of existing systems theory and to date there are few results on the specification and design of control schemes for them. The paper uses an LMI setting to develop the first really significant results in this problem domain.