This paper presents the author’s views on the development of identification for control. The paper reviews the emergence of this subject as a specific topic over the last 15 years, at the boundary between system identification and robust control. It shows how the early focus on identification of control-oriented nominal models has progressively shifted towards the design of control-oriented uncertainty sets. This recent trend has given rise to an important revival of interest in experiment design issues in system identification. Some recent results on experiment design are presented.
This paper describes actuator fault identification in unknown, input-affine, nonlinear systems using neural networks. Neural net tuning algorithms have been derived and identifier have been developed using the Lyapunov approach. The paper defines and analyses the fault dynamics i.e., the dynamical properties of a failure process. A rigorous detectability condition is given for actuator faults in nonlinear systems relating the actuator desired input signal and neural net-based observer sensitivity. Sufficient conditions are given in terms of the input signal and related actuator fault such that a fault can be detected. Simulation results are presented to illustrate the detectability criteria and fault detection in nonlinear systems
This paper addresses the problem of designing a state feedback
control in order to track a given periodic output reference signal for
single input single output feedback and linearizable systems with
uncertain maximal relative degree matching unstructured uncertainties
(no parameterization available). An adaptive learning control is
designed which "learns" with arbitrary precision the unknown reference
control input on the basis of its Fourier series expansion, while
transient performances are guaranteed during the learning phase
We survey some recent research directions within the field of approximate dynamic programming, with a particular emphasis on rollout algorithms and model predictive control (MPC). We argue that while they are motivated by different concerns, these two methodologies are closely connected, and the mathematical essence of their desirable properties (cost improvement and stability, respectively) is couched on the central dynamic programming idea of policy iteration. In particular, among other things, we show that the most common MPC schemes can be viewed as rollout algorithms and are related to policy iteration methods. Furthermore, we embed rollout and MPC within a new unifying suboptimal control framework, based on a concept of restricted or constrained structure policies, which contains these schemes as special cases.
Worldwide air traffic levels are growing at a rate expected to double the current traffic level by 2020. The current technology Air Traffic Control systems are stretched to their limit and are prone to large delays during the peak summer travel season. There is doubt that the current systems can be scaled up to meet the expected demand levels. Many Air Traffic Management automation systems have been proposed to increase controller capability, and some are in operation. While ATM automation systems will help handle more traffic, it is still doubtful that they can grow to meet the doubling in traffic levels foreseen. This paper presents an introduction to Distributed ATM using the capability of airborne electronic systems to further relieve the controller workload. An overview of avionics capabilities is presented, followed by a detailed description of five specific examples of airborne capability that can be used to increase airspace capacity, as listed below. 1. An onboard method to control an aircraft to cross a terminal area waypoint at a Required Time of Arrival. 2. A trajectory negotiation process whereby the groundbased ATM system uses the 4D predicted trajectory computed by the aircraft, gives the aircraft RTA constraints to solve traffic conflicts, and contracts the aircraft to stay within a specified tolerance of the predicted 4D trajectory. 3. A formation flight system whereby multiple aircraft can be flown close together and controlled as a single aircraft. 4.
In this paper, a new method for distributed simulation of differential algebraic equation systems is developed based on purely decentralized sliding mode control. Due to the large amount of computation and communication associated with large scale matrix inversion problems in the existing centralized approaches, this new distributed method is much more efficient. The necessary conditions for stability of the distributed approach are developed. The new method is applied for simulation of a triple pendulum system to demonstrate the validity of the approach
Necessary and sufficient conditions for existence of a solution to a new class of extended Algebraic Riccati Equations (ARE) are presented. The class, which is of interest in general dissipativity theory, and in particular in robust H ∞ control, contains arbitrary – possibly singular – quadratic term and possibly degenerate frequency domain function. Instrumental to establish our results is the analysis of a particular matrix pencil associated with the extended ARE that was recently introduced by Ionescu and Weiss. The conditions for existence of solutions of the extended ARE – including stabilizing solutions – are formulated in terms of this pencil.
Modeling and analysis of chemical reactions are critical problems because they can provide new insights into the complex interactions between systems of reactions and chemicals. One such set of chemical reactions defines the creation of biodiesel from soybean oil and methanol. Modeling and analyzing the biodiesel creation process is a challenging problem due to the highly-coupled chemical reactions that are involved. In this paper we model a biodiesel production system as a stochastic hybrid system, and we present a probabilistic verification method for reachability analysis. Our analysis can potentially provide useful insights into the complicated dynamics of the chemicals and assist in focusing experiments and tuning the production system for efficiency. The verification method employs dynamic programming based on a discretization of the state space and therefore suffers from the curse of dimensionality. To verify the biodiesel system model we have developed a parallel dynamic programming implementation that can handle large systems. Although scalability is a limiting factor, this work demonstrates that the technique is feasible for realistic biochemical systems.
Two versions of continuous-time feedback nonlinear predictive control laws with a fixed end point prediction and a finite horizon prediction are presented. They are applied in a cascade structure to induction motor that includes both electrical and mechanical dynamics. Both speed and torque/flux tracking objectives are achieved in matched and mismatched parameters case. The rotor flux is estimated by the Kalman filter. The derived nonlinear predictive laws minimize a quadratic performance index of the predicted tracking error. A key feature of the control law is that its implementation does not need to perform an online optimization and asymptotic tracking of smooth reference signal is guaranteed. Simulations show that the proposed controllers are suitable for high dynamic performance applications. A good robustness with respect to parameters variation and load torque disturbance are achieved.
A new type of feedback stabilization strategy for a class of drift
free systems is presented. The approach is based on the construction of
a cost function which is a maximum of a finite number of component
functions. The stabilizing control is defined in terms of a set of
nested, discrete processes, whose task is to minimize the
non-differentiable cost. Repeated application of these processes yields
a sequence of points along the controlled trajectory. While the
corresponding sequence of cost values is decreasing monotonically, the
cost, as a continuous function of time, decays asymptotically along the
controlled system trajectories only. Stabilizing properties of the
resulting feedback strategy are discussed
We develop an optimal mixed-norm L<sub>1</sub> bound/H<sub>∞
</sub> controller synthesis framework for continuous-time linear
systems. This multiobjective problem is treated by forming a convex
combination of both L<sub>1</sub> (time domain worst-case peak amplitude
response) and entropy (frequency domain worst-case H<sub>∞</sub>
disturbance attenuation) performance measures. For flexibility in
controller synthesis, we adopt the approach of fixed-structure
controller design which allows consideration of arbitrary controller
structures, including order, internal structure, and decentralization.
Finally, using a quasi-Newton continuation algorithm, we demonstrate the
effectiveness of the proposed mixed-norm L<sub>1</sub>/H<sub>∞
</sub> approach via a numerical design example
In a recent paper principles and digital control of Fabry-Perot interferometers (FPI) have been presented, showing a few on-going and potential applications in the field of precision engineering. Among them, metrology lines were mentioned, aiming to reveal sub-nanometric displacements in view of dimensional stabilization/monitoring of demanding space telescopes. The core is a confocal optical cavity, in vacuum, whose light path is sensible to supporting structure length variations. The latter are tracked and revealed by a frequency actuator which acting on the incident light keeps the FPI signal centered to zero although the optical path is varying. Concept and digital control of metrology lines will be outlined and some experimental results from an on-ground breadboard will be discussed. Due to on-ground and test contingencies, a displacement actuator was also active on the cavity, which asked for actuator coordination
In this paper, we propose novel LMI conditions for the stability and l<sub>2</sub> gain performance analysis of discrete-time linear periodically time-varying (LPTV) systems. These LMIs are convex with respect to all of the coefficient matrices of the LPTV systems and this property is expected to be promising when dealing with several control system analysis and synthesis problems. For example, we can apply those LMIs straightforwadly to robust performance analysis problems of LPTV systems that are affected by polytopic-type uncertainties. Even though our approach for robust performance analysis is conservative in general, we can reduce the conservatism gradually by artificially regarding the original N-eriodic system as pN-periodic and increasing p. In addition, thanks to the simple structure of the LMI conditions, we can readily derive a viable test to verify the exactness of the computation results.
This paper defines a theoretical framework based on Markov Decision Processes (MDP) to deal with fault-tolerant routing algorithms in heterogeneous home networks, which are realized through the integration of different wired and wireless telecommunication technologies. Such networks are characterized by fast dynamics of link availability, mainly due to the wide use of wireless technologies. The novelty of this paper is the MDP approach to the fault-tolerant routing problem, which is addressed by introducing a re-routing policy: when a path becomes unavailable, the flows transmitted over that path are re-routed on another available path; the new path is selected taking into consideration the probability that also the new path can become unavailable in the future, in order to minimize re-routing occurrences. Numerical simulations show the effectiveness of the proposed approach.
A unifying view of existing disturbance decoupling observers is
proposed. The different approaches of linear algebraic and geometric
design methods and variable structure/sliding modes methods are put
together into a single framework. Some new results are obtained: a
discrete-time sliding modes observer, a new continuous-time sliding
modes observer, and a bound for the degrees of freedom in the error
dynamic assignment for some particular cases of the general observer. A
systematic view is also posed in already existing disperse results,
concerning the class of admissible disturbances, the role of the
disturbances input matrix, the mechanism of disturbances decoupling and
the obtainable error dynamics in particular cases of the general model.
An heuristic procedure is also proposed for dealing with the invariant
Passivity is a well known phenomenon in several engineering areas. Due to its interesting properties, it is used in several areas of control engineering. Generally, this property is lost under direct discretization. In this work a new methodology which allows preserving continuous-time passivity is presented. This methodology is based on choosing a proper output, which preserves the passivity structure, while keeping the continuous-time energy function. Analytic formulation and numerical examples, both for open and closed loop, are provided in the paper
The paper tailors the so-called wave-based control popular in the field of
flexible mechanical structures to the field of distributed control of vehicular
platoons. The proposed solution augments the symmetric bidirectional control
algorithm with a wave-absorbing controller implemented on the leader, and/or on
the rear-end vehicle. The wave-absorbing controller actively absorbs an
incoming wave of positional changes in the platoon and thus prevents
oscillations of inter-vehicle distances. The proposed controller significantly
improves the performance of platoon manoeuvrers such as
acceleration/deceleration or changing the distances between vehicles without
making the platoon string unstable. Numerical simulations show that the
wave-absorbing controller performs efficiently even for platoons with a large
number of vehicles, for which other platooning algorithms are inefficient or
require wireless communication between vehicles.
In this paper we investigate when a parameterized controller, designed for a
plant depending on unknown parameters, admits a realization which is
independent of the parameters. It is argued that adaptation is unnecessary for
this class of parameterized controllers. We prove that standard model reference
controllers (state and output--feedback) for linear time invariant systems with
a filter at the plant input admit a parameter independent realization. Although
the addition of such a filter is of questionable interest, our result formally,
and unquestionably, establishes the deleterious effect of such a modification,
which has been widely publicized in the control literature under the name
Weight-balanced and doubly stochastic digraphs are two classes of digraphs
that play an essential role in a variety of cooperative control problems,
including formation control, distributed averaging, and optimization. We refer
to a digraph as doubly stochasticable (weight-balanceable) if it admits a
doubly stochastic (weight-balanced) adjacency matrix. This paper studies the
characterization of both classes of digraphs, and introduces distributed
algorithms to compute the appropriate set of weights in each case.
The fundamental problem of the calculus of variations on time scales concerns
the minimization of a delta-integral over all trajectories satisfying given
boundary conditions. In this paper we prove the second Euler-Lagrange necessary
optimality condition for optimal trajectories of variational problems on time
scales. As an example of application of the main result, we give an alternative
and simpler proof to the Noether theorem on time scales recently obtained in
[J. Math. Anal. Appl. 342 (2008), no. 2, 1220-1226].
We consider the numerically reliable computation of reachability and observability Kalman decompositions of a periodic system with time-varying dimensions. These decompositons generalize the controllability/observability Kalman decompositions for standard state space systems and have immediate applications in the structural analysis of periodic systems. We propose a structure exploiting numerical algorithm to compute the periodic controllability form by employing exclusively orthogonal similarity transformations. The new algorithm is computationally efficient and strongly backward stable, thus fulfils all requirements for a satisfactory algorithm for periodic systems.
This article deals with the consensus problem involving agents with
time-varying singularities in the dynamics or communication in undirected graph
networks. Existing results provide control laws which guarantee asymptotic
consensus. These results are based on the analysis of a system switching
between piecewise constant and time-invariant dynamics. This work introduces a
new analysis technique relying upon classical notions of persistence of
excitation to study the convergence properties of the time-varying multi-agent
dynamics. Since the individual edge weights pass through singularities and vary
with time, the closed-loop dynamics consists of a non-autonomous linear system.
Instead of simplifying to a piecewise continuous switched system as in
literature, smooth variations in edge weights are allowed, albeit assuming an
underlying persistence condition which characterizes sufficient inter-agent
communication to reach consensus. The consensus task is converted to
edge-agreement in order to study a stabilization problem to which classical
persistence based results apply. The new technique allows precise computation
of the rate of convergence to the consensus value.
We derive sufficient conditions for the solvability of the observer design
problem for a wide class of nonlinear time-varying systems, including those
having triangular structure. We establish that, under weaker assumptions than
those imposed in the existing works in the literature, it is possible to
construct a switching sequence of time-varying noncausal dynamics, exhibiting
the state determination of our system.
The present work establishes necessary and sufficient conditions for a
nonlinear system with two inputs to be described by a specific triangular form.
Except for some regularity conditions, such triangular form is flat. This may
lead to the discovery of new flat systems. The proof relies on well-known
results for driftless systems with two controls (the chained form) and on
geometric tools from exterior differential systems. The paper also illustrates
the application of its results on an academic example and on a reduced order
model of an induction motor.
In this paper we introduce a general descriptor-type LFT representation of rational parametric matrices. This generalized representation allows to represent arbitrary rationally dependent multivariate functions in LFT-form. As applications, we develop explicit LFT realizations of the transfer-function matrix of a linear descriptor system whose state space matrices depend rationally on a set of uncertain parameters. The resulting descriptor LFT-based uncertainty models generally have smaller orders than those obtained by using the standard LFT-based modelling approach.
A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and optimal control problems.
How does "information" interact with control of a system, in particular feedback control, and what is the value of "information " in achieving performance objectives for the system through the exercise of control? In answering this question we have to remember that in contrast to a variety of communications settings, the issue of time-delay is of primary importance for control problems, especially control of systems which are unstable. We discuss various issues arising from these fundamental questions.
A biotechnological aerobic process is modelled as an ordinary differential equation which, under mild assumptions, ensures invariance of the positive orthant and boundedness of the concentrations. An adaptive controller is designed for this general class of processes so that the external substrate can be regulated by the dilution rate into a prespecified arbitrarily small neighbourhood of a constant setpoint reference. The adaptive controller is robust, simple in its design without invoking any identification mechanisms, and is based on output data only. It is shown that the prominent example of a baker's yeast fermentation belongs to this setup, and adaptive tracking is illustrated by simulations. Keywords: Adaptive control, input saturation, tracking, aerobic processes, yeast fermentation 1 Introduction The purpose of the paper is threefold. First, it is a contribution to the general modelling of biotechnological aerobic processes including proofs which show that the intuit...
This paper gives an excellent quasi-survey of area of control for storage systems and how advanced control techniques can be applied. It is worth elaborating on a few of the points made in the paper from the perspective of this author's own limited experience. The first point is that a complete design using the only modern analysis and design techniques is a rare case in the storage industry. This is partly because of the di#culty (mentioned in the paper) of posing the industrial problem into the modern frameworks. However, a compounding factor is that of time constraints on design time. Any design method which requires the controls engineer to use di#erent techniques in every aspect of the drive design is bound to take far more time to implement than making marginal improvements on a current design method.
This paper addresses the control of linear systems with input saturations. We seek a controller that guarantees for the closed loop system: (i) stability for a given polytope of initial conditions, (ii) a prescribed weak L 2 gain attenuation between inputs and outputs of interest. Two approaches are proposed based on: (i) ensuring that the controller never saturates: the obtained controller is Linear Time Invariant (LTI), (ii) ensuring absolute stability against the saturations: the controller is then Linear Time Varying (LTV). Existence conditions for these two control structures can be cast as (convex) optimization problems over Linear Matrix Inequalities. At last, using numerical experiments, we compare both approaches. In this numerical examples, the LTI controller presents some advantages.
In this paper we deal with the stability analysis problem of cascaded non autonomous nonlinear systems. In particular we answer to the following questions: (i) What happens with the solutions of a time-varying nonlinear system which is globally uniformly stable, when it is perturbed by the output of a globally exponentially stable system (GES), in particular, when both systems form a cascade?. (ii) If a time varying nonlinear system is globally uniformly asymptotically stable (GUAS), is this stability property preserved when it is perturbed by an exponentially decaying input?. Our proofs are based on a standard "delta-epsilon" Lyapunov analysis. Finally, we show the utility of our results by applying our theorems to the problem of stabilisation of a turbo charged diesel engine. Keywords. Cascaded systems, Lyapunov theory, analysis. Notation. In this paper the solution of a differential equation x = f(t; x) where f : IR 0 Theta IR n ! IR n , with initial conditions 1 (...
This paper is a straightforward application of NL q stability criteria to neural model based controller design. We discuss the design of a linear dynamic output feedback controller for a ball and beam system for which a neural state space model is identified. This is done by applying dynamic backpropagation, constrained by internal or I/O stability conditions for NL q systems. The performance of the controller has been tested both by computer simulations and on a real ball and beam set-up. Keywords: neural control, multi-layer perceptrons, recurrent neural networks, global asymptotic stability, NL q theory, dynamic backpropagation 1 Introduction A widely used algorithm in neural model based controller design is Narendra's dynamic backpropagation procedure . In this procedure the free variables of the controller are determined by means of optimizing a cost function. This cost function itself is based on the controller's tracking performance, defined on a set of specific reference ...
Recently introduced methods of iterative identification and control design are directed towards the design of high performing and robust control systems. These methods show the necessity of identifying approximate models from closed-loop plant experiments. In this paper a method is proposed to identify approximate normalised coprime plant factors from closed-loop data. The fact that normalised plant factors are estimated gives specific advantages, both from an identification and from a robust control design point of view. It will be shown that the proposed method leads to identified models that are specifically accurate around the bandwidth of the closed-loop system. The identification procedure fits very naturally into a recently developed iterative identification/control design scheme based on H∞ robustness optimisation. The identification scheme is illustrated with experiments on the radial servo mechanism in a compact disc player.
Recently an algorithm has been developed for column reduction of polynomial matrices. In a previous report the authors described a Fortran implementation of this algorithm. In this paper we compare the results of that implementation with an implementation of the algorithm originally developed by Wolovich. We conclude that the complexity of the Wolovich algorithm is lower, but in complicated cases the first mentioned algorithm yields better results. Keywords: Polynomial matrices, column reduction, numerical stability, complexity # Corresponding author 1 Introduction Numerical manipulation of polynomial matrices has acquired attention from the field of systems theory since the seventies. De Jong exposes the numerical instability of various realization algorithms in  and derives an alternative, numerically stable algorithm. Van Dooren studies in [2, 3, 4] the generalized eigenstructure problem of matrix pencils. Beelen  develops an algorithm to compute the Kronecker indices ...
. We consider the infinite horizon quadratic cost minimization problem for a linear time-invariant distributed parameter system with finitely may inputs and outputs. Our approach is to work in an input/output framework, and to reduce the problem to a symmetric Wiener-Hopf problem, that can be solved by means of a canonical factorization of the symbol. We have earlier solved the case where the system is stable, and this work is devoted to an extension of the theory to the unstable case. The extension is based on a right coprime factorization of the impulse response and on a preliminary stabilizing feedback, which makes it possible to reduce the unstable case to the stable one. 1. Introduction. This is a continuation of our earlier work  on the quadratic cost minimization problem for a linear time-invariant distributed parameter system with an impulse response of a certain type. In  we solved this problem for stable systems by means of spectral factorization, and here we extend ...
One of the most interesting questions in control theory is that of constructing observers. Observers compute estimates of the internal states of a dynamical system, using data provided by measurement probes or partial state information. For linear systems, Luenberger observers (also known as "deterministic Kalman filters" since they amount to Kalman filters designed without regard to the statistics of measurement noise) provide a general solution, but, for nonlinear systems, establishing generally applicable conditions for existence and convergence of observers is an open and active area of research. This paper provides a necessary and sufficient condition for detectability, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type.
Promulgated by some with religious-like fervor, viewed with skepticism by others, adaptive control has for almost forty years been one of the most alluring, intriguing, and often misunderstood areas within the field of automatic control. In truth, despite its present shortcomings fe.g., its failure to adequately address performance issuesg adaptive control has come quite a long way since first conceived. Once amounting to little more than a collection of seemingly unrelated heuristic ideas, adaptive control now rests on a bona fide foundational theory which serves to explain basic concepts and constructions in a principled manner. An early advance contributing to the theory's development was the formulation and resolution of the now classical siso "model reference control problem." The main obstacle to the problem's resolution was dealing with nominal process models of high "relative degree." The assault on the relative degree problem involved many people and took place over a period of several years. The problem's first solution appeared in the late 1970s and used what is now called "integrator backstepping." A second solution emerged about two years later and relied on the idea of "error normalization." The latter approach led to an overall control algorithm which was far simpler in form than that provided by backstepping. As a result the backstepping approach was totally eclipsed by the error normalization approach and remained so for more than a decade. Ironically, integrator backstepping has quite recently enjoyed renewed and considerable attention because of its apparently unique ability to deal with certain types of nonlinearities in both adaptive and nonadaptive systems. The aims of this paper are to explain what backstepping is, to chronicle the events leadin...
The problem of global output feedback tracking control of robot manipulators has been open for several years. In this short note we propose a computed torque plus (nonlinear) PD like controller to solve the output feedback tracking control problem of one degree of freedom (dof) Euler-Lagrange (EL) systems. We prove in this case global asymptotic stability. Our approach is the extension of our previous semi-global result . Even though we can not claim the same result for systems of more than one dof, as far as we know, none of the semi-global solutions present in the literature has been proved to be global even for 1 dof systems. keywords. Global asymptotic stability, EL systems, one degree of freedom, position measurements. 1 Introduction The problem of global output feedback 1 tracking control of robot manipulators has been open for several years and has attracted the interest of several researchers in this field. Among the first attempts,  proposed a high gain linear obse...
: In this paper we consider a large class of partial differential equations (PDEs) with distributed control and with a time-delay in the feedback loop. We analyze the relationship between the poles of the closed-loop transfer function and the exponential modes of the underlying retarded PDE in order to derive internal stability properties from external ones. Our approach is based on a combination of input-output methods and modal analysis. We give a number of sufficient conditions for robustness/nonrobustness of closed-loop modal stability with respect to delays. The theory is illustrated by two examples. Keywords: Partial differential equations; distributed control; small time delays; stability; robustness; transfer functions. AMS subject classifications: 93C20, 93D09, 93D15, 93D25. This work was supported by Nato (Grant CRG 950179) and by the National Science Foundation (Grant DMS-9206986). 1. Introduction The literature on robustness and lack of robustness of distributed par...
: We review several existing detectability and isolability definitions. We argue that two types of definitions have to be distinguished. On one hand, intrinsic definitions capture the signature of the fault on the system. On the other hand, performance-based definitions involve indexes of performance of fault detection algorithms. In particular, since many fault detection algorithms involve a residual generation mechanism, such definitions may capture, among other performance indexes, the signature of the fault on the residuals. In the particular case of sensor and actuator faults in linear dynamic systems, we exhibit an equivalence among several definitions based on different concepts. Key-words: Fault detectability, fault isolability, model-based fault detection and isolation (fdi), fault information content of fdi residuals. (R'esum'e : tsvp) A condensed version of this report has been accepted for presentation at the 5th European Control Conference - ECC'99, Karlsruhe, FRG, Aug.31...
We demonstrate how the separable least-squares technique of Golub and Pereyra can be exploited in the identi#cation of both linear and non-linear systems based on the prediction error formulation. The model classes to be considered here are the output error model and innovations model in the linear case and the Wiener system in the non-linear case. This technique together with a suitable choice of parameterization allow us to solve, in the linear case, the associated optimization problem using only np parameters instead of the usual n#m + p#+mp parameters when canonical forms are used, where n, m and p denote respectively the number of states, inputs and outputs. We also prove under certain assumptions that the separable optimization method is numerically better conditioned than its non-separable counterpart. Successful operations of these identi#cation algorithms are demonstrated by applying them to two sets of industrial data: an industrial dryer in the linear case and a high purity ...
In this paper we rst recall the general theory of Popov realizations of parahermitian transfer functions in the context of generalized state space systems. We then use this general framework to derive linear matrix inequalities for various problems in systems and control. Finally, we indicate how these problems can be solved numerically and what specic numerical diculties can be encountered. 1
The "input to state stability" (iss) property provides a natural framework in which to formulate notions of stability with respect to input perturbations. In this expository paper, we review various equivalent definitions expressed in stability, Lyapunov-theoretic, and dissipation terms. We sketch some applications to the stabilization of cascades of systems and of linear systems subject to control saturation. 1 Introduction There are two very conceptually different ways of formulating the notion of stability of control systems. One of them, which we may call the input/output approach, relies on operator-theoretic techniques. Among the main contributions to this area, one may cite the foundational work by Zames, Sandberg, Desoer, Safanov, Vidyasagar, and others. In this approach, a "system" is a causal operator F between spaces of signals, and "stability" is taken to mean that F maps bounded inputs into bounded outputs, or finite-energy inputs into finite-energy outputs. More stringe...
| We consider a single intersection of two two-way streets with controllable trac lights on each corner. We construct a model that describes the evolution of the queue lengths in each lane as a function of time, and we discuss how (sub)optimal trac light switching schemes for this system can be determined. I. Introduction In this paper we study the optimal trac light control problem for a single intersection. Given the arrival rates and the maximal departure rates of vehicles at the intersection we compute trac light switching schemes that minimize criteria such as average queue length, worst case queue length, average waiting time, : : : , thereby augmenting the ow of trac and diminishing the eects of trac congestion. We show that for a special class of objective functions (i.e., objective functions that depend strictly monotonously on the queue lengths at the trac light switching time instants) , the optimal trac light switching scheme can be computed very eciently. Moreover, if t...
The interplay of random phenomena and continuous real-time control deserves increased attention for instance in wireless sensing
and control applications. Safety verification for such systems thus needs to consider probabilistic variations of systems
with hybrid dynamics. In safety verification of classical hybrid systems we are interested in whether a certain set of unsafe
system states can be reached from a set of initial states. In the probabilistic setting, we may ask instead whether the probability
of reaching unsafe states is below some given threshold. In this paper, we consider probabilistic hybrid systems and develop
a general abstraction technique for verifying probabilistic safety problems. This gives rise to the first mechanisable technique
that can, in practice, formally verify safety properties of non-trivial continuous-time stochastic hybrid systems—without
resorting to point-wise discretisation. Moreover, being based on arbitrary abstractions computed by tools for the analysis
of non-probabilistic hybrid systems, improvements in effectivity of such tools directly carry over to improvements in effectivity
of the technique we describe. We demonstrate the applicability of our approach on a number of case studies, tackled using
a prototypical implementation.
The main purpose of this article is to summarize the activities related to control and control systems supported by the European Commission Research and Development (R&D) programmes (so called Framework Programmes—FPs) with focus on the last two decades and to present and discuss the synergies, gaps and possible new challenges identified during several brainstorming and informal meetings and in related reports and position papers covering topics from loop performance improvements to distributed, stochastic and large scale systems of systems.
The paper by T. Kaczorek [”Positive switched 2D linear systems described by the Roesser models”, Eur. J. Control 18, No. 3, 239-246 (2012; Zbl 1264.93076)] in the references list for complete details) addresses the problem of esablishing asymptotic stability of positive swichted 2D linear systems described by the Roesser models. For this problem, the paper provides necessary and sufficient conditions that ensure asymptotic stability for any switching. Moreover, the paper illustrates the use of some of the provided conditions through numerical examples.
The positive switched 2D linear systems described by the Roesser models are addressed. Necessary and sufficient conditions for the asymptotic stability of the positive switched system are established for any switching. The considerations are illustrated by numerical examples.