International Journal of Robust and Nonlinear Control

Published by Wiley
Online ISSN: 1099-1239
Print ISSN: 1049-8923
A DC-to-AC power conversion scheme is presented which uses a conventional DC-to-DC switched power converter of the “boost” type. The control scheme is constituted by a sliding mode controller which indirectly tracks a suitable inductor current reference trajectory resulting in a corresponding tight approximation to the desired AC capacitor voltage as the corresponding trajectory for the ideal sliding dynamics. The differential flatness property of the “boost” converter allows one to approximately express the (input) inductor current reference trajectory in terms of a static nonlinear differential function of the (output) desired capacitor voltage AC signal. The AC signal generation features of the approach are demonstrated on a biased sinusoidal signal but, in fact, any sufficiently biased differentiable voltage reference signal is achievable in principle. This approximate differential relation between the reference current and the desired voltage is obtained as the outcome of a rapidly convergent offline iterative procedure devised as part of a trajectory planning task (only one or two iterations are sufficient to obtain a remarkable precision). Simulation results are presented for the first few sliding surface candidates obtained from the proposed algorithm
In this paper, we study the problem of disturbance attenuation by output feedback for linear systems subject to actuator saturation. A nonlinear feedback control law, expressed in the form of a quasi-LPV system with state dependent scheduling parameter, is constructed that leads to the attenuation of the effect of the disturbance on the output of the system. The level of disturbance attenuation is measured in terms of the restricted L 2 gain and the restricted L 2 to L ∞ gain over a set of bounded disturbances.
A strategy is proposed for fault-tolerant control system (FTCS) design using multiple controllers. The design of such multiple controllers is shown to be unique in the sense that the resulting control system does neither have the problem of conservativeness of conventional passive fault-tolerant control (FTC) nor the risk of instability associated with active FTCS in case of an incorrect fault detection and isolation (FDI) decision. In other words, the stability of the closed-loop system is always ensured regardless the FDI decisions. The correct FDI decision will further lead to optimal performance of the system. The paper presents an interesting way to deal with the conflicting requirements among stability, redundancy, and graceful degradation in performance for fault-tolerant control systems. Detailed design procedure has been presented with consideration of possible parameter uncertainties
We study controller synthesis for systems subject to actuator magnitude and rate saturation constraints, where each actuator has a dynamic model of order at least one. The solvability conditions are expressed as finite-dimensional linear matrix inequalities. Disturbance attenuation in terms of the energy-to-peak gain from the disturbance to the controlled output is considered, though other performance measures are also possible. The results apply to the more general case of systems under actuator and state constraints.
A new approach employing both adaptive and robust methodologies is proposed for stick-slip friction compensation for tracking control of an one-DOF DC-motor system. It is well-known that the major components of friction are Coulomb force, viscous force, exponential force (used to model the downward bend of friction at low velocity) and position-dependent force. Viscous force is linear and Coulomb force is linear in parameter; thus, these two forces can be compensated by adaptive feedforward cancellation. Meanwhile, the latter two forces, which are neither linear nor linear in parameters, can only be partially compensated by feedforward cancellation. Therefore, a robust compensator with an embedded adaptive law to online “learn” the upper bounding function is proposed to compensate the uncanceled exponential and position-dependent friction. Lyapunov's direct method is utilized to prove the globally asymptotic stability of the servo-system under the proposed friction compensation method
The control of an aircraft encountering windshear after takeoff is treated as a problem of stabilizing the climb rate about a desired value. An adaptive strategy is developed which uses only climb rate information. Robustness vis-a-vis windshear structure and intensity is illustrated via simulations employing four different windshear models. Simulations were carried out for a Boeing-727 aircraft with three JT8D-17 turbofan engines
In this paper, we present a unified approach of direct adaptive motion control laws for robot manipulators that have been studied during the last years by several authors. It provides a general approach based on passivity to demonstrate global asymptotic stability of adaptive schemes applied to rigid multilinked manipulators. It is shown that most of the schemes fit within this framework, which presents the advantage of being more systematic than other techniques and therefore will enable a unified presentation of the several schemes proposed to date and will increase our understanding of adaptive control of robot manipulators.
Hysteresis switching adaptive control systems designed using certain types of L 2e -gain type cost functions are shown to be robustly stabilizing if and only if certain plant-independent conditions are satisfied by the candidate controllers. These properties ensure closed-loop stability for the switched multi-controller adaptive control (MCAC) system whenever stabilization is feasible. The result is a safe adaptive control system that has the property that closing the adaptive loop can never induce instability provided only that at least one of the candidate controllers is capable of stabilizing the plant.
This paper considers the problem of fault detection and isolation in continuous- and discrete-time systems while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems together with methods for appropriate design of observer based fault detectors. The -step delayed fault detection problem is also considered for discrete-time systems. Moreover, certain indirect fault detection methods such as unknown input observers, eigenstructure assignment, factorization, and parity equation approaches are generalized by including the almost estimation methods in addition to exact estimation methods. Copyright
For both continuous-time and discrete-time systems, the authors establish the necessary and sufficient conditions under which an H<sub>2 </sub> almost disturbance decoupling problem with internal stability is solvable by proper controllers and/or strictly proper controllers
The frequency domain design of robust feedback control systems involves the fitting of a designable complex function of frequency to specification/uncertainty derived constraints. At present there are two basically different approaches to these problems: the several gain vs. frequency approaches and the two gain-phase vs. frequency approaches. Unfortunately, the commonalities, advantages and disadvantages of these approaches are not widely appreciated. In this paper the authors develop a common framework for examining these alternatives and use this framework to reveal some of their similarities, strengths and weaknesses.
Develops a fixed-architecture controller analysis and synthesis framework that addresses the problem of multivariable linear time-invariant systems subject to plant input and output nonlinearities while accounting for robust stability and robust performance over the allowable class of nonlinearities. The proposed framework is based on the classical Lur'e problem and related Aizerman conjecture concerning the stability of a feedback loop involving a sector-bounded nonlinearity. Specifically, the authors extend the classical notions of absolute stability theory to guarantee closed-loop stability of multivariable systems in the presence of input nonlinearities. In order to capture closed-loop system performance the authors also consider the minimization of a quadratic performance criterion over the allowable class of input nonlinearities. The principal result is a set of constructive sufficient conditions for absolute stabilization characterized via a coupled system of algebraic Riccati and Lyapunov equations
In this paper we develop an optimality-based framework for backstepping controllers. Specifically, using a nonlinear-nonquadratic optimal control framework we develop a family of globally stabilizing backstepping controllers parametrized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Hamilton-Jacobi-Bellman equation for the controlled system and thus guarantees both optimality and stability. The results are specialized to the case of integrator backstepping
The rotational/translational actuator (RTAC) provides a low-dimensional nonlinear system for investigating nonlinear control techniques. The lossless formulation of this problem involves coupling of an undamped oscillator with a rotational rigid body mode. Stabilization and disturbance rejection objectives for this problem have been formulated as a benchmark problem. We implement four nonlinear controllers on the RTAC, including an integrator backstepping controller and three passivity-based controllers. The integrator backstepping design is based on the work of Wan et al. (1996). This approach requires that the equations of motion be reformulated by partial feedback linearization. Integrator backstepping is then used to produce a family of globally asymptotically stabilizing control laws. Next, three passivity-based controllers are developed for the RTAC. These controllers have intuitively appealing energy-dissipative properties and thus also inherent stability robustness to plant and disturbance uncertainty. Two of these controllers are encompassed by the classical passivity framework. The final controller is based upon the novel concept of resetting absorbers
A global optimization algorithm for solving bilinear matrix inequalities (BMI) problems is developed. It is based on a dual Lagrange formulation for computing lower bounds that are used in a branching procedure to eliminate partition sets in the space of nonconvex variables. The advantage of the proposed method is twofold. First, lower bound computations reduce to solving easily tractable linear matrix inequality (LMI) problems. Secondly, the lower bounding procedure guarantees global convergence of the algorithm when combined with an exhaustive partitioning of the space of nonconvex variables. Another important feature is that the branching phase takes place in the space of nonconvex variables only, hence limiting the overall cost of the algorithm. Also, an important point in the method is that separated LMI constraints are encapsulated into an augmented BMI for improving the lower bound computations. Applications of the algorithm to robust structure/controller design are considered
The computation of the general structural singular value (μ) is NP hard. Therefore, quick solutions to medium sized problems must often be approximate. In many of the cases where the current approximate methods are unsatisfactory, improved solutions can be obtained. It is shown that, despite its combinatoric nature, branch and bound techniques can give substantially improved solutions with only moderate computational cost
This article concerns piecewise linear systems and determining if they meet given H<sup>∞</sup> performance specifications. Such problems occur in control of linear systems with saturation nonlinearities. While one could imagine many mathematically natural piecewise linear systems problems we took care to extract one which does correspond to control of saturated plants. We think many such problems will fall into the category treated here. After a serious compromise (which makes our test for meeting specifications conservative), we arrive at a type of piecewise Riccati equation. Even these look formidable, however we begin a study of them
In this paper, it is shown how derivative bounds on uncertain time-varying parameters can be exploited in robustness analysis of linear systems. A new stability criterion is derived, based on integral quadratic constraints in the frequency domain. The new stability criterion interpolates between well known robust stability results, which are obtained in the limit. As the derivative bounds tend to zero, the new criterion turns into the usual upper bound for the structured singular value. The stability analysis, which involves a search for suitable multipliers, can be formulated as a convex optimization problem in terms of linear matrix inequalities
We derive bounds on the parameters of systems represented by a transfer functions such that any system satisfying these bounds will satisfy a bound on the H<sub>∞</sub>-norm of the difference between this transfer function and a nominal one. We develop the bound and give examples for illustration
We develop a graphical stability criterion using a Nichols chart rather than the standard complex plane. The motivation for this development is that use of Nichols charts can often simplify control design. Chief among the techniques that employ Nichols charts is the quantitative feedback theory (QFT). Numerous examples have demonstrated that the design procedure used in single-input, single-output QFT does indeed lead to a stable design and even to robust stability in the case of uncertain plants. However, a rigorous proof for the stability of this and, for that matter, of any other Nichols chart-based techniques has never been formulated. Indeed, in Reference 2, it was remarked that in some cases it may be difficult to define closed-loop stabilizing using Nichols plots. In this note we present a simple and natural proof that is based on the celebrated Nyquist criterion. In either continuous time or discrete time, the new criterion is illustrated with several examples, and extended to a class of uncertain systems.
In this paper we propose a new self-tuning type variable structure control (VSC) method for a class of nonlinear dynamical systems with parametric uncertainties. The control law is designed to satisfy the sliding mode condition while the online parameter identification is incorporated in the control system. Necessary modifications are made for the parameter identification to avoid the singularity of control input. By virtue of sliding mode, the proposed identification algorithm can be applied to those nonlinear systems which may not be linear in parametric space but are linear while in sliding mode. A model-based strategy is further introduced to estimate the uncertainty bound. The new approach attains the gain scheduling property by tuning the switching gain in accordance with the estimated system uncertainties, that is, the switching gain tends to reduce asymptotically while ensuring that the sliding mode condition is maintained
Considers robust stability analysis and synthesis problems for closed loop vibrational control. In the analysis problem, the authors derive an upper bound on the allowable unstructured uncertainty, which preserves the stability of a closed loop vibrationally stabilized system. In the synthesis problem, the authors establish a necessary and sufficient condition for the existence of a single vibrational controller that stabilizes a polytope of plants
In this work we investigate a new approach for stabilizing nonlinear systems using sliding mode control. The idea behind this method is the following: given an approximately feedback linearizable system, we define a local coordinate transformation and then find a sliding mode controller, in the new coordinates, which steers the state to the origin. Our results are compared to those obtained using approximate feedback linearization-based sliding mode control. Copyright (C) 2007 John Wiley & Sons, Ltd.
Feedback interconnection of G and G 
Rotational/translational proof-mass actuator 
Closed-loop response to 3 cm initial displacement 
Control torque 
A general framework for designing nonlinear fixed order (i.e., full- and reduced-order) dynamic passive controllers for passive systems is developed using nonlinear dissipation theory. Specifically, by extending linear passive controller synthesis frameworks a family of globally asymptotically stabilizing nonlinear passive controllers is developed that can serve to enhance system performance and energy dissipation. The proposed approach is applied to the rotational/translational proof mass actuator nonlinear benchmark problem to develop fixed-order dynamic output feedback nonlinear controllers
This paper considers the problem of robust performance of a linear time-invariant system in &Hscr;<sub>∞</sub> norm. The concepts of complex and real performance radii are introduced to describe the smallest size of dynamic or parametric perturbations to a feedback system that either destabilize the system or destroy a performance bound in certain closed loop transfer matrix of the system. An algorithm to compute the complex performance radius is given. For the real performance radius, a lower bound, which often turns out to be exact, is obtained
This paper presents an explicit noniterative method for computing the positive real matrices and Youla's spectral factorization of an MIMO strictly positive real system. All the computations are performed based on a minimal state space realization (A, B, C, D) with no restriction on D. The algorithm is tested on a seventh order MIMO system
A set of integral quadratic constraints (IQC) is derived for a class of “rate limiters”, modelled as a series connections of saturation-like memoryless nonlinearities followed by integrators. The result, when used within the standard IQC framework, is expected to be widely useful in nonlinear system analysis. For example, it enables “discrimination” between “saturation-like” and “deadzone-like” nonlinearities and can be used to prove stability of systems with saturation in cases when replacing the saturation block by another memoryless nonlinearity with equivalent slope restrictions makes the whole system unstable. In particular, it is shown that the L<sub>2</sub> gain of a unity feedback system with a rate limiter in the forward loop cannot exceed √2
In this paper we study discrete-time linear systems with full or partial constraints on both input and state. It is shown that the solvability conditions of stabilization problems are closely related to important concepts, such as the right-invertibility of the constraints, the location of constraint invariant zeros and the order of constraint infinite zeros. The main results show that for right-invertible constraints the order of constrained infinite zeros cannot be greater than one in order to achieve global or semi-global stabilization. This is in contrast to the continuous-time case. Controllers for both state feedback and measurement feedback are constructed in detail. Issues regarding non-right invertible constraints are discussed as well.
A successful controller design paradigm must take into account both model uncertainty and design specifications. In this paper we propose a design procedure, based upon the use of convex optimisation, that takes explicitly into account both time and frequency domain specifications. The main result of the paper shows that these controllers can be obtained by solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and a standard, unconstrained &Hscr;<sub>∞</sub> problem. Additionally, the paper serves as a brief tutorial on the issues involved in addressing design problems with multiple design specifications via convex optimization
Presented is a nonlinear controller design methodology for a class of regulating systems subjected to quantitative time domain constraints. The output and actuator saturation performance specifications are given as allowable time domain tolerances. The controller design is executed in the frequency domain and is applicable when the frequency response of a linear design cannot satisfy the gain and phase characteristics required by quantitative time domain specifications. A describing function (DF) approach, automated by the Volterra series, facilitates the nonlinear controller design. The resulting gain and phase distortions associated with the DF of the dynamic nonlinear element are used to achieve the desirable open loop gain and phase characteristics identified by the time domain constraints. The design methodology is illustrated on the idle speed control of a Ford 4.6L V-8 fuel injected engine. The engine input is the by-pass air valve and the regulated output is engine speed. The power steering pump generates the nonmeasureable external torque load
Reference governors for discrete-time linear systems with state and control constraints are considered. The governors attenuate, but only when necessary, the reference inputs to the linear system so that the constraints are enforced and the system maintains it desirable linear behavior in the presence of nonlinear effects such as actuator saturation. Results of Gilbert and Kolmanovsky (1994) are extended in significant ways. It is possible to treat disturbance inputs and provide flexibility in the choice of the nonlinear function that determines the operation of the reference governor. It is proved that constraint satisfaction is guaranteed for all reference inputs and disturbance inputs. Moreover, under reasonable conditions on the reference input, the eventual action of the reference governor is a unit delay. An example, which illustrates the results of the paper, is given. It shows, among other things, that high sample rates need not increase the complexity of an effective reference governor
The problem of closed-loop approximation of a continuous-time controller by a low order discrete-time controller is investigated. The operator representing the error in approximation can be approximated (arbitrarily closely) by a time-invariant discrete-time system resulting from applying fast sampling and lifting. We propose a method for obtaining a low-order discrete-time controller which makes small the approximation error based on recasting the approximation problem as a four-block H<sub>∞</sub> problem
This paper presents an application of H<sub>∞</sub> and μ-synthesis controller design methods to a coal-fired power generation unit and compares the closed loop performance and robustness of H<sub>∞</sub> and μ-synthesis control laws with those of an H<sub>2</sub> control law. All three controller synthesis procedures are applied to a two-input two-output plant model which has time delay, differential part, colored noise output disturbance and sensor noise disturbance. Application of the procedures to the model shows that when the shape of the closed loop control signals of all three designs Is closely matched, in the low frequency range the μ-synthesis and H<sub>∞</sub> control laws have robustness much better than that of H<sub>2</sub> control law, while providing adequate robustness in the high frequency range. H<sub>∞</sub> control law gives the best performance, and H<sub>2</sub>-the worst of the three designs, exhibiting the largest overshoot. The balancing procedure permits significant reduction of the order of the controllers without degradation in performance and robustness. The comparative evaluation of three designs shows that in power plant control problem H<sub>∞ </sub> and μ-synthesis designs provide much more consistent and convenient performance/robustness trade-off than H<sub>2</sub> design
We consider the theoretical aspects of the control problem for robots with rigid links which consist of some rigid joints and some non-negligible elastic joints. We start from the reduced model of robots with all elastic joints introduced by Spong, which is linearizable by static feedback (as for the rigid robot model). For the mixed rigid/elastic joints, we give the structural necessary and sufficient conditions for input-output decoupling and full state linearization via static state feedback. These turn out to be very restrictive. However, when a robot fails to satisfy these conditions, we show that a dynamic state feedback always guarantees the same result. This implies that, for the mixed rigid/elastic joint case, the role of dynamic feedback is essential. The explicit forms of the needed nonlinear controllers are provided in terms of the dynamic model elements
This paper considers the problem of output-feedback guaranteed cost controller design for uncertain time-delay systems The uncertainty in the system is assumed to be norm-bounded and time-varying. The time-delay is allowed to enter the state and the measurement equations. It is proved that the existence of the guaranteed cost controller is equivalent to the feasibility of certain matrix inequalities. A numerical algorithm is developed to construct a full order output-feedback controller that minimizes a specific cost bound for a quadratic performance index
In this paper, constructive control techniques have been proposed for controlling strict feedback (lower triangular form) nonlinear systems with a time-varying time delay in the state. The uncertain nonlinearities are assumed to be bounded by polynomial functions of the outputs multiplied by unmeasured states or delayed states. Based on the using of a linear dynamic high gain observer in combination with a linear dynamic high gain controller, the delay-independent output feedback controller making the closed-loop system globally asymptotically stable (GAS) is explicitly constructed
A discretized Lyapunov functional method for systems with multiple delay is refined. The main ideas used are variable elimination and integral inequality. The resulting new stability criterion is simpler. Numerical examples indicate that the new method is much less conservative for a given discretization mesh. In most applications, it appears that a most coarse discretization mesh compatible with the delays is sufficient
We consider the problem of designing encoders, decoders and controllers which stabilize feed forward nonlinear systems over a communication network with finite bandwidth and large delay. The control scheme guarantees minimal data-rate semi-global asymptotic and local exponential stabilization of the closed-loop system. The analysis rests on the stability properties of a class of cascade impulsive time-delay systems.
This paper addresses the reduced-order H∞ filter design for linear time varying discrete-time systems in which all measurements are not noise-free. The proposed filter has a Luenberger observer structure and its order is n - p, where n and p are the order of signal systems and the number of measurements, respectively. Several bounded real lemmas are developed and they are the only tools used to establish the reduced-order filter design in this paper. It is shown that the full order a priori and a posteriori filters can be obtained by properly choosing the filter order and parameters based on the reduced-order filter design results. The resultant filters are the same as the known full-order optimal H∞ filters for time-invariant systems.
This paper extends the Riccati equation approach to quadratic stabilizability of an uncertain system. The main result gives a guaranteed cost control which is in a sense optimal with respect to a quadratic cost index.
This paper considers the application of the skewed structured singular value to the robust stability of systems subject to strictly real parametric uncertainty. Three state-space formulations that counteract the discontinuous nature of this problem are detailed. It is shown that the calculation of the supremum of the structured singular value over a frequency range using these formulations transforms into a single skewed structured singular value calculation. Like the structured singular value, the calculation of the exact value of the skewed structured singular value is a NP-hard problem, therefore alternative, less computationally demanding algorithms to determine upper and lower bounds are necessary. Two algorithms that determine upper and lower bounds on the skewed structured single value are presented. These algorithms are critically assessed by performing a robust stability analysis on a safety-critical experimental drive-by-wire vehicle.
In this paper, we develop new results concerning the risk-sensitive dual control problem for output feedback nonlinear systems, with unknown time-varying parameters. A dynamic programming equation solution is given to an optimal risk-sensitive dual control problem penalizing outputs, rather than the states, for a reasonably general class of nonlinear signal models. This equation, in contrast to earlier formulations in the literature, clearly shows the dual aspects of the risk-sensitive controller regarding control and estimation. The extensive computational burden for solving this equation motivates our study of risk-sensitive versions for one-step horizon cost indices and suboptimal risk-sensitive dual control. The idea of a more generalized optimal risk-sensitive dual controller is briefly introduced
This paper is concerned with a walking robot with knees on level ground imitating the passive walking on a given slope. Basic principle of a proposed control method is that dynamics of the active walking robot is matched to that of the passive walking one. However, since it is hard for the knee-jointed walking robot to successively or robustly realize a stable passive walking on the downhill slope, the passive walking robot is first actively controlled to continue to walk with an actuator at the hip. Then the dynamics of the walking robot on the level grand is matched to that of the stabilized passive walking robot on the slope by implementing actuators at the ankles as well as at the hip. Copyright
Domains of attraction D cl and D A based on closed and open Lyapunov surfaces.  
Compartmental mammillary model for disposition of propofol.  
BIS Index versus effect site concentration.  
In this paper we develop optimal output feedback controllers for set-point regulation of linear nonnegative dynamical systems. Specifically, using a constrained fixed-structure control framework we develop optimal output feedback control laws that guarantee that the trajectories of the closed-loop system remain in the nonnegative orthant of the state space for nonnegative initial conditions. In addition we characterize domains of attraction predicated on closed and open Lyapunov level surfaces contained in the nonnegative orthant for unconstrained optimal linear-quadratic output feedback controllers. Output feedback controllers for compartmental systems with nonnegative inputs are also given.
An aircraft's response to control inputs varies widely throughout its flight envelope. The aircraft configuration also impacts control response through variations in center of gravity and moments of inertia. Hence, designing a flight control system (FCS) to accommodate the full flight envelope and configuration set of an aircraft is clearly a complex undertaking. Quantitative feedback theory (QFT) is a robust control design method which provides an avenue of approach to full-envelope flight control design. Furthermore, a QFT-based design method gives the engineer direct control over compensator order and gain. In this paper, a full subsonic flight envelope FCS is designed for the VISTA F-16 aircraft using QFT for four representative aircraft configurations. In addition, flying qualities are imbedded in the longitudinal design by using a control variable which varies with the aircraft's energy state throughout the flight envelope. This variable is a linear combination of the aircraft's pitch channel states and is synthesized to closely reflect the actual control desires of the pilot throughout the aircraft flight envelope. The strict control of the compensator order and gain allowed by QFT facilitates the attainment of desired performance while avoiding physical actuator saturations. Linear simulations with realistically large control inputs are used to validate the design
It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suitable damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which aims, at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the lattice objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propagation condition. This allows us to determine a class of Euler-Lagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set-point control of elastic joints robots. Our research contributes, if modestly, to the development of a theory for stabilization of nonlinear systems with physical structures which effectively exploits its energy dissipation properties
The authors provide an alternative solution to the problem of semiglobal stabilization of a class of minimum phase nonlinear systems that was considered by A.R. Teel (1991). The method used yields a stabilizing linear state feedback law in contrast to a nonlinear state feedback law proposed by Teel. The peaking phenomenon is eliminated by inducing a specific time-scale structure in the linear part of the closed-loop system. This structure consists of a very slow and a very fast time scale. The crucial component in the method is the relation between the slow and the fast time-scales. The proposed linear state feedback control law has a single tunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in some a priori given (arbitrarily large) bounded set
In this document, we present the main ideas and results concerning high-gain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating second-order example is used to illustrate the key features of high-gain observers and their use in feedback control. This is followed by a general presentation of high-gain-observer theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of high-gain observers in the robust control of minimum-phase nonlinear systems.
This paper considers the problem of optimal guaranteed cost control of an uncertain system via output feedback. The uncertain system under consideration contains a single uncertainty block subject to an integral quadratic constraint. The cost function considered is a quadratic cost function defined over an infinite time interval. The main result of the paper gives a necessary and sufficient condition for the existence of a guaranteed cost controller guaranteeing a specified level of performance. This condition is given in terms of the existence of suitable solutions to an algebraic Riccati equation and a Riccati differential equation. The resulting guaranteed cost controller is in general time-varying
In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman-Bucy filter
Top-cited authors
Ella M Atkins
  • Virginia Tech (Virginia Polytechnic Institute and State University)
C. Edwards
  • University of Exeter
Leonid Fridman
  • Universidad Nacional Autónoma de México
Lihua Xie
  • Nanyang Technological University
Guanrong Chen
  • City University of Hong Kong