Controller Gain Variations Research Articles

Synchronization of a class of chaotic dynamic systems with controller gain variations

Abstract In this paper, the nonfragile control problem for synchronization of a class of chaotic dynamical systems with controller gain variations is studied. Using the Lyapunov method and LMI (linear matrix inequality) technique, a criterion for the existence of the nonfragile controller for synchronization is derived in terms of LMI. To show the effectiveness of the proposed method, the control problem is applied to Genesio chaotic system.

Design of Non-Fragile H∞ Controller for Active Vehicle Suspensions

In this paper we present an approach to design the non-fragile H ∞ controller for active vehicle suspensions. A quarter-car model with active suspension system is considered in this paper. By suitably formulating the sprung mass acceleration, suspension deflection and tire deflection as the optimization object and considering a priori norm-bounded controller gain variations, the non-fragile state-feedback H ∞ controller can be obtained by solving a linear matrix inequality. The designed controller not only can achieve the optimal performance for active suspensions but also preserves the closed-loop stability in spite of the controller gain variations.

Robust H∞ Non‐Fragile Controller Design for Uncertain Descriptor Systems with Time‐Varying Discrete and Distributed Delays

AbstractThis paper is concerned with the design problem of non‐fragile H∞ controller for uncertain descriptor systems with time‐varying discrete and distributed delays and controller gain variations. The designed controller is shown to be robust not only to parameter uncertainties, but also to errors in the controller coefficients. The obtained criterion to derive an efficient non‐fragile H∞ control design is expressed as a set of nonconvex matrix inequalities, which can be solved by combining both linear matrix inequalities technique and come complementarity method. A numerical example is given to demonstrate effectiveness of the proposed methods.

Robust non-fragile guaranteed cost control of uncertain large-scale systems with time-delays in subsystem interconnections

In this paper, the robust non-fragile guaranteed cost-control problem is studied for a class of uncertain linear large-scale systems with time-delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design a state feedback control law such that the closed-loop system is asymptotically stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. A numerical example is given to illustrate the proposed method.

On robust stabilization for neutral delay-differential systems with parametric uncertainties and its application

This paper considers the problem of robust stabilization for uncertain neutral delay-differential systems. Based on the Lyapunov method, a delay-dependent criterion for determining the stability of systems is obtained in terms of matrix inequalities, which can be easily solved by efficient convex optimization algorithms. Then, the method presented is extended to systems with controller gain variations, that is, the design problem for the nonfragile controller is considered. A numerical example is included to illustrate the design procedure of the proposed method.

Non-fragile output feedback H∞ vehicle suspension control using genetic algorithm

This paper presents an approach to design static output feedback and non-fragile static output feedback H ∞ controllers for active vehicle suspensions by using linear matrix inequalities and genetic algorithms. A quarter-car model with active suspension system is considered in this paper. By suitably formulating the minimization problem of the sprung mass acceleration, suspension deflection and tyre deflection, a static output feedback H ∞ controller and a non-fragile static output feedback H ∞ controller are obtained. The controller gain is naturally constrained in the design process. The approach is validated by numerical simulation which shows that the designed static output feedback H ∞ controller can achieve good active suspension performance in spite of its simplicity, and the non-fragile static output feedback H ∞ controller has significantly improved the non-fragility characteristics over controller gain variations.

Non-fragile H∞ vibration control for uncertain structural systems

The paper deals with the robust non-fragile H ∞ control problem for uncertain structural systems with additive controller gain variations. The parameter uncertainties for the mass, damping and stiffness of the structural systems are unknown but norm bounded. Based on the H ∞ control theory and a linear matrix inequality formulation, a new method for designing a robust state-feedback control law is presented. The objective is to reduce the disturbance on the controlled output to a prescribed level for all admissible parametric uncertainties and controller gain variations. A four-degree-of-freedom building model subject to seismic excitation is used to illustrate the effectiveness of the approach through simulation.

On the design of nonfragile guaranteed cost controller for a class of uncertain dynamic systems with state delays

In this article, the nonfragile guaranteed cost control problem is studied for a class of uncertain dynamic systems with multiple time delays and controller gain variation. The multiple time-varying delays are considered. The uncertainty is nonlinear time-varying and is bounded in magnitude. For all admissible uncertainties, time delays, and controller gain variations, the problem is to design a memoryless state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound of a given cost function. Several criteria for the existence of such controllers are derived using the Lyapunov method. A feature of the proposed method is that an upper bound on the guaranteed cost is minimized by solving a convex optimization problem with linear matrix inequalities. A numerical example is given to illustrate the proposed method.

Robust non-fragile control for uncertain discrete-delay large-scale systems with a class of controller gain variations

This paper considers the problems of robust non-fragile control for uncertain discrete-delay large-scale systems under state feedback gain variations. Two classes of controller gain variations are considered. Based on the Lyapunov method, the state feedback control design for robust stability is given in terms of solutions to a linear matrix inequality (LMI). The solutions of the LMI can be easily obtained using efficient convex optimization techniques. A numerical example is included to illustrate the design procedures.

Robust Nonfragile Decentralized Controller Design for Uncertain Large-Scale Interconnected Systems With Time-Delays

This paper describes the synthesis of robust nonfragile decentralized controllers for uncertain large-scale systems with time-delays in the subsystem interconnections and controller gain variations. Based on the Lyapunov method, a sufficient condition for robust stability is derived in terms of a linear matrix inequality (LMI), and the measure of nonfragility in controller is presented.

Non-fragile guaranteed cost control of uncertain large-scale systems with time-varying delays

The robust non-fragile guaranteed cost control problem is studied in this paper for a class of uncertain linear large-scale systems with time-varying delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. Finally, in order to show the application of the proposed method, a numerical example is included.

Non-fragile H∞ control for linear systems with multiplicative controller gain variations

Non-fragile H∞ control for linear systems with multiplicative controller gain variations

Non-fragile H∞ control for linear systems with multiplicative controller gain variations

This paper is concerned with the problem of non-fragile H ∞ controller design for linear time-invariant systems. The controller to be designed is assumed to have multiplicative gain variations. Design methods are presented in terms of symmetric positive-definite solutions of algebraic Riccati inequalities. The resulting design is such that the closed-loop system is robustly stable and has an H ∞ disturbance attenuation bound with respect to the multiplicative controller gain variations. A numerical example is given to illustrate the design methods.

Non-fragile H∞ flight controller design for large bank-angle tracking manoeuvres

This paper is concerned with the design of non-fragile H∞ output feedback control of a high-performance aircraft similar to F-16 in executing a large bank-angle tracking manoeuvre. The non-fragile H∞ flight controllers are designed to tolerate multiplicative gain variations in the controller matrices. The designs are based on three linear trim models of the high-performance aircraft. From the linear and non-linear simulations, the results show that the resulting closed-loop systems using the non-fragile H∞ flight controllers are robustly stable and have H∞ disturbance attenuation bounds with respect to some admissible controller gain variations. Corresponding performance comparisons with the standard robust design approach show that the resulting closed-loop systems using the standard H∞ flight controllers are unstable under the same controller gain variations.

Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations

One of the fundamental problems in feedback control design is the ability of the control system to maintain stability and performance in the face of system uncertainties. To this end, elegant multivariable robust control design frameworks such as H control, L control and mu synthesis have been developed to address the robust stability and performance control problem. An impl1icit assumption inherent in these design frameworks is that the controller will be implemented exactly. In a recent paper by Keel and Bhattacharyya, it was shown that even though such frameworks are robust with respect to system uncertainty, they are extremely fragile with respect to errors in the controller coefficients. In this paper, we extend the robust fixed-structure controller synthesis approach to develop controllers which are robust to system uncertainties and non-fragile or resilient to controller gain variations.

H8 control for linear systems with additive controller gain variations

(2000). H8 control for linear systems with additive controller gain variations. International Journal of Control: Vol. 73, No. 16, pp. 1500-1506.

Robust non-fragile LQ controllers: The static state feedback case

This paper describes the synthesis of non-fragile or resilient regulators for linear systems. A general framework for fragility is described using state-space methodologies, and the LQ/H2 static state-feedback problem is examined in detail. We discuss the multiplicative structured uncertainties case, and propose remedies of the fragility problem using an optimization programming framework via matrix inequalities. A special case that leads to a convex optimization framework via linear matrix inequalities (LMIs) will be considered. The benchmark problem is taken as an example to show how special controller gain variations can affect the performance of the closed-loop system.