Delay-Dependent Robust Reliable Guaranteed Cost Control for Nonlinear Systems with Time-Varying State Delays

This paper deals with the problem of reliable guaranteed cost control problem for nonlinear singular systems governed by a set of differential-algebraic equations. A more practical model of actuator failures than outage is adopted. The objective is to design a reliable guaranteed cost state feedback law, which can tolerant actuator failure, such that the cost function of the closed-loop system is guaranteed to be no more than a certain upper bound. Based on the Hamilton-Jacobi inequality (HJI), the sufficient condition of existence and design method of desiring reliable controller is presented. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Robust reliable guaranteed cost control for uncertain singular systems with time-delay

This paper focuses on the problem of guaranteed cost control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delayed state. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. Then, the guaranteed cost control of the closed-loop fuzzy system is discussed, and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer-based output feedback. When these conditions, which are given in terms of the feasibility of linear matrix inequalities (LMIs), are satisfied, the designed state feedback controller and observer-based controller gain matrices can be obtained via a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper.

An LMI Method to Robust Iterative Learning Fault-tolerant Guaranteed Cost Control for Batch Processes

This paper is concerned with the problem of optimal guaranteed cost control via memory state feedback for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the Roesser model with norm-bounded uncertainties. A linear matrix inequality (LMI)-based sufficient condition for the existence of memory state feedback guaranteed cost controllers is established and a parameterized representation of such controllers (if they exist) is given in terms of feasible solutions to a certain LMI. Furthermore, a convex optimization problem with LMI constraints is formulated to select the optimal guaranteed cost controllers that minimize the upper bound of the closed-loop cost function. The proposed method yields better results in terms of least upper bound of the closed-loop cost function as compared with a previously reported result.

This paper considers the problem of adaptive reliable guaranteed cost controller design for linear time-delay systems against actuator faults via dynamic output feedback. Based on indirect adaptive method, a new reliable dynamic output feedback controller is established. The controller gains are affinely dependent on the estimations of fault parameters, which are updating automatically according to the proposed adaptive laws. New delay-dependent sufficient conditions for the existence of the reliable guaranteed cost dynamic output feedback controller are derived in terms of linear matrix inequalities, which have less conservativeness than the corresponding reliable dynamic output feedback controller with fixed gains. An example is presented to show the effectiveness of the proposed method.

The reliable fuzzy control with guaranteed cost for T-S fuzzy systems with actuator failure is proposed in this paper. The cost function is a quadratic function with failure input. When the initial state of such systems is known, a design method of the reliable fuzzy controller with reliable guaranteed cost is presented, and the formula of the guaranteed cost is established. When the initial state of such systems is unknown but belongs to a known bounded closed domain, a notion of the reliable domain guaranteed cost (RDGC) for such systems is proposed. For two classes of initial state domain, polygon domain and ellipsoid domain, some design methods for reliable fuzzy controllers with the RDGC are provided. The efficiency of our design methods is finally verified by numerical design and simulation on the Rossler chaotic system.

An LMI approach to guaranteed cost control of linear uncertain time-delay systems

This paper addresses the problem of delay-range-dependent iterative learning reliable guaranteed cost control of a class of batch processes with uncertainties, state delay and actuator failures, where the main contribution is in the relevant concept of H∞ iterative learning fault-tolerant guaranteed cost control based on an equivalent two-dimensional system description of these processes. The H∞ iterative learning reliable guaranteed cost controller (ILRGCC) is formulated to include a robust extended feedback control for ensuring the performances over time and an iterative learning control (ILC) for improving the tracking performance from cycle to cycle, such that it can not only guarantee the closed-loop convergence along both the time and the cycle directions but also satisfy both the H∞ performance index and a cost function preserving upper bounds for all admissible uncertainties and any actuator failures. To achieve the least guaranteed cost for the closed-loop system, a convex optimization problem wi...

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty

This paper presents a new guaranteed cost control for exponential stability of a nonlinear system with mixed time-delays in state and feedback control. The considered mixed time-delays are both discrete and distributed time-varying delays, but not necessarily differentiable. The proposed conditions allow us to design the state feedback controllers which stabilize the closed-loop system. By constructing an appropriate Lyapunov–Krasovskii functional, new delay-dependent sufficient conditions for the existence of guaranteed cost control are given in terms of linear matrix inequalities (LMIs). Moreover, we design new quadratic cost functions and minimize their upper bound. Finally, numerical examples are given to illustrate the effectiveness and improvement over some existing results in the literature.

Frequency-based multivariable control design with stability margin constraints: A linear matrix inequality approach

This paper deals with the guaranteed cost control problem for a class of uncertain linear discrete-time switched systems with time-delay under arbitrary switching laws. The purpose 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. A sufficient condition on the existence of guaranteed cost controllers is derived based on Lyapunov theory together with linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMIs constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.