Output feedback optimal guaranteed cost control of uncertain piecewise linear systems

The paper presents an output feedback optimal guaranteed cost control result for a new class of uncertain linear systems. The cost function considered is a quadratic cost function defined over a finite time interval. The new uncertainty class introduced in the paper involves structured uncertainties which are required to satisfy a certain averaged integral quadratic constraint. The introduction of this new structured uncertainty description enables us to solve a previously unsolved problem of optimal guaranteed cost control via output feedback for an uncertain system with structured uncertainties. The solution is obtained by solving a pair of parametrized Riccati differential equations of the game type. >

This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs). In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP). Finally, numerical examples are given to illustrate the results.

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

This paper is concerned with the design of robust H∞ output feedback controller for uncertain piecewise-linear systems based on piecewise-quadratic Lyapunov function technique. We assume that the uncertainty is norm-bounded and enters all system matrices. By constructing piecewise-continuous Lyapunov function for the closed-loop augmented system, we construct the H∞ output feedback controller design procedure as solving a set of bilinear matrix inequalities (BMIs). The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities (LMIs) which can be efficiently solved numerically. A numerical example is used to illustrate the proposed method.

In this paper, robust constrained model predictive control of uncertain fuzzy affine systems is considered. Based on piecewise quadratic Lyapunov functions, highly efficient robust constrained predictive control approaches are developed so that the closed-loop stability is guaranteed, and the transient control performance is improved even under input or state constraints. Moreover, by using approximate ellipsoid and S -procedure, the solution to the fuzzy affine model based predictive control can be cast as a convex optimization problem subject to some linear matrix inequalities, rather than a nonconvex problem via bilinear matrix inequalities as in conventional fuzzy affine model-based control. The proposed controllers are thus easier for real-time implementation in industry. Simulation results on the fluidized bed combustion plant have demonstrated the performance of the proposed approaches.

This paper focuses on the problem of robust guaranteed cost control for a class of nonlinear systems described by the Takagi-Sugeno (T-S ) fuzzy descriptor model with time-varying delay and parameter uncertainties. The less conservative sufficient conditions for the existence of robust guaranteed cost controller via state feedback are given in terms of linear matrix inequalities (LMIs). And the design of optimal guaranteed cost controller can be reduced to a convex optimization problem. The designed controller not only guarantees the robust quadratic stability of the closed-loop system, but also provides a minimized upper bound of the guaranteed cost. At last, a numerical example is given to illustrate the effectiveness of the proposed method and the perfect performance of the optimal guaranteed cost controller.

The problem of robust guaranteed cost control for a class of uncertain stochastic systems with Markov jump parameters subject to actuator saturation is discussed. The concept of domain of attraction is used to analyze the stochastic stability and a sufficient condition which guarantees the intersection of ellipsoid invariant set under different modes in the domain of attraction is presented. The solvability condition of robust guaranteed cost controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller such that the closed-loop system is stochastically stable and the cost function value is minimized. A numerical example is given to verify the effectiveness of this method.

Non-synchronized Observer-based Control of Discrete-time Piecewise Affine Systems: an LMI Approach

In this paper, the problem of designing robust guaranteed cost control law for a class of uncertain neutral system with a given quadratic cost function is considered. Based on Lyapunov–Krasovskii functional theory, a delay‐dependent criterion for the existence of guaranteed cost controller is expressed in the form of two linear matrix inequalities (LMIs), which can be solved by using effective LMI toolbox. Moreover, a convex optimization problem satisfying some LMI constraints is formulated to solve a guaranteed cost controller which achieves the minimization of the closed‐loop guaranteed cost. An efficient approach is proposed to design the guaranteed cost control for uncertain neutral systems. Computer software Matlab can be used to solve all the proposed results. Finally, a numerical example is illustrated to show the usefulness of our obtained design method. Copyright © 2006 John Wiley & Sons, Ltd.

Convex reformulations for self-optimizing control optimization problem: Linear Matrix Inequality approach

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 presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions. A recently introduced non-quadratic Lyapunov function, the convex hull quadratic function, is used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least /spl Lscr//sub 2/ gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Optimization problems with BMI constraints are formulated and solved effectively by combining the path-following algorithm and the direct iterative algorithm. The design results are guaranteed to be at least as good as the existing results obtained from LMI conditions. In most examples, significant improvements on system performances have been achieved, which demonstrate the advantages of using nonlinear feedback control over linear feedback control for linear differential inclusions. It is also observed through numerical computation that nonlinear control strategies may help to reduce control effort substantially.

Studies the optimal guaranteed control problem for a class of linear uncertain time-delay systems. The systems under consideration are described by state differential equations with time-varying unknown but norm-bounded uncertain parameters and time-varying unknown but bounded delay in states. An upper bound of the performance measured by standard quadratic function is constructed and based on the delay-dependent stabilizing approach, a method of designing a state feedback robust quadratic stabilizing control law guaranteeing this quadratic performance index be less than the constructed upper bound is derived. A procedure is given to select an optimal state feedback controller in the sense of minimizing this upper bound of the quadratic performance index. The results depend on the size of delay and are given in terms of several linear matrix inequalities.

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

In this paper, the problem of finite-time stability is studied for a class of networked predictive control systems with parameter uncertainties. Firstly, both the modelling uncertainties and the network-induced delays are considered. A networked predictive control scheme is proposed to actively compensate the network-induced delays. Secondly, a sufficient condition is given to ensure the finite-time stability of the augmented closed-loop system with time delay, where both bilinear matrix inequality and linear matrix inequality conditions are derived with the help of Lyapunov stability theorem. At the same time, an alternate algorithm is designed to obtain the gain matrices of observer and controller from bilinear matrix inequality and linear matrix inequality. Finally, a numerical example is given to confirm the feasibility of the proposed results.