Improved Adaptive Controller Synthesis of Piecewise‐Affine Systems

Abstract

This paper considers the adaptive H ∞ control problem for piecewise affine systems (PWS), a novel synthesis framework is presented based on the piecewise quadratic Lyapunov function (PQLF) instead of the common quadratic Lyapunov function to achieve the less conservatism. First, by designing the projection-type piecewise adaptive law, the problem of the adaptive H ∞ control of PWS can be reduced to the H ∞ control problem of augmented piecewise systems. Then, we construct the piecewise affine control law for augmented piecewise systems in such a way that the PQLF can be employed to establish the stability and H ∞ performance. In particular, the Reciprocal Projection Lemma is employed to formulate the synthesis condition as linear matrix inequalities (LMIs), which enables the proposed PQLF approach to be numerically solvable. Finally, an engineering example is shown to illustrate the synthesis results.

Robust Tracking Controller Design for a Class of Block Lower‐Triangular Systems

“…Li considered an adaptive tracking control method for a class of nonlinearly parameterized MIMO dynamic systems with time-varying delay and unknown nonlinear dead-zone inputs [31]. Zhang investigated the adaptive H ∞ control problem for piecewise affine systems with a new frame based on the piecewise quadratic Lyapunov function [32]. Xu proposed an adaptive finite-time fault-tolerant control algorithm for a class of MIMO nonlinear systems with constraint requirement on the system output tracking error [33].…”

A Piecewise Envelope Approach to H∞ Control of Nonlinear Systems

“…The key idea is to find piecewise-linear systems (PLS) as the approximation of nonlinear systems, then analyze and design the approximated PLS instead of original nonlinear systems. In this way, the analysis and synthesis methods (see [16][17][18][19][20][21][22][23][24]) for PLS can be extended to nonlinear systems area. Due to the approximation process, the controller designed for PLS can only be effective under the condition of small approximation error.…”