Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Abstract

Summary This paper considers the global feedback exponential stabilization and L2 gain disturbance attenuation problems of the switched nonlinear polynomial systems with passive and nonpassive subsystems for any given average dwell time. In the existing result, it needs that there exists at least one open loop passive subsystem in the switched nonlinear system, which is unnecessary for the switched nonlinear polynomial system in this paper because the passivity of the subsystem can be obtained according to the passivity‐based feedback dissipative Hamiltonian realization. In addition, a parameterization of controller approach–based feedback exponential stabilization method of nonlinear polynomial system is described and utilized such that the Lyapunov function of the passive subsystem possesses the required decay rate to exponentially stabilize the switched nonlinear polynomial system. Comparing with the controller designed with the existing method, the obtained controller in this paper has much simpler structure and better performance. An example simulation is provided to illustrate the effectiveness of the proposed approach.

Polynomial filtering for nonlinear stochastic systems with state‐ and disturbance‐dependent noises

“…In recent years, much research attention has been devoted to the filtering and control problems of nonlinear polynomial systems (NPSs), which may represent a large class of nonlinear systems. 12,[21][22][23][24][25][26][27][28] For instance, the problems of H ∞ filtering and least squares filtering were investigated for the discrete-time NPSs in References 22 and 24, respectively. In the continuous-time case, the linear and polynomial H ∞ filters were respectively designed in References 25 and 23 for NPSs by means of the sum-of-squares (SOS) approach, and the problem of distributed H ∞ filtering was studied in Reference 12 for polynomial NSDSs over sensor networks.…”

“…In recent years, much research attention has been devoted to the filtering and control problems of nonlinear polynomial systems (NPSs), which may represent a large class of nonlinear systems 12,21‐28 . For instance, the problems of H ∞ filtering and least squares filtering were investigated for the discrete‐time NPSs in References 22 and 24, respectively.…”

A mixed PI/VI design method for nonlinear H∞ Control

“…Furthermore, iterative methods can be classified as PI and VI . Iterative methods mainly include neural network approaches, higher‐order expansion methods, successive approximations, while noniterative methods mainly involve finite element methods, SDRE methods, parameterized‐controller approach, and polynomial nonlinear control method . Recently, iterative methods, especially neural network approaches, dominate the design of nonlinear H ∞ controllers.…”

“…The SDRE method was used to approximate the solution through online computation . Zhu and Hou put forward a parameterized‐controller approach to design the nonlinear H ∞ control for uncertain switched nonlinear polynomial systems. We proposed a new polynomial nonlinear control method to design the nonlinear H ∞ control by using the Taylor series expansions of system matrices.…”

Design of Parametric Controller for Two-Dimensional Polynomial Systems Described by the Fornasini-Marchesini Second Model

“…Many achievements in [30]- [32] on the parametric controller design have been made, they both focus on 1D systems. However, to our best knowledge, no work considering the design of parametric controller for 2D system has been done up to now.…”