A Piecewise Envelope Approach to H_∞ Control of Nonlinear Systems

Abstract

This paper provides a computable approach for the H ∞ control synthesis of nonlinear systems using the piecewise envelope method. Firstly, the computation method of piecewise envelope is presented such that the required piecewise linear differential inclusions (PWLDIs) can be obtained by solving a linear optimization problem. Then, we propose the H ∞ control design method for PWLDIs using piecewise Lyapunov function theory, all the synthesis conditions are formulated as the feasibility of linear matrix inequalities, hence computationally tractable. Because of the inclusion relationship, the H ∞ controllers designed for PWLDIs are also effective for original nonlinear systems. The validity of the proposed approach is tested by application to control a wheeled mobile robot.

Robust approximate optimal control for air‐breathing hypersonic vehicle

“…i in finite time with properly parameters designed. 11,30 In this section, the input/output linearization ( 8) is firstly developed for AHV dynamics, and by introducing auxiliary variables the AHV dynamics are transformed to a second-order feedback decoupling model (15). The tracking reference is given by filter (11).…”

“…▪ Theorem 2. Considering the system (15), the virtual command (18) and the controller (23) ensure that the auxiliary variables 𝜎 1i and 𝜎 2i (with i = V, h) are UUB.…”

“…SMC is a conventional robust control method to handle the nonlinear and perturbed system, 11,12 but it generally requires the bound of uncertainties to design the switching gains 13,14 . Furthermore, the implementation of sliding mode control is often irritated by high frequency oscillations known as “chattering” 15,16 . Some novel high‐order sliding model (HOSM) methods can obtain a continuous control law and guarantee the finite‐time convergence of tracking error 17 .…”

“…13,14 Furthermore, the implementation of sliding mode control is often irritated by high frequency oscillations known as "chattering". 15,16 Some novel high-order sliding model (HOSM) methods can obtain a continuous control law and guarantee the finite-time convergence of tracking error. 17 But the implementation of HOSM has to take the sign function into the integral term of the control law and increase the relative degree, which introduces the calculation error in practice.…”

Concurrent PI Controller Design for Indirect Vector Controlled Induction Motor

“…In addition, it is also of importance to devise a design procedure that can be easily facilitated to design controllers using advanced methods, e.g. , H ∞ control and of higher‐order such as two degree of freedom control.…”