Gain-scheduled controllers design for interceptor parameter-varying system with multi-saturated constraint

Abstract

Based on homogeneous polynomial parameter dependent Lyapunov function (HPPDLF) theory and the algorithm that the nonlinear matrix differential equations converted into convex polyhedron state equations, the robust optimal control system is designed, for the interceptor with time-varying parameters and actuator nonlinear multisaturated constraint. First, the model of the actuator saturation operator is established, which provides the control system topology. The nonlinear differential equations with time-varying parameters converted into the linear polytopic vertex system by introduced the normalization factors of the amplitude and rate actuator saturation, and then it converted into HPPD matrix differential equations, based on HPPDLF theory and the extension of Pólya's theorem to the case of matrix-valued polynomials. The dynamic performance of the closed-loop control system is obtained by setting the minimum allowable value of the scaling factor, when solving the minimum of the maximum homothetic set in the iterative processing. Finally the simulations of the interceptor have demonstrated the effectiveness of the approach proposed.

Design of saturating state feedback control laws for discrete‐time linear parameter varying systems through homogeneous polynomial parameter‐dependent functions

“…One may cite, piecewise quadratic Lyapunov functions for continuous 8 and discrete‐time 9 systems. With the advent of polynomial homogeneous Lyapunov functions, 10 new formulations were developed to reduce the conservatism on analysis and design of continuous‐time LPV systems, including position and velocity saturating actuators, 11 discrete‐time LPV systems with bounded variation rate in the time‐varying parameters to deal with stability analysis, control, and filter design 12‐14 . Approaches based on composite quadratic Lyapunov functions for stability and stabilizability of linear differential inclusions, which may be used to capture the LPV behavior with a certain degree of accuracy, 2 have been presented in Reference 15.…”