Energy-to-Peak Output Tracking Control of Actuator Saturated Periodic Piecewise Time-Varying Systems With Nonlinear Perturbations
针对一类带有执行器饱和和非线性扰动的连续时间周期分段时变系统，设计了基于矩阵多项式的输出跟踪控制方案，通过凸优化求解控制器增益，降低保守性并保证跟踪性能。
This article is focused on the design of an output tracking control scheme for a class of continuous-time periodic piecewise time-varying systems (PPTVSs) with actuator saturation and nonlinear perturbations. The energy-to-peak tracking performance is studied based on an equivalent condition on the definiteness property of matrix polynomials. Considering the actuator saturation and nonlinear perturbation, matrix polynomial-based sufficient conditions are derived through the Lyapunov method using periodic matrix functions. From a perspective of subinterval segmentation aimed at PPTVSs, the proposed conditions can achieve less conservatism for tracking the output of a periodic time-varying reference system, while the controller gains can be computed using convex optimization. Moreover, a heuristic algorithm is constructed to simultaneously guarantee the closed-loop state convergence and the output tracking performance. The reduction in conservatism and the effectiveness of algorithm are demonstrated by illustrative case studies.