具有前馈结构的非线性切换系统的控制设计

This project studies the problem of control design for switched nonlinear feedforward systems. The focus includes: controllers of subsystems and common Lyapunov function will be constructed by using forwarding, and the stabilizability condition under arbitrary switchings and systematic design methods will be derived; stabilizability conditions will be given in the sense of simultaneous design of controllers and switching laws using the multiple Lyapunov functions technique under the solvability of the stabilization problem for individual subsystems is unnecessary, and a switched-cross-term based forwarding technique will be established; the stabilization problem of switched systems will also be studied by exploiting the average dwell time method, the mechanism and interaction between the chose of switched-cross-term and the design of switching laws and their impact on the dwell time will be revealed, and the minimum average dwell time will be obtained; the solvability conditions of the observer-based output feedback control problem and adaptive control in the presence of nonlinear parameterization will be studied, and design methodes will be provided..The results of the project studies will develop and refine the existing switched nonlinear system theories, and also provide effective methods of the dual design of switching laws and controllers for subsystems. Furthermore, the results will be expected to apply to control design of practical systems including robot control system with feasible strategies presented.

本项目研究具有前馈结构的非线性切换系统的控制设计问题。研究内容包括：利用Forwarding技术构造共同Lyapunov函数及其相应子系统控制器，探求切换系统在任意切换律作用下可镇定的条件和系统化的设计方法；在各子系统的镇定问题都不可解的情况下，利用多Lyapunov函数方法寻求在切换律和子系统控制器同时设计意义下的系统可镇定条件，建立基于"切换交叉项"的Forwarding技术；研究切换系统在切换信号满足一定平均驻留时间条件下的镇定问题，探索切换交叉项的选取和子系统控制器的设计之间的相互作用机理及对驻留时间的影响，获得最小平均驻留时间；研究基于状态观测器的输出反馈控制以及含有非线性参数的自适应控制问题的可解性条件和设计方法。 .项目的研究将拓展和完善非线性切换系统理论，提供切换律和子系统控制器同时设计的方法。研究成果还可望应用于机器人控制系统等实际系统的控制设计中。

本项目研究了非线性切换系统的控制设计问题。研究内容包括：在各子系统的自适应控制问题都不可解的情况下，通过设计切换规则实现了切换系统的自适应镇定，建立了这样的切换规则的存在性条件，同时提出了切换律和子系统控制器同时设计方案；探索了非线性切换系统在切换信号满足一定平均驻留时间条件下的自适应控制问题，得到了切换更新律的选取和子系统自适应控制器设计之间的相互作用机理及对驻留时间的影响，获得了最小平均驻留时间的计算方法；得到了基于切换状态观测器的自适应控制问题的可解性条件和设计方案；建立了非线性切换系统反馈联结下的小增益定理，为解决互联切换系统的控制问题提供了新途径。项目的研究揭示了控制器与切换律之间的耦合作用规律及对系统整体动态行为的影响，完善和发展了非线性切换系统理论。研究结果还可应用于机器人系统等诸多实际系统中。