摘要:
针对一类具有不确定性和变量约束的非线性切换系统, 提出了一种基于Lyapunov函数的预测控制方法, 其中状态约束分为两种情况: 1)要求状态变量在所有时刻都满足约束(称为硬约束); 2)允许状态在某些时刻超出约束(称为软约束). 主要思想是: 对切换系统的每一个子系统, 在输入和状态均受约束的情况下, 设计基于Lyapunov函数的有界控制器和预测控制器, 在两者之间适当切换, 得到初始稳定区域的描述并使得子闭环系统保持稳定. 对整个切换系统, 设计适当的切换律以保证: 1)在切换时刻, 闭环系统的状态处在切入系统的稳定区域内; 2)切入模块的Lyapunov函数是非增的, 从而可保证稳定性. 在状态变量的约束是软约束时, 对每一子模块首先设计一个控制策略, 尽快将状态控制到初始稳定区域, 然后再利用稳定区域内的控制律使系统稳定.
Abstract:
In this paper, a Lyapunov-based constrained predictive controller is proposed for a kind of nonlinear switched systems with uncertainty and constraints for the cases that the state constraints need to be enforced at all times (hard constraints) and they can be relaxed for some time (soft constraints). The main idea is to design a Lyapunov-based limited controller and a predictive controller for each subsystem, also a suitable switched law to stablize the closed-loop subsystem, and provide an explicitly characterized set of initial conditions. For the whole switched system, a suitable switched law is designed to ensure: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into; 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing the stability. For the case where the state constraints are soft, we propose a control strategy for each subsystem such that the state is driven into the stabilization region, then the closed-loop system is stablized by the controller defined in the stabilization region.