约束不确定非线性系统的鲁棒优化镇定

Optimization-based robust stabilization of constrained nonlinear uncertain systems

中文关键词  非线性仿射系统  约束控制  鲁棒镇定  鲁棒控制Lyapunov函数  滚动优化

英文关键词  nonlinear affine systems  constrained control  robust stabilization  robust control Lyapunov functions  receding optimization

中文摘要

      针对状态和输入约束不确定非线性仿射系统, 提出一种鲁棒镇定的优化控制器设计方法. 基于弱鲁棒控制Lyapunov函数概念, 构造一个参数可调控制器. 再利用LaSalle定理和逆优化理论, 验证该控制器的鲁棒镇定性和逆最优性. 进一步, 采用滚动优化原理在线计算控制器的可调参数, 实现闭环系统的鲁棒优化镇定. 最后对一个开环不稳定振荡器系统进行鲁棒优化镇定, 其结果验证了文中方法的有效性.

英文摘要

      The design method of optimization-based controllers with robust stabilization is presented for nonlinear affine systems subject to uncertainties and constraints on the state and input. A controller with adjustable parameters is constructed based on the concept of weak robust control Lyapunov functions. Then the LaSalle’s theorem and inverse optimization theory are employed to validate the robust stabilization and inverse optimization for the controller with respect to the uncertainty. Furthermore, the receding optimization principle is exploited to compute online the adjustable parameters in the controller, which leads to the optimization-based robust stabilization of the closed-loop system. The robust stabilization method has been applied to an open-loop unstable oscillator system and the successful results validates the effectiveness of the method presented here.