不依赖观测器的不确定性系统输出反馈鲁棒控制

Output⁃feedback robust control of uncertain systems without observer

针对非匹配不确定性系统的静态输出反馈鲁棒控制问题在线求解难的难题,提出了一种基于数据驱动学习的自适应学习算法。首先,将不确定性系统的鲁棒控制问题转化为具有性能指标函数的标称系统的最优控制问题。其次,为实现输出反馈最优控制,根据状态反馈控制项构造了输出反馈黎卡提方程。再次,为实现该输出反馈黎卡提方程的在线求解,使用克罗内克积和向量化操作重构输出反馈黎卡提方程,进而设计了基于输入/输出数据的自适应学习算法,摒弃了传统观测器的使用,实现可一步求解的输出反馈鲁棒控制。最后,为实现被估参数的快速收敛,进一步放松了所要求的持续激励条件。仿真结果验证了本文控制方法和学习算法的有效性。

A novel data-driven learning method to achieve static output-feedback robust control of unmatched dynamic systems was proposed,which uses the techniques originally developed for optimal control.The robust control was first transformed into the optimal control of an augmented system,taking unmatched dynamics into consideration.Then,to design the output-feedback optimal control,an output-feedback algebraic Riccati equation was derived by tailoring its state-feedback control counterpart.Once more,an adaptive online learning method was designed to avoid using the observer,where two operations(i.e.,vectorization and Kronecker's product)were adopted to reconstruct the output-feedback algebraic Riccati equation.Finally,the required persistent excitation condition was further relaxed to realize the rapid convergence of the estimated parameters.Simulation results show the effectiveness of the proposed control method and learning algorithm.