基于观测器的非线性时变时滞系统自适应重复控制

针对一类未知时变时滞非线性系统，提出一种基于观测器的重复控制方案．采用线性矩阵不等式设计非线性观测器，所设计的控制律含有ＰＩＤ 反馈项，常值参数自适应律是微分差分型的，时变参数学习律是差分型的．在假设未知时变时滞、时变参数和参考输出的周期有已知的最小公倍数下，通过构造一个Ｌｙaｐｕｎｏｖ-Ｋｒａｓｏｖｓｋｉｉ型复合能量函数，证明了所有闭环信号有界且输出跟踪误差收敛．仿真实例表明了算法的有效性．

Observer-based adaptive repetitive control for nonlinear systems with time-varying delays

An observer-based repetitive control scheme is developed for a class of nonlinear systems with unknown time-varying delays. Linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a PID feedback term. The adaptive law of unknown constant parameter is differentialdifference type, and the adaptive law of unknown time-varying parameter is difference type. It is assumed that the lease common multiple of periods of unknown time-varying parameters, time-varying delay and reference signal are known. By constructing a Lyapunov-Krasovskii-like composite energy function(CEF), it is proved that all closed-loop signals are bounded and the tracking error converges. Simulation examples show the effectiveness of control algorithm.