基于观测器的受扰非线性系统近似最优跟踪控制

An observer-based approximate optimal tracking control for nonlinear systems with persistent disturbances

研究一类受扰非线性系统的最优输出跟踪控制问题.给出了有限时域最优输出跟踪控制律的近似设计算法.首先将求解受扰非线性系统最优跟踪控制问题转换为求解状态向量与伴随向量耦合的非线性两点边值问题,然后利用逐次逼近方法构造序列将其转化为求解两个解耦的线性微分方程序列问题.通过迭代求解伴随向量的序列,可得到由解析的线性前馈-反馈控制部分和伴随向量的极限形式的非线性补偿部分组成的最优输出跟踪控制律.利用参考输入降维观测器和扰动降维观测器,解决了前馈控制的物理可实现问题.最后仿真结果表明了该方法的有效性.

The optimal output tracking control （OOTC） problem for a class of nonlinear systems with persistent disturbances is considered. An approximate design algorithm of the OOTC law is presented in the finite time domain. Firstly, the two-point boundary value （TPBV） problem, which is derived from the original OOTC theory, is transformed to a coupled nonlinear TPBV problem in state vectors and adjoint vectors. The coupled TPBV problem is further transformed to two decoupled linear differential sequences via a recently developed successive approximation approach （SAA）. By iteratively solving the adjoint vector sequence, the OOTC law can be obtained, which consists of analytic linear feedforward and feed- back terms, as well as a nonlinear compensation term determined by the limit of the adjoint vector sequence. Furthermore, a reduced-order reference input observer and a reduced-order disturbance observer are constructed in order to solve the physically realizable problem of feedforward control. Finally, simulation examples show the effectiveness of the presented approach.