受扰非线性时滞系统近似最优跟踪控制

为了研究一类参考输入和扰动由外系统描述的非线性时滞系统最优输出跟踪问题,利用逐次逼近法将原最优跟踪问题转化为一族不含时滞项和超前项的非齐次线性两点边值问题序列,通过迭代求解该问题序列,提出了一个伴随向量解序列近似求解过程。最优输出跟踪控制律由解析的前馈-反馈项和以伴随向量的极限形式给出的非线性时滞补偿项组成,通过截取伴随向量序列的有限步迭代值,得到了问题的次优控制律。利用构造扰动和参考输入降维观测器,解决了前馈控制律的物理可实现问题;仿真结果表明,该方法计算量较小,容易工程实施,能有效地解决非线性时滞系统的最优跟踪控制问题。

Approximate optimal tracking control for nonlinear time-delay systems under persistent disturbances

The optimal output tracking(OOT) problem for a class of nonlinear time-delay systems is considered where the reference input and the external disturbance are described by the exosystems.This problem was transformed into a sequence of nonhomogeneous linear two-point boundary value(TPBV) problems without time-delay and time-advance terms using the successive approximation approach.An approximate procedure was presented to obtain the adjoint vector sequence by iteratively solving the sequence of TPBV problems.The OOT control law obtained consisted of analytic feedback and feedforward terms,and a nonlinear time-delay compensation term which was the limit of the adjoint vector sequence.By using the finite-step iteration of the adjoint vector sequence,a suboptimal output tracking control law could be obtained.A reduced-order disturbance observer and a reference input observer were constructed to make the feedforward control law physically realizable.Simulation results demonstrate the validity of this design algorithm.