受扰非线性离散系统的前馈反馈最优控制

利用逐次逼近法研究含外部扰动的非线性离散系统的线性二次型前馈反馈最优控制问题.首先将系统的最优控制问题转化为非线性两点边值问题族.其次,构造了该问题族的由精确线性项和非线性补偿项组成的解序列,并证明了解序列一致收敛到系统的最优解.最后,通过截取最优控制序列解中非线性补偿项的有限项,得到系统的前馈反馈次优控制(FFSOC)律及设计算法.仿真算例表明,该算法容易实现,且对抑制外部扰动的鲁棒性优于经典的反馈次优控制(FSOC).

Feedforward and feedback optimal control for nonlinear discrete-time systems with deterministic disturbances

Based on successive approximation approach,the problem of the linear-quadratic feedforward and feedback optimal control for nonlinear discrete-time systems with external disturbances is considered.The original optimal control problem is transformed first into a sequence of nonlinear two-point boundary value(TPBV) problems.Then a solution sequence,which consists of an accurate linear term and nonlinear compensation term,is constructed and its uniform convergence to the optimal solution of the system is proven.By taking a finite-step iteration of the nonlinear compensation term of optimal solution sequence,a feedforward and feedback sub-optimal control(FFSOC) law is obtained,and the design scheme is given.Simulations indicate that the algorithm proposed is easy to implement,and more robust with respect to external disturbances than that of the classical feedback sub-optimal control(FSOC) law.