非线性离散系统最优控制——逐次逼近方法

Optimal control for a class of nonlinear discrete-time systems:a successive approximation approach

研究了非线性离散系统最优控制问题,提出一种逐次逼近方法;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,然后通过构造线性两点边值问题族,将非线性两点边值问题转化为非奇次线性两点边值问题族;得到的最优控制律由精确控制项和非线性补偿项两部分组成,精确控制项可以通过求解R iccati方程求出其精确解,非线性补偿项由逐次逼近法求解一族线性伴随向量方程的解序列求得;仿真结果证明了逐次逼近方法的有效性。

A successive approximation approach designing optimal controllers is developed for a class of nonlinear discrete- time systems. The original optimal control problem is transformed first into a sequence of nonlinear two - point boundary value （TPBV） problems. By constructing a sequence of linear TPBV problems, the original optimal control problem is transformed to a sequence of inhomogeneous linear TPBV problems. The optimal control law consists of an accurate term and a nonlinear compensating term. The accurate term can be found by solving a Riccati matrix equation. In the present approach, only the nonlinear compensating term, solution of a sequence of adjoint vector differential equations, is required iteration. A simulation example is employed to verify the validity of the proposed algorithm.