一种非线性离散动态投入产出系统的最优控制

阐述了基于动态投入产出模型的最优控制理论,并对当前国内外的研究成果进行了对比研究。在分析其优缺点的同时,针对非线性离散动态投入产出系统的特点,提出了一种动态投入产出系统最优控制的逐次逼近方法。此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齐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Riccati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;最优控制律的最终目标是在规划期内使实际产出尽可能地与理想产出接近。实验仿真测试表明,采用逐次逼近法获得了非线性离散动态投入产出的最优系统控制,从而为最优控制问题的有效解决提供了参考和借鉴。

Optimal Control of a Nonlinear Discrete Dynamic Input-Output System

The optimal control theory based on dynamic input output model was described and a contrastive research on the previous studies at home and abroad at present was conducted. On the basis of analysis of their merits and demerits and in light of the characteristics of nonlinear discrete dynamic input output system, a successive approximation method of optimal control of dynamic input-output system was put forward. First, optimal control of the system is transformed into nonlinear two-point boundary value problem family, and then, nonlinear two-point boundary value problem is transformed into nonsingular sulrlincar two-point boundary value problem family by means of constructing a linear two-point boundary value problem family. The obtained optimal control law consists of accurate control term and nonlinear compensating term, in which the accurate solution of accurate control term can be obtained from Riccati Equation and the solution of nonlinear compensating term can be obtained from a series of solution of linear adjoint vector ectuations. The objective of optimal control law is to make the actual output close to the ideal output in the planning period. Finally, the simulation experiment shows that the optimal system control based on nonlinear discrete dynamic input output is obtwined by means of successive approximation method,which provides references for the solution of the realization of optimal control.