基于策略迭代的连续时间系统的随机线性二次最优控制

针对模型参数部分未知的随机线性连续时间系统, 通过策略迭代算法求解无限时间随机线性二次(LQ) 最优控制问题. 求解随机LQ最优控制问题等价于求随机代数Riccati 方程(SARE) 的解. 首先利用伊藤公式将随机微分方程转化为确定性方程, 通过策略迭代算法给出SARE 的解序列; 然后证明SARE 的解序列收敛到SARE 的解, 而且在迭代过程中系统是均方可镇定的; 最后通过仿真例子表明策略迭代算法的可行性.

Stochastic linear quadratic optimal control for continuous-time systems based on policy iteration

The stochastic linear quadratic(LQ) optimal control problem is solved for stochastic linear continuous-time systems with the partly unknown parameter by using the policy iteration approach. The feasibility of the stochastic LQ optimal control problem is equivalent to the solvability of the stochastic algebra Riccati equation(SARE). Firstly, the stochastic differential equation is converted into the deterministic equation by using Itˆo formula, and the solution sequence of SARE is obtained by using the policy iteration approach. Then, convergence analysis is presented to prove that the solution sequence of SARE reaches the solution of SARE, and the proof of mean square stability of the systems in the process of iteration is also given. Finally, a simulation example is given to illustrate the feasibility of the policy iteration approach.