用连续Hopfield网络实现无限时域上的最优控制

Infinite horizon optimal control using continuous Hopfield neural networks

为避免直接采用Riccati方程求解时变系统无限域最优控制问题时的计算困难,本文提出一种基于时间连续状态连续型Hopfield网络(CTCSHNN)实现无限域动态最优控制的方法．该方法通过建立CTCSHNN能量函数与移动域控制指标间的等价关系,可在线构建CTCSHNN．理论分析表明,依据该方法设计的CTCSHNN具有稳定性,而且移动域控制量可由网络稳态输出直接产生．将该方法与滚动优化策略相结合,可实现无限时域上的闭环最优控制．仿真实验验证了理论设计的正确性与采用基于CTCSHNN的移动域控制实现无限域闭环最优控制的可行性．

To avoid the computational difficulty in solving infinite horizon optimal control problem with Riccati equation for time-varying systems, an infinite horizon dynamic optimal control method is developed using continuous time continuous state Hopfield neural networks （CTCSHNN）. The CTCSHNN can be constructed online by establishing the equivalent relation between the energy function of CTCSHNN and the performance index of receding horizon control. Theoretical analysis is then given to show that the designed CTCSHNN has stability, and the receding horizon control can be produced directly from CTCSHNN＇s stable outputs. Moreover, the closed loop optimal control in infinite horizon can also be implemented by integrating the method with rolling optimization strategy. Finally, simulation experiment shows that the proposed theoretical design is effective, and the closed-loop optimal control in infinite-horizon is feasible by using receding horizon control based on CTCSHNN.