Multistep Look-Ahead Policy Iteration for Optimal Control of Discrete-Time Nonlinear Systems With Isoperimetric Constraints
提出一种多步前瞻策略迭代方法，解决离散时间非线性系统在等周约束下的无限时域最优控制问题，证明了收敛性和最优性。
In this article, a novel multistep look-ahead policy iteration with isoperimetric constraints (MLPIIC) method is developed to solve infinite horizon optimal control problems (OCPs) with isoperimetric constraints for discrete-time nonlinear systems. In order to overcome the difficulty that Bellman’s principle of optimality does not hold directly in OCPs with isoperimetric constraints, a method to approximate OCPs with isoperimetric constraints by OCPs with new constraints is developed. For the MLPIIC method initialized with an admissible control law, the convergence and optimality of the iterative value function and the feasibility of the iterative control law are proven. Utilizing the function approximator, the implementation of the MLPIIC method is described. Finally, simulation results are provided.