In this paper, a generalized technique for solving a class of nonlinear optimal control problems is proposed. The optimization problem is formulated based on the cost-to-go functional approach and the optimal solution can be obtained by Bellman’s technique. Specifically, a continuous nonlinear system is first discretized and a set of equality constraints can be obtained from the discretization. We show that, under a certain condition, the optimal solution of a problem in this class can be approximated by a solution of the set of equality constraints within any precision and the system is guaranteed to be stable under a control signal obtained from the solution. An iterative approach is then applied to numerically solve the set of equality constraints. The technique is tested on a nonlinear control problem from the class and simulation results show that the approach is not only effective but also leads to a fast convergence and accurate optimal solution.

中文翻译：

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动态规划的非线性系统最优控制

本文提出了一种解决一类非线性最优控制问题的通用技术。根据成本函数函数法制定了优化问题，并且可以通过Bellman的技术获得最佳解决方案。具体来说，首先离散化连续非线性系统，然后从离散化中获得一组等式约束。我们表明，在一定条件下，此类问题的最优解可以通过在任何精度范围内的一组等式约束的解来近似，并且在从该解获得的控制信号下，系统可以保证稳定。然后将迭代方法应用于数值求解一组相等约束。