具有未知参数的非线性系统动态优化

针对具有未知参数和不等式路径约束的非线性系统动态优化问题,提出一种新颖有效的数值求解方法.首先,将未知参数视为一个动态优化问题的决策变量;其次,利用多重打靶法将无限维的含未知参数动态优化问题转化为有限维的非线性规划问题,进而在不等式路径约束违反的时间段内,用有限多个内点约束替代原不等式路径约束;然后,用内点法求解转化后的非线性规划问题,在路径约束违反的一定容许度下,经过有限多次步数迭代后得到未知参数值的同时得到控制策略,并在理论上对所提出算法的收敛性进行相应证明;最后,对两个经典的含未知参数非线性系统的动态优化问题进行数值仿真以验证所提出算法的有效性.

Dynamic optimization of nonlinear systems with unknown parameters

This paper proposes a novel and effective numerical solution method for dynamic optimization problems of nonlinear systems with unknown parameters and inequality path constraints. Firstly, the unknown parameters are regarded as decision variables of the dynamic optimization problem. Then, the infinite-dimensional dynamic optimization problem with unknown parameters is transformed into a finite-dimensional nonlinear programming problem by using the multiple shooting method. Furthermore, within the time interval where the inequality path constraints are violated, the path constraint of inequality is replaced by finite multiple interior point constraint. Moreover, the transformed nonlinear programming problem is solved by using the interior point method. Under a certain tolerance for the violation of path constraints, after finite number of steps iteration, the unknown parameter value is obtained and the control strategy is obtained, and then the convergence of the proposed algorithm is proved theoretically. Finally, two classic examples are given to verify the effectiveness of the proposed algorithm.