基于神经动态优化的非线性系统近似最优跟踪控制

提出一种输入约束下一类连续时间非线性系统最优跟踪控制问题的近似求解方法.针对有限时间跟踪性能指标下一类单输入单输出非线性系统,利用所提出的最优跟踪控制方法实现目标系统所对应性能指标近似最优.首先将系统的性能指标沿时间泰勒展开,得到一个近似的性能指标;其次,在系统状态可观测条件下,将该问题进一步转化为以控制输入为决策变量的非线性规划问题;再次,利用神经动态优化方法,求解含不等式约束下的近似最优控制问题并给出相应的递归神经网络模块原理图;进而,针对整个闭环系统进行理论分析,证明在一定条件下闭环系统的稳定性;最后,通过两个实例仿真验证所提出方法的有效性.

Approximate optimal tracking control for nonlinear systems based on neurodynamic optimization

This paper proposes an approach to approximately solve the optimal tracking control problem of a class of continuous-time nonlinear systems with input constraints. For a class of single-input single-output nonlinear systems with the tracking cost function in finite time, the proposed optimal tracking control method will make the corresponding cost function of the target system approximately optimal. Firstly, the cost function of the optimal control problem is expanded along the time by Taylor series, and an approximate cost function is obtained. Then, based on the observability condition, the problem is further transformed into a nonlinear programming problem. Then, the neurodynamic approach is applied to solve the approximate optimal control problem, where the control input is the decision variable with inequality constraints and the corresponding recurrent neural network module is given. In addition, the stability of the closed-loop system is proved under certain conditions. Finally, two examples are provided to verify the effectiveness of the proposed method.