求解边界约束最优控制问题的神经网络

提出了一种求解控制变量含有边界约束最优控制问题的神经网络模型(COCNN).该模型将控制系统动态方程的等式约束隐含于神经网络COCNN结构中,克服了动态方程约束所带来的求解优化问题的困难;仅将控制系统的控制变量选为COCNN的状态变量,从而降低了神经网络的维数;利用饱和特性处理边界约束,可以求得最优控制问题的精确最优解;该COCNN无论是在硬件实现,还是在用数字计算机进行软件仿真方面,都特别适合于并行处理,可显著提高问题的求解速度,具有广阔的应用前景。

A Neural Network for Optimal Control Problems with Bound Constraints

A novel neural network (COCNN) is presented for solving optimal control problems with bound constraints of the control variables. The features of COCNN are as follows: (1)The system dynamic equations are embedded in COCNN, which overcomes the difficulty caused by the system dynamic equations.(2)Only the control variables are taken to be the state variables of COCNN, hence the dimension of COCNN is reduced significantly. (3) A saturation approach is employed to deal with the bound constraints so that COCNN can give the exact solution of the optimal control problem,(4)COCNN is very suitable for parallel processing. It is also proved that COCNN is completely stable and that there exists one to one correspondence between the steady state of COCNN and the local optimal solution of the optimal control problem under mild conditions. As a result of the above features, COCNN can greatly speed up the problem solving. Therefore, COCNN has promising applications to real-time control problems.