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.