Neural Network Solution For Fixed-final Time Optimal Control Of Nonlinear Systems

In this research, practical methods for the design of H2 and H-Infinity optimal state feedback controllers for unconstrained and constrained input systems are proposed. The dynamic programming principle is used along with special quasi-norms to derive the structure of both the saturated and optimal controllers in feedback strategy form. The resulting Hamilton-Jacobi-Bellman (HJB) and Hamilton-Jacobi-Isaacs (HJI) equations are derived respectively. Neural networks are used along with the least-squares method to solve the Hamilton-Jacobi differential equations in the H2 case, and the cost and disturbance in the H-Infinity case. The result is a neural network unconstrained or constrained feedback controller that has been tuned a priori offline with the training set selected using Monte Carlo methods from a prescribed region of the state space which falls within the region of asymptotic stability. The obtained algorithms are applied to different examples including the linear system, chained form nonholonomic system, and Nonlinear Benchmark Problem to reveal the power of the proposed method. Finally, a certain time-folding method is applied to solve optimal control problem on chained form nonholonomic systems with above obtained algorithms. The result shows the approach can effectively provide controls for nonholonomic systems.