Neural network solution for fixed-final time optimal control of nonlinear systems

In this research, practical methods for the design of H 2 and Hinfinity 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 H2 and Hinfinity 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 H 2 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.