Neural Network Solution For Fixed Final Time Optimal Control Of Nonlinear Systems
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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.
Self-Learning Optimal Control of Nonlinear Systems
This book presents a class of novel, self-learning, optimal control schemes based on adaptive dynamic programming techniques, which quantitatively obtain the optimal control schemes of the systems. It analyzes the properties identified by the programming methods, including the convergence of the iterative value functions and the stability of the system under iterative control laws, helping to guarantee the effectiveness of the methods developed. When the system model is known, self-learning optimal control is designed on the basis of the system model; when the system model is not known, adaptive dynamic programming is implemented according to the system data, effectively making the performance of the system converge to the optimum. With various real-world examples to complement and substantiate the mathematical analysis, the book is a valuable guide for engineers, researchers, and students in control science and engineering.
A Neural Network Solution for Fixed-Final Time Optimal Control of Nonlinear Systems
We consider the use of neural networks and Hamilton-Jacobi-Bellman equations towards obtaining fixed-final time optimal control laws in the input nonlinear systems. The method is based on Kronecker matrix methods along with neural network approximation over a compact set to solve a time-varying Hamilton-Jacobi-Bellman equation. The result is a neural network feedback controller that has time-varying coefficients found by a priori offline tuning. Convergence results are shown. The results of this paper are demonstrated on two examples.