In this paper, a novel iterative Q-learning algorithm, called "policy iteration based deterministic Qlearning algorithm", is developed to solve the optimal control problems for discrete-time deterministic no...In this paper, a novel iterative Q-learning algorithm, called "policy iteration based deterministic Qlearning algorithm", is developed to solve the optimal control problems for discrete-time deterministic nonlinear systems. The idea is to use an iterative adaptive dynamic programming(ADP) technique to construct the iterative control law which optimizes the iterative Q function. When the optimal Q function is obtained, the optimal control law can be achieved by directly minimizing the optimal Q function, where the mathematical model of the system is not necessary. Convergence property is analyzed to show that the iterative Q function is monotonically non-increasing and converges to the solution of the optimality equation. It is also proven that any of the iterative control laws is a stable control law. Neural networks are employed to implement the policy iteration based deterministic Q-learning algorithm, by approximating the iterative Q function and the iterative control law, respectively. Finally, two simulation examples are presented to illustrate the performance of the developed algorithm.展开更多
基金supported in part by National Natural Science Foundation of China(Grant Nos.6137410561233001+1 种基金61273140)in part by Beijing Natural Science Foundation(Grant No.4132078)
文摘In this paper, a novel iterative Q-learning algorithm, called "policy iteration based deterministic Qlearning algorithm", is developed to solve the optimal control problems for discrete-time deterministic nonlinear systems. The idea is to use an iterative adaptive dynamic programming(ADP) technique to construct the iterative control law which optimizes the iterative Q function. When the optimal Q function is obtained, the optimal control law can be achieved by directly minimizing the optimal Q function, where the mathematical model of the system is not necessary. Convergence property is analyzed to show that the iterative Q function is monotonically non-increasing and converges to the solution of the optimality equation. It is also proven that any of the iterative control laws is a stable control law. Neural networks are employed to implement the policy iteration based deterministic Q-learning algorithm, by approximating the iterative Q function and the iterative control law, respectively. Finally, two simulation examples are presented to illustrate the performance of the developed algorithm.
