A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct t...A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged Ito stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs （HJI） equation. Numerical results for a controlled and stochastically excited DulTlng oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.展开更多
A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the pro...A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the process are Boolean functions, the optimal control problem related to the process can be solved by relating between the transfer functions and the objective functional. An analogue of Bellman function for the optimal control problem mentioned is defined and consequently suitable Bellman equation is constructed.展开更多
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the National Natural Science Foundation of China (No. 10772159)the Specialized Research Fund for DoctorProgram of Higher Education of China (No. 20060335125) theNatural Science Foundation of Zhejiang Province (No. Y607087),China
文摘A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged Ito stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs （HJI） equation. Numerical results for a controlled and stochastically excited DulTlng oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.
文摘A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the process are Boolean functions, the optimal control problem related to the process can be solved by relating between the transfer functions and the objective functional. An analogue of Bellman function for the optimal control problem mentioned is defined and consequently suitable Bellman equation is constructed.
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.
