Data-based Optimal Control for Discrete-time Zero-sum Games of 2-D Systems Using Adaptive Critic Designs

Wei, Qinglai; Zhang, Huaguang; Cui, Lili

doi:10.3724/sp.j.1004.2009.00682

Cited by 20 publications

(10 citation statements)

References 25 publications

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“…Hence, some studies have attempted to solve the optimal control solution based on ADP technique without an a priori system model [15]- [18]. For linear discrete-time systems, Q-learning was introduced to relax some of the exact model-matching restrictions in [15] and [16], which allows model-free tuning of the action and critic networks. For linear continuous-time systems, Vrabie et al proposed a new formulation of the proportional algorithm which converges to the optimal control solution without using internal dynamics of the system in [17].…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Robust Approximate Optimal Tracking Control for Unknown General Nonlinear Systems Using Adaptive Dynamic Programming Method

Zhang

Cui

Zhang

et al. 2011

IEEE Trans. Neural Netw.

567

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In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

show abstract

Section: Introductionmentioning

confidence: 99%

Data-Driven Robust Approximate Optimal Tracking Control for Unknown General Nonlinear Systems Using Adaptive Dynamic Programming Method

Zhang

Cui

Zhang

et al. 2011

IEEE Trans. Neural Netw.

567

View full text Add to dashboard Cite

show abstract

“…Game theory [22][23][24][25][26] has been applied in modeling strategic behavior, where the performance of each player depends on the action of himself and all the other players. In practice, a large class of practical systems such as wireless communication systems is controlled by more players (controllers) with every player trying to optimize individual performance objective.…”

Section: Introductionmentioning

confidence: 99%

Online finite-horizon optimal learning algorithm for nonzero-sum games with partially unknown dynamics and constrained inputs

et al. 2016

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“…Since proposed by Werbos [1], ACD has been used to solve optimal control problem forward in time in many works, such as [2], [4], [5], [7], [6], [17], [18], [27], [15]. In recent years, ACD has also been utilized to solve for zero-sum games [21], [16], [20]. Some recent surveys in [10] and [19] on ACD techniques present excellent overview of the state-of-the-art developments.…”

Section: Introductionmentioning

confidence: 99%

“…In [3], the optimal strategies for discrete-time linear system quadratic zero-sum games without knowing the system dynamical matrices by using Q-learning method was proposed. In [16], an iterative ADP algorithm was proposed to solve a class of discrete-time two-person zero-sum for Roesser type 2-D system based on Q-learning method. It is important to note that the controller designed based on Q-learning method is still a state feedback controller which demand the state of the system to be measurable.…”

Section: Introductionmentioning

confidence: 99%

Data-based adaptive critic design for discrete-time zero-sum games using output feedback

Cui

Zhang

et al. 2011

2011 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)

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A novel data-based adaptive critic design (ACD) using output feedback is proposed for discrete-time zero-sum games in this paper. The proposed data-based adaptive critic design (ACD) is actually a direct adaptive output feedback control scheme. The main contribution of this paper is that not only knowledge of system model but also information of system states are not required. Only the data measured from input and output are required for reaching the saddle point of the zero-sum games by using proposed data-based iterative ACD algorithm. Moreover, the property of the proposed databased iterative ACD algorithm is discussed. Simulation results demonstrate satisfactory performance of the proposed controller.

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Data-based Optimal Control for Discrete-time Zero-sum Games of 2-D Systems Using Adaptive Critic Designs

Cited by 20 publications

References 25 publications

Data-Driven Robust Approximate Optimal Tracking Control for Unknown General Nonlinear Systems Using Adaptive Dynamic Programming Method

Data-Driven Robust Approximate Optimal Tracking Control for Unknown General Nonlinear Systems Using Adaptive Dynamic Programming Method

Online finite-horizon optimal learning algorithm for nonzero-sum games with partially unknown dynamics and constrained inputs

Data-based adaptive critic design for discrete-time zero-sum games using output feedback

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