Policy Iteration Algorithm for Online Design of Robust Control for a Class of Continuous-Time Nonlinear Systems

Wang, Ding; Liu, Derong; Li, Hongliang

doi:10.1109/tase.2013.2296206

Cited by 199 publications

(97 citation statements)

References 23 publications

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“…In addition, from the data-based PI algorithm (12), u * (x) can be successively approximated with enough nominal system data, which can be generated by the original system while the actuator is healthy. Furthermore, Theorem 1 displays a different conclusion compared with the results in [30][31][32][33]. The works [30][31][32][33] show that the optimal control policy of the nominal system is nothing but a guaranteed cost controller of the original system.…”

Section: Guaranteed Cost Controllermentioning

confidence: 83%

“…More recently, the robust optimal guaranteed cost control problem for uncertain systems was investigated in [30][31][32][33], where the problem was transformed into an optimal control problem of the nominal system. Although the guaranteed cost FTC problem is different from the robust optimal guaranteed cost control problem for uncertain systems, there are still some similarities between them.…”

Section: Definition 1 ([9]mentioning

confidence: 99%

“…Although the guaranteed cost FTC problem is different from the robust optimal guaranteed cost control problem for uncertain systems, there are still some similarities between them. Inspired by the works of [30][31][32][33], in the next section, we will show that the guaranteed cost FTC problem can be transformed into an optimal control problem of the nominal system by modifying the cost function to account for actuator faults. It is stressed that a guaranteed cost controller can be constructed by modifying the optimal control policy of the nominal system.…”

Section: Definition 1 ([9]mentioning

confidence: 99%

See 2 more Smart Citations

Approximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faults

Xie

Yang

2015

Nonlinear Dyn

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In this paper, the guaranteed cost faulttolerant control problem for unknown multi-input continuous nonlinear systems with loss of actuator effectiveness faults is investigated using the adaptive dynamic programming algorithm. Initially, by modifying the cost function to account for actuator faults, the problem is transformed into an optimal control problem of the nominal system. Subsequently, by using an existing policy iteration (PI) algorithm to solve the corresponding optimal control problem, a guaranteed cost controller is constructed approximately. Furthermore, a rigorous proof is given to show the convergence of the aforementioned PI algorithm while taking the neural network approximation errors into consideration. Finally, simulation examples are provided to show the effectiveness of the proposed approach.

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Section: Guaranteed Cost Controllermentioning

confidence: 83%

Section: Definition 1 ([9]mentioning

confidence: 99%

Section: Definition 1 ([9]mentioning

confidence: 99%

See 1 more Smart Citation

Approximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faults

Xie

Yang

2015

Nonlinear Dyn

View full text Add to dashboard Cite

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“…The general structure for implementing the ADP algorithm is actor-critic architecture, where the actor performs actions by interacting with its environment, and the critic evaluates actions and offers feedback information to the actor, leading to the improvement in performance of the subsequent actor [4]. Since then, various ADP methods have been developed [4][5][6][7][8][9][10][11][12][13][14]. However, most of the existing ADP-related results require an exact knowledge of nonlinear dynamics, which is often unavailable, thus these ADP algorithms are intractable to real-time control applications.…”

Section: Introductionmentioning

confidence: 99%

Data‐Driven Adaptive Critic Approach for Nonlinear Optimal Control via Least Squares Support Vector Machine

Sun

Liu

2017

Asian Journal of Control

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This paper develops an online adaptive critic algorithm based on policy iteration for partially unknown nonlinear optimal control with infinite horizon cost function. In the proposed method, only a critic network is established, which eliminates the action network, to simplify its architecture. The online least squares support vector machine (LS-SVM) is utilized to approximate the gradient of the associated cost function in the critic network by updating the input-output data. Additionally, a data buffer memory is added to alleviate computational load. Finally, the feasibility of the online learning algorithm is demonstrated in simulation on two example systems.

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“…As is shown in Adhyaru et al (2011), Haddad et al (1998Haddad et al ( , 2000, Lin (2000), Wang et al (2014) the unavoidable discrepancies between system models and real-world dynamics can sometimes result in the degradation of system performance. Hence, the feedback control should be designed to be robust with respect to system uncertainties.…”

Section: Introductionmentioning

confidence: 99%

A neural-network-based online optimal control approach for nonlinear robust decentralized stabilization

Wang

Liu

et al. 2014

Soft Comput

Self Cite

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In this paper, the robust decentralized stabilization of continuous-time uncertain nonlinear systems with multi control stations is developed using a neural network based online optimal control approach. The novelty lies in that the well-known adaptive dynamic programming method is extended to deal with the nonlinear feedback control problem under uncertain and large-scale environment. Through introducing an appropriate bounded function and defining a modified cost function, it can be observed that the decentralized optimal controller of the nominal system can achieve robust decentralized stabilization of original uncertain system. Then, a critic neural network is constructed for solving the modified Hamilton-Jacobi-Bellman equation corresponding to the nominal system in an online fashion. The weights of the critic network are tuned based on the standard Communicated by V. Loia. steepest descent algorithm with an additional term provided to guarantee the boundedness of system states. The stability analysis of the closed-loop system is carried out via the Lyapunov approach. At last, two simulation examples are given to verify the effectiveness of the present control approach.

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Policy Iteration Algorithm for Online Design of Robust Control for a Class of Continuous-Time Nonlinear Systems

Cited by 199 publications

References 23 publications

Approximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faults

Approximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faults

Data‐Driven Adaptive Critic Approach for Nonlinear Optimal Control via Least Squares Support Vector Machine

A neural-network-based online optimal control approach for nonlinear robust decentralized stabilization

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