Neural-network-based robust optimal control design for a class of uncertain nonlinear systems via adaptive dynamic programming

Wang, Ding; Liu, Derong; Li, Hongliang; Ma, Hongwen

doi:10.1016/j.ins.2014.05.050

Cited by 142 publications

(45 citation statements)

References 40 publications

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“…where α i and b are solutions of (12). In summary, the following lemma can be formulated to explain the principle of LS-SVM approximation.…”

Section: Least Squares Support Vector Machinementioning

confidence: 99%

“…Lemma 1. For the LS-SVM model, giving a training set of L data points λ i X ð Þ; X i ð Þ L i¼1 , the necessary parameters (e.g., α , b) can be obtained by solving the linear equations (11), which is equivalent to the formula (12). Then, the goal function can be approximated by applying (13).…”

Section: Least Squares Support Vector Machinementioning

confidence: 99%

“…As is evident from (11), with some choice of the kernel function K(X, X i ) and the punishment factor C, formula (11) represents a set of linear equations that can easily be solved according to (12). That is to say, the choice of kernel function K(X, X i ) is important for the LS-SVM model.…”

Section: Least Squares Support Vector Machinementioning

confidence: 99%

“…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%

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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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“…where α i and b are solutions of (12). In summary, the following lemma can be formulated to explain the principle of LS-SVM approximation.…”

Section: Least Squares Support Vector Machinementioning

confidence: 99%

Section: Least Squares Support Vector Machinementioning

confidence: 99%

Section: Least Squares Support Vector Machinementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…For nonlinear systems in the strict-feedback form with unknown static parameters, a robust adaptive control law was designed by Montaseri and Mohammad (2012), which guarantees the asymptotic output tracking despite matched and unmatched uncertainties. The neural-network-based robust control design, via an adaptive dynamic programming approach, was investigated in (Wang et al, 2014) to obtain the optimal performance under a specified cost function. Some applications have been also introduced in the literature, in the presence of time-varying uncertainties and disturbances (Koofigar and Amelian, 2013).…”

Section: Introductionmentioning

confidence: 99%

Adaptive fuzzy control for a class of constrained nonlinear systems with application to a surface vessel

Jamalzade

Koofigar

Ataei

2016

jtam

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In this paper, adaptive control for a class of uncertain nonlinear systems with input constraints is addressed. The main goal is to achieve a self-regulator PID controller whose coefficients are adjusted by using some adaptive fuzzy rules. The constraints on the control signal are taken into account as a saturation operator. The stability of the closed-loop system is analytically proved by using the Lyapunov stability theorem. The proposed method is then applied to a surface vessel with uncertain dynamic equations. The simulation results show the effectiveness of the proposed control strategy.

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Online identifier–actor–critic algorithm for optimal control of nonlinear systems

Lin

Wei

Liu

2016

Optim Control Appl Methods

Self Cite

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Summary In this paper, a novel identifier–actor–critic optimal control scheme is developed for discrete‐time affine nonlinear systems with uncertainties. In contrast to traditional adaptive dynamic programming methodology, which requires at least partial knowledge of the system dynamics, a neural‐network identifier is employed to learn the unknown control coefficient matrix working together with actor–critic‐based scheme to solve the optimal control online. The critic network learns the approximate value function at each step. The actor network attempts to improve the current policy based on the approximate value function. The weights of all neural networks are updated at each sampling instant. Lyapunov theory is utilized to prove the stability of closed‐loop system. It shows that system states and neural network weights are uniformly ultimately bounded. Finally, simulations are provided to illustrate the effectiveness of the developed method. Copyright © 2016 John Wiley & Sons, Ltd.

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Neural-network-based robust optimal control design for a class of uncertain nonlinear systems via adaptive dynamic programming

Cited by 142 publications

References 40 publications

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

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

Adaptive fuzzy control for a class of constrained nonlinear systems with application to a surface vessel

Online identifier–actor–critic algorithm for optimal control of nonlinear systems

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