Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach

Abu-Khalaf, Murad; Lewis, Frank L.

doi:10.1016/j.automatica.2004.11.034

Cited by 1,136 publications

(643 citation statements)

References 27 publications

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“…Since the function approximation error ε HJB is generated by the error ε c , the error ε HJB can be kept very small. Therefore, in this paper, based on the Weierstrass higher-order approximation theorem [38], the LS-SVM approximator, rather than the NNs approximator, is proposed to approximate the gradient of the cost function. Compared with traditional NNs-based adaptive dynamic programming, the LS-SVM can converge more quickly towards the optimal position and enhance the generalization performance of the model.…”

Section: (Policy Evaluation Step) Solve For the Value Functionmentioning

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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Section: (Policy Evaluation Step) Solve For the Value Functionmentioning

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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“…For the infinite final time case, the NN weights are constant [1]. The NN weights will be selected to minimize a residual error in a least-squares sense over a set of points sampled from a compact set Ω inside the RAS of the initial stabilizing control [10].…”

Section: Nonlinear Fixed-final-time Hjb Solution By Nn Least-squmentioning

confidence: 99%

A Neural Network Solution for Fixed-Final Time Optimal Control of Nonlinear Systems

Cheng

Lewis

Abu-Khalaf

2006

2006 14th Mediterranean Conference on Control and Automation

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Section: Introductionmentioning

confidence: 99%

“…Specifically, policy iteration represents a class of algorithms containing two basic iterations, i.e., policy evaluation and policy improvement [41]- [46]. Abu-Khalaf and Lewis [41] derived an offline optimal control scheme for nonlinear systems with saturating actuators. Then, Vrabie and Lewis [42] and Vamvoudakis and Lewis [43] used online policy iteration algorithm to study the infinite horizon optimal control of continuous-time nonlinear systems, respectively.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Stabilization for a Class of Continuous-Time Nonlinear Interconnected Systems Using Online Learning Optimal Control Approach

Liu

Wang

2014

IEEE Trans. Neural Netw. Learning Syst.

304

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Abstract-In this paper, using a neural-network-based online learning optimal control approach, a novel decentralized control strategy is developed to stabilize a class of continuoustime nonlinear interconnected large-scale systems. First, optimal controllers of the isolated subsystems are designed with cost functions reflecting the bounds of interconnections. Then, it is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control policies of the isolated subsystems. Next, an online policy iteration algorithm is presented to solve the Hamilton-Jacobi-Bellman equations related to the optimal control problem. Through constructing a set of critic neural networks, the cost functions can be obtained approximately, followed by the control policies. Furthermore, the dynamics of the estimation errors of the critic networks are verified to be uniformly and ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness of the present decentralized control scheme.Index Terms-Adaptive dynamic programming, decentralized control, large-scale systems, neural networks, nonlinear interconnected systems, optimal control, policy iteration, reinforcement learning.

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Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach

Cited by 1,136 publications

References 27 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

A Neural Network Solution for Fixed-Final Time Optimal Control of Nonlinear Systems

Decentralized Stabilization for a Class of Continuous-Time Nonlinear Interconnected Systems Using Online Learning Optimal Control Approach

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