Neural networks-based optimal tracking control for nonzero-sum games of multi-player continuous-time nonlinear systems via reinforcement learning

Zhao, Jingang

doi:10.1016/j.neucom.2020.06.083

Cited by 36 publications

(21 citation statements)

References 35 publications

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“…It is a common treatment to convert the infinite-horizon nonlinear optimal control problem with discount factor into the problem of solving a Bellman equation. 9,24,25,36,[44][45][46] It should be pointed out that Bellman equation ( 10) plays a crucial role in determining the optimal control policy u * (s). Although Bellman equation ( 10) is a nonlinear difference equation, and it is intractable to obtain the analytical solution, luckily there are some methods to tackle the approximate solutions of the Equation (10).…”

Section: Problem Formulationmentioning

confidence: 99%

“…18 There are abundant researches on the optimal control problems by using ADP for both discrete-time system 8,15,[20][21][22][23][24][25][26][27][28] and continuous-time systems. 11,12,[29][30][31][32][33][34][35][36] For example, the control constraints were solved in References 37 and 38 where nonquadratic performance indexes were introduced. The optimal control problem of nonlinear discrete-time systems was studied based on VIHDP method in Reference 20, whose convergence was discussed there.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Learning‐based T‐sHDP() for optimal control of a class of nonlinear discrete‐time systems

Liu

et al. 2021

Intl J Robust & Nonlinear

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Learning‐based T‐sHDP() for optimal control of a class of nonlinear discrete‐time systems

Liu

et al. 2021

Intl J Robust & Nonlinear

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“…The method of strategy improvement was realized through trial and error and environment interaction. It has the ability of self-learning and online learning [23][24][25][26][27][28][29][30]. A popular reinforcement learning model is the Markov decision process (MDP) model, which was used for discrete or random problems [25].…”

Section: Introductionmentioning

confidence: 99%

Motion generation for walking exoskeleton robot using multiple dynamic movement primitives sequences combined with reinforcement learning

Zhang

2022

Robotica

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In order to assist patients with lower limb disabilities in normal walking, a new trajectory learning scheme of limb exoskeleton robot based on dynamic movement primitives (DMP) combined with reinforcement learning (RL) was proposed. The developed exoskeleton robot has six degrees of freedom (DOFs). The hip and knee of each artificial leg can provide two electric-powered DOFs for flexion/extension. And two passive-installed DOFs of the ankle were used to achieve the motion of inversion/eversion and plantarflexion/dorsiflexion. The five-point segmented gait planning strategy is proposed to generate gait trajectories. The gait Zero Moment Point stability margin is used as a parameter to construct a stability criteria to ensure the stability of human-exoskeleton system. Based on the segmented gait trajectory planning formation strategy, the multiple-DMP sequences were proposed to model the generation trajectories. Meanwhile, in order to eliminate the effect of uncertainties in joint space, the RL was adopted to learn the trajectories. The experiment demonstrated that the proposed scheme can effectively remove interferences and uncertainties.

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“…[39] transformed the optimal control of a nonlinear interconnected system into a nonzero-sum differential game problem , and the optimal solution of Hamilton-Jacobi (HJ) equation was obtained by using the proposed distributed ADP algorithm. Zhao et al [40] proposed a reinforcement learning (RL) method to solve HJ equation for the nonlinear system optimal control problem of nonzero-sum game. Ma et.…”

Section: Introductionmentioning

confidence: 99%

Event-triggered-based cooperative game optimal tracking control for modular robot manipulator with constrained input

Wei

et al. 2022

Nonlinear Dyn

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In this paper, a cooperative game optimal tracking control method based on event-triggered mechanism for constrained input modular robot manipulators (MRMs) system is introduced. According to the joint torque feedback (JTF) technique, the dynamics model of the constrained input subsystem is established and the global state space equation is derived. The control inputs of n joints in the MRM system with constrained input are taken as n participants of cooperative game, the tracking control problem of the manipulator system is transformed into the optimal control problem based on the cooperative game. Next, a fusion function containing position and velocity errors is defined to construct the performance index function. In order to improve the control performance and robustness of the manipulator system, part of the known model information is used to devise controller, the model uncertainty is dealt by the neural network (NN) observer, and the

show abstract

Neural networks-based optimal tracking control for nonzero-sum games of multi-player continuous-time nonlinear systems via reinforcement learning

Cited by 36 publications

References 35 publications

Learning‐based T‐sHDP() for optimal control of a class of nonlinear discrete‐time systems

Learning‐based T‐sHDP() for optimal control of a class of nonlinear discrete‐time systems

Motion generation for walking exoskeleton robot using multiple dynamic movement primitives sequences combined with reinforcement learning

Event-triggered-based cooperative game optimal tracking control for modular robot manipulator with constrained input

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