Hamiltonian-Driven Adaptive Dynamic Programming With Approximation Errors

Yang, Yongliang; Modares, Hamidreza; Vamvoudakis, Kyriakos G.; He, Wei; Xu, Cheng‐Zhong; Wunsch, Donald C.

doi:10.1109/tcyb.2021.3108034

Cited by 75 publications

(56 citation statements)

References 47 publications

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“…In order to verify the correctness of the cantilever beam model established in this paper, the natural frequencies the first three modals are obtained by the following method: we assume that the initial displacement at node x 6 is 0.028 m, the open-loop response of the system can be obtained from (18). Figure 4 shows the open-loop time-domain response and frequency-domain response of node x 6 .…”

Section: Simulation Of Frequency Domain Responsementioning

confidence: 99%

“…The main control algorithms used in the active vibration control of piezoelectric cantilever beam are as follows: PD control based on optimal position feedback, 15 robust control, 16,17 adaptive control, [18][19][20][21][22][23][24][25][26][27][28][29] fuzzy control, 30 artificial neural network control, 31 LQR control method [32][33][34][35][36][37][38] etc. The purpose of control is to quickly suppress bending and torsional modal vibration.…”

Section: Introductionmentioning

confidence: 99%

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Active vibration optimal control of piezoelectric cantilever beam with uncertainties

Cui

Liu

Jiang

et al. 2022

Measurement and Control

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Considering the stiffness characteristics of piezoelectric layer, the bending stiffness of piezoelectric cantilever beam is obtained by applying the first-order shear deformation theory. The finite element model of piezoelectric cantilever beam is established by Hamilton variation principle, and the modal superposition method is employed to reduce the order of the finite element model. At the maximum strain point, the sensors/actuators are equipped in pairs. Based on the uncertain dynamic model of piezoelectric cantilever beam, the independent modal space control method based on LQR (linear quadratic regulator) control is employed for the active control of the smart beam structure, and the weighted matrices Q and R are selected according to the energy criterion. The numerical simulations and experiments verify the effectiveness of the proposed finite element model and the active vibration optimal control.

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Section: Simulation Of Frequency Domain Responsementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Active vibration optimal control of piezoelectric cantilever beam with uncertainties

Cui

Liu

Jiang

et al. 2022

Measurement and Control

View full text Add to dashboard Cite

show abstract

“…In Reference 30, an integral reinforcement learning method incorporating experience replay technique is presented to solve the optimal control problem of partially unknown constrained‐input systems. Hamiltonian‐driven ADP method is proposed in Reference 31 and used to solve the infinite‐horizon optimal control problem of continuous‐time nonlinear systems in Reference 32. In Reference 33, consider a class of continuous time nonlinear systems with unmodeled dynamics, a robust actor‐critic RL method is presented.…”

Section: Introductionmentioning

confidence: 99%

Off‐policy integral reinforcement learning‐based optimal tracking control for a class of nonzero‐sum game systems with unknown dynamics

Zhao

Chen

2022

Optim Control Appl Methods

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This article studies the optimal tracking control problem of a class of multi‐input nonlinear system with unknown dynamics based on reinforcement learning (RL) and nonzero‐sum game theory. First of all, an augmented system composed of the tracking error dynamics and the command generator dynamics is constructed. Then, a tracking coupled Hamilton–Jacobi (HJ) equations associated with discounted cost function is derived, which gives the Nash equilibrium solution. The existence of Nash equilibrium is proved. To approximate the Nash equilibrium solution of tracking coupled HJ equations, we give two model‐based policy iteration (PI) algorithms, and analyze their equivalence and convergence. Further, to get rid of the prior knowledge of system dynamics, an off‐policy integral reinforcement learning (OP‐IRL) algorithm implemented by neural networks (NNs) is proposed. The weights of critic NNs and actor NNs are updated simultaneously by the gradient descent method. The convergence of the NNs weights and the stability of the closed‐loop error systems are proved. Finally, numerical simulation results are provided to demonstrate the effectiveness of the proposed OP‐IRL method.

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“…For example, Hordijk and Kallenberg [17] used linear programming to nd the average optimal strategy of general Markov decision processes (abbreviated as MDPs), Denard and fox [18] obtained the algorithm of linear programming to solve some special cases of nondiscounted semi-Markov decision processes (semi-MDP), and Vrieze [19] gave a linear programming algorithm for nondiscounted stochastic games with nite state and action space. Recently, Yang et al [9,20,21] proposed some new algorithms for optimal control problems, such as a novel adaptive optimal control design method for the constrained control problem in [9], an iterative adaptive dynamic programming (ADP) algorithm for the infinite-horizon optimal control problem in continuous time for nonlinear systems in [20], and λ-policy iteration (λ-PI) for the discrete-time linear quadratic regulation problem in [21].…”

Section: Introductionmentioning

confidence: 99%

Numerical Calculation of Optimal Policy Pairs in Zero‐sum Stochastic Games with Varying Discount Factors

Tang

2022

Discrete Dynamics in Nature and Society

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In this study, the numerical calculation of optimal policy pairs in two-person zero-sum stochastic games with unbounded reward functions and state-dependent discount factors are studied. First, the expected discount criterion, ε −optimal values, and policy pairs are defined for zero-sum stochastic game model. Then, an iterative algorithm is given and the correctness of the algorithm is verified. At last, an example of inventory system is stated, the numerical simulation is obtained according to the iterative algorithm steps, and the difference between varying discount factors and a constant discount factor is obtained in further discussion.

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Hamiltonian-Driven Adaptive Dynamic Programming With Approximation Errors

Cited by 75 publications

References 47 publications

Active vibration optimal control of piezoelectric cantilever beam with uncertainties

Active vibration optimal control of piezoelectric cantilever beam with uncertainties

Off‐policy integral reinforcement learning‐based optimal tracking control for a class of nonzero‐sum game systems with unknown dynamics

Numerical Calculation of Optimal Policy Pairs in Zero‐sum Stochastic Games with Varying Discount Factors

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