Dual Heuristic dynamic Programming for nonlinear discrete-time uncertain systems with state delay

Wang, Bin; Zhao, Dan; Alippi, Cesare; Liu, Derong

doi:10.1016/j.neucom.2013.06.037

Cited by 40 publications

(7 citation statements)

References 24 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(20) twice integration by parts with respect to t and four times integration by parts with respect to x, using Eqs. (18)(19), one observes the following relation:…”

Section: Theorem 2 (Maximum Principle) the Maximization Problem Statmentioning

confidence: 99%

“…Such delays occur as a result of the finite time-response of actuators used in the implementation of control law [11]. Since time delay leads to a decrement in the performance of the actuator, the state variable can-not reflect the changes in the system [18]. Active vibration control of mechanical systems, which are modeled as DPS without time delays, has been excessively studied in the literature by several authors, such as, but not limited to [3,7,[12][13][14][15][16]; however, the optimal control of DPS with time delay has not received considerable attention yet.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A time-delay equation: well-posedness to optimal control

Yildirim

Alkan

2016

Open Physics

View full text Add to dashboard Cite

Abstract:In this paper, well-posedness, controllability and optimal control for a time-delay beam equation are studied. The equation of motion is modeled as a timedelayed distributed parameter system(DPS) and includes Heaviside functions and their spatial derivatives due to the finite size of piezoelectric patch actuators used to suppress the excessive vibrations based on displacement and moment conditions. The optimal control problem is defined with the performance index including a weighted quadratic functional of the displacement and velocity which is to be minimized at a given terminal time and a penalty term defined as the control voltage used in the control duration. Optimal control law is obtained by using Maximum principle and hence, the optimal control problem is transformed the into a boundary-, initial and terminal value problem.The explicit solution of the control problem is obtained by eigenfunction expansions of the state and adjoint variables. Numerical results are presented to show the effectiveness and applicability of the piezoelectric control.

show abstract

“…(20) twice integration by parts with respect to t and four times integration by parts with respect to x, using Eqs. (18)(19), one observes the following relation:…”

Section: Theorem 2 (Maximum Principle) the Maximization Problem Statmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A time-delay equation: well-posedness to optimal control

Yildirim

Alkan

2016

Open Physics

View full text Add to dashboard Cite

show abstract

“…On the other hand, time delay often occurs in various engineering systems, which can degrade the control performance in the actual control process. The research studies on time‐delay control designs have important theoretical significance and great application value . Song et al developed a finite‐horizon optimal control strategy for nonlinear time‐delay systems.…”

Section: Introductionmentioning

confidence: 99%

A novel neural network discrete‐time optimal control design for nonlinear time‐delay systems using adaptive critic designs

Liang

Zhang

et al. 2020

Optim Control Appl Methods

View full text Add to dashboard Cite

In this article, a novel neural network (NN) optimal control approach using adaptive critic designs is developed for nonlinear discrete-time (DT) systems with time delays. First, to eliminate the delay term of control input, a time-delay matrix function is developed by designing a M network. Furthermore, the cost function is approximated by the critic NN, and the control signal can be obtained directly by using the information of critic NN according to the equilibrium condition. In addition, to shorten the learning time and reduce the computational burden in the control process, a novel control strategy with less adjustable parameters for the time-delay DT nonlinear systems is proposed in this article, in which the norm of the weight estimations of critic NN is updated to generate a novel long-term performance function.The proposed control algorithm using adaptive critic designs has the advantage of reducing adaptive learning parameters and lessening calculative burden. The Lyapunov stability analysis shows that the time-delay DT controlled systems can be uniformly ultimately bounded stable. Finally, three simulations are presented to demonstrate the control performance of the developed method. K E Y W O R D Sadaptive critic designs, discrete-time systems, neural network, optimal control, time delay 1 748

show abstract

“…Data-driven optimal control based on reinforcement learning was proposed in [27] for discrete-time multi-agent systems with unknown dynamics. Wang et al [28] proposed a dual heuristic dynamic programming algorithm for a class of nonlinear discrete-time systems affected by time-varying delay. The method of policy iteration in reinforcement learning was used in [29] to find the optimal control for zero-sum games.…”

Section: Introductionmentioning

confidence: 99%

Distributed Reinforcement Learning Algorithm for Dynamic Economic Dispatch With Unknown Generation Cost Functions

Dai

Wen

et al. 2020

IEEE Trans. Ind. Inf.

View full text Add to dashboard Cite

In this paper, the dynamic economic dispatch (DED) problem for smart grid is solved under the assumption that no knowledge of the mathematical formulation of the actual generation cost functions is available. The objective of the DED problem is to find the optimal power output of each unit at each time so as to minimize the total generation cost. To address the lack of a priori knowledge, a new distributed reinforcement learning optimization algorithm is proposed. The algorithm combines the state-action-value function approximation with a distributed optimization based on multipliers splitting. Theoretical analysis of the proposed algorithm is provided to prove the feasibility of the algorithm, and several case studies are presented to demonstrate its effectiveness.

show abstract

Dual Heuristic dynamic Programming for nonlinear discrete-time uncertain systems with state delay

Cited by 40 publications

References 24 publications

A time-delay equation: well-posedness to optimal control

A time-delay equation: well-posedness to optimal control

A novel neural network discrete‐time optimal control design for nonlinear time‐delay systems using adaptive critic designs

Distributed Reinforcement Learning Algorithm for Dynamic Economic Dispatch With Unknown Generation Cost Functions

Contact Info

Product

Resources

About