Single‐network ADP for near optimal control of continuous‐time zero‐sum games without using initial stabilising control laws

Mu, Chaoxu; Wang, Ke

doi:10.1049/iet-cta.2018.5464

Cited by 24 publications

(8 citation statements)

References 43 publications

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“…The closed-loop system (18) and the estimation error θi , ∀i ∈ 𝕀 are proved to be UUB according to the Lyapunov extension theorem. To facilitate analysis, several common assumptions are given, which also used in literatures [30][31][32].…”

Section: Stability Analysismentioning

confidence: 99%

“…The closed‐loop system (18) and the estimation error

{\overset{ϑ}{true}}_{i}, \forall i \in I

are proved to be UUB according to the Lyapunov extension theorem. To facilitate analysis, several common assumptions are given, which also used in literatures [30–32]. Assumption The ideal weight vector

ϑ_{i}

, activation function

σ (Z, t_{f} - t)

, and approximation error

ε_{i} false(Z, t_{f} - t false)

are assumed to be norm bounded, and their upper bound are

ϑ_{M i}, {scriptB}_{σ}

and

B_{ε_{i}}

, respectively.…”

Section: Distributed Optimal Tracking Controller Design Via Aperiodic...mentioning

confidence: 99%

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Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games

Duan

Liu

2021

IET Control Theory & Appl

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This paper proposes a distributed adaptive dynamic programming scheme to investigate the optimal tracking control problem for finite-horizon non-linear interconnected systems with constraint inputs under aperiodic sampling. A N-player nonzero-sum differential game system is constructed with the presented non-linear interconnected system and the tracking error system by introducing the augment vectors. To address the problems of constrained-input and finite-horizon control, a non-quadratic utility function and a finitehorizon cost function are utilized which will arise in the time-varying Hamilton-Jacobi (HJ) equation. Then, a periodic event-triggered scheme is designed to realize aperiodic sampling, where the consumption of communication resources is reduced and the Zeno behavior is avoided. Under the designed periodic event-triggered scheme, the time-varying HJ equation is almost impossible to get an analytical solution due to its hybrid properties and non-linearity. Therefore, the critic neural networks are used to estimate the optimal solution of the HJ equation, and the weight update law is constructed to guarantee the uniformly ultimate bounded of approximated errors. Further, the hybrid nonzero-sum differential game is confirmed to be uniformly ultimate bounded by using the Lyapunov theory. Finally, the obtained distributed PET control strategy is successfully applied to dispose the missile-target intercepter problem. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Stability Analysismentioning

confidence: 99%

“…The closed‐loop system (18) and the estimation error

{\overset{ϑ}{true}}_{i}, \forall i \in I

ϑ_{i}

, activation function

σ (Z, t_{f} - t)

, and approximation error

ε_{i} false(Z, t_{f} - t false)

are assumed to be norm bounded, and their upper bound are

ϑ_{M i}, {scriptB}_{σ}

and

B_{ε_{i}}

, respectively.…”

Section: Distributed Optimal Tracking Controller Design Via Aperiodic...mentioning

confidence: 99%

Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games

Duan

Liu

2021

IET Control Theory & Appl

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“…Deterministic two‐person zero‐sum game [5] and nonzero‐sum game [11] were studied. There are various kinds of two‐person games with indeterminacy.…”

Section: Introductionmentioning

confidence: 99%

“…In 1928, von Neumann [2] proved the minimax theorem for finding the saddle-point equilibrium of a two-person zero-sum game. Later, many useful results have been developed from studying two-person zero-sum games [3][4][5][6][7]. These served as a firm foundation for the advancement of game theory.…”

Section: Introductionmentioning

confidence: 99%

Two‐person games for uncertain random singular dynamic systems

Chen

Zhu

Park

2022

IET Control Theory & Appl

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A complex system exhibiting uncertainty as well as randomness may be portrayed by an uncertain random singular difference equation. This paper investigates two-person nonzero-sum and zero-sum games based on uncertain random singular difference equations. First, an approach is proposed to translate the two-person nonzero-sum game into an equivalent game for a standard uncertain random dynamic system. The relevant recursive equations are developed to search the Nash equilibrium for the converted game. Solving the related recursive equations yields the solution to such a game. Following that, a Max-Min Theorem is provided for finding the saddle-point equilibrium of an uncertain random two-person zero-sum game. Finally, a numerical example is offered to demonstrate the validity of the findings.

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“…In addition, some gradient method (Wu et al , 2014), (Vuong and Shehu, 2019), variable scale method (Ge et al , 2018), differential dynamic programming (Murray and Yakowitz, 1979) are used to solve OCPs. For the numerical solutions of OCPs, iterative dynamic programming (Mu et al , 2017; Mu et al , 2018; Mu and Wang, 2018), intelligent algorithm (Ding et al , 2017; Mu et al , 2019a; Mu et al , 2019b) and state parameterizations method (Mehne and Borzabadi, 2006; Sirisena and Chou, 2010) are commonly used. At present, the numerical methods of solving OCPs are mainly focused on state parameterizations.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for solving optimal control problems via Legendre polynomials

Yan

Zhu

2020

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Purpose The purpose of this paper is to propose an iterative Legendre technique to deal with a continuous optimal control problem (OCP). Design/methodology/approach For the system in the considered problem, the control variable is a function of the state variables and their derivatives. State variables in the problem are approximated by Legendre expansions as functions of time t. A constant matrix is given to express the derivatives of state variables. Therefore, control variables can be described as functions of time t. After that, the OCP is converted to an unconstrained optimization problem whose decision variables are the unknown coefficients in the Legendre expansions. Findings The convergence of the proposed algorithm is proved. Experimental results, which contain the controlled Duffing oscillator problem demonstrate that the proposed technique is faster than existing methods. Originality/value Experimental results, which contained the controlled Duffing oscillator problem demonstrate that the proposed technique can be faster while securing exactness.

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Single‐network ADP for near optimal control of continuous‐time zero‐sum games without using initial stabilising control laws

Cited by 24 publications

References 43 publications

Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games

Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games

Two‐person games for uncertain random singular dynamic systems

A numerical method for solving optimal control problems via Legendre polynomials

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