Linear quadratic Pareto optimal control problem of stochastic singular systems

Zhang, Weihai; Lin, Yaning; Xue, Lingrong

doi:10.1016/j.jfranklin.2016.11.021

Cited by 32 publications

(12 citation statements)

References 30 publications

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“…In order to achieve simultaneous optimization of H 2 / H ∞ tracking objectives, Chen and Ho used the LMI‐based multiobjective evolution algorithm to efficiently search the set of Pareto optimal solutions for the stochastic T‐S fuzzy systems. Zhang et al considered the LQ Pareto optimal control problem of stochastic singular systems in finite horizon. However, up to now, there are few works on the Pareto game of the discrete‐time systems.…”

Section: Introductionmentioning

confidence: 99%

“…The differential game is the situation in which the environment can be modeled by a set of differential equations. In the past few decades, there have been a lot of works on various strategies of differential game, such as Pareto strategy,() Stackelberg strategy,() and Nash equilibria. () Compared with the differential game, the difference game is far less developed.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, Pareto solutions have been considered for a wider range of systems. () Mukaidani and Xu obtained the decentralized stochastic Pareto optimal static output feedback strategy for a class of weakly coupled systems with state‐dependent noise in infinite horizon. Mukaidani discussed Pareto and Nash strategies for a class of linear stochastic delay systems, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Necessary/sufficient conditions for Pareto optimum in cooperative difference game

Lin

Zhang

2017

Optim Control Appl Methods

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Summary This paper is concerned with the necessary/sufficient conditions for the Pareto optimum of the cooperative difference game in finite horizon. Utilizing the necessary and sufficient characterization of the Pareto optimum, the problem is transformed into a set of constrained optimal control problems with a special structure. Employing the discrete version of Pontryagin's maximum principle, the necessary conditions for the existence of the Pareto solutions are derived. Under certain convex assumptions, it is shown that the necessary conditions are sufficient too. Next, the obtained results are extended to the linear‐quadratic case. For a fixed initial state, the necessary conditions resulting from the maximum principle and the convexity condition on the cost functional provide the necessary and sufficient description of the well‐posedness of the weighted sum optimal control problem. For an arbitrary initial state, the solvability of the related difference Riccati equation provides a sufficient condition under which the Pareto‐efficient strategies are equivalent to the weighted sum optimal controls. In addition, all Pareto solutions are derived based on the solutions of a set of difference equations. Two examples show the effectiveness of the proposed results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Necessary/sufficient conditions for Pareto optimum in cooperative difference game

Lin

Zhang

2017

Optim Control Appl Methods

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“…Zhang et al . [14] and Lin et al . [15] studied the linear quadratic (LQ) Pareto game of the stochastic singular systems in finite horizon and infinite horizon, respectively.…”

Section: Introductionmentioning

confidence: 99%

Pareto optimality in the infinite horizon cooperative difference game

Lin

2020

IET Control Theory & Applications

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“…The researches on the stability of NNs, FOS, and stochastic systems have attracted the attention of a large number of researchers, and many achievements have been made [29][30][31][32][33][34][35][36][37][38][39][40][41]. The sliding mode control (SMC) is a very popular strategy for a general class of nonlinear uncertain systems, with a very large frame of applications fields.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

Meng

Wang

2018

Mathematical Problems in Engineering

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Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

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Linear quadratic Pareto optimal control problem of stochastic singular systems

Cited by 32 publications

References 30 publications

Necessary/sufficient conditions for Pareto optimum in cooperative difference game

Necessary/sufficient conditions for Pareto optimum in cooperative difference game

Pareto optimality in the infinite horizon cooperative difference game

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

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