Fixed-Time Distributed Optimization for Multi-Agent Systems with Input Delays and External Disturbances

Xu, Xuening; Yu, Zhiyong; Jiang, Haijun

doi:10.3390/math10244689

Cited by 3 publications

(1 citation statement)

References 40 publications

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“…In [23,24], novel fractional FTGDs were proposed based on fractional-order system theory. The fixed-time scheme has also been widely applied for multi-agent systems and distributed optimization [25,26]. Though existing fixed-time GDs could reach the minimum point in a fixed time, they have too many tuning parameters, and their discrete form can easily lead to instability.…”

Section: Introductionmentioning

confidence: 99%

Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

Chen,

Sun,

Wang

2023

Mathematics

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Optimization algorithms have now played an important role in many fields, and the issue of how to design high-efficiency algorithms has gained increasing attention, for which it has been shown that advanced control theories could be helpful. In this paper, the fixed-time scheme and reset scheme are introduced to design high-efficiency gradient descent methods for unconstrained convex optimization problems. At first, a general reset framework for existing accelerated gradient descent methods is given based on the systematic representation, with which both convergence speed and stability are significantly improved. Then, the design of a novel adaptive fixed-time gradient descent, which has fewer tuning parameters and maintains better robustness to initial conditions, is presented. However, its discrete form introduces undesirable overshoot and easily leads to instability, and the reset scheme is then applied to overcome the drawbacks. The linear convergence and better stability of the proposed algorithms are theoretically proven, and several dedicated simulation examples are finally given to validate the effectiveness.

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Section: Introductionmentioning

confidence: 99%

Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

Chen,

Sun,

Wang

2023

Mathematics

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Distributed consensus time‐varying optimization algorithm for multi‐agent systems in predefined time via event‐triggered sliding mode control

Zhao,

Wu,

Cao

2024

Math Methods in App Sciences

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This paper proposes a distributed consensus algorithm in predefined time of time‐varying optimization with inequality constrains for multi‐agent systems (MASs) with external disturbances over an undirected graph. Firstly, by utilizing exponential function, a novel criterion with respect to the stability in predefined time is developed for the nonlinear systems. Secondly, a new distributed switching control protocol, which can inhibit the external unbounded disturbances, is piecewise designed to drive the states of agents to the sliding mode surface via the predefined‐time set by users. Subsequently, under the designed event‐triggered controller (ETC), the states of agents achieve consensus in predefined time on the sliding mode surface. Meanwhile, with the help of log barrier function, the consensus states of agents reach the feasible region and converge to the optimal solution in predefined time. Finally, the correctness and availability of the proposed optimization control algorithm are verified by a simulation example.

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Delay-Dependent Stability Region for the Distributed Coordination of Delayed Fractional-Order Multi-Agent Systems

et al. 2023

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Delay and especially delay in the transmission of agents’ information, is one of the most important causes of disruption to achieving consensus in a multi-agent system. This paper deals with achieving consensus in delayed fractional-order multi-agent systems (FOMAS). The aim in the present note is to find the exact maximum allowable delay in a FOMAS with non-uniform delay, i.e., the case in which the interactions between agents are subject to non-identical communication time-delays. By proving a stability theorem, the results available for non-delayed networked fractional-order systems are extended for the case in which interaction links have nonequal communication time-delays. In this extension by considering a time-delay coordination algorithm, necessary and sufficient conditions on the time delays and interaction graph are presented to guarantee the coordination. In addition, the delay-dependent stability region is also obtained. Finally, the dependency of the maximum allowable delay on two parameters, the agent fractional-order and the largest eigenvalue of the graph Laplacian matrix, is exactly determined. Numerical simulation results are given to confirm the proposed methodologies.

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Fixed-Time Distributed Optimization for Multi-Agent Systems with Input Delays and External Disturbances

Cited by 3 publications

References 40 publications

Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

Distributed consensus time‐varying optimization algorithm for multi‐agent systems in predefined time via event‐triggered sliding mode control

Delay-Dependent Stability Region for the Distributed Coordination of Delayed Fractional-Order Multi-Agent Systems

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