Necessary and Sufficient Conditions on Consensus of General Fractional-Order Multi-Agent Systems Over Directed Networks

Fractional-order models can describe atypical and nonlinear dynamic behaviors more flexibly than integer-order systems. This article investigates the consensus problem of positive fractional-order multi-agent systems over directed graphs using a distributed observer-based approach. First, a distributed observer is used to estimate the agents’ states, offering larger design flexibility than the classical Luenberger observer. Second, sufficient and necessary conditions for the positive consensus of fractional-order multi-agent systems are established based on positive system theory. As these conditions involve Laplacian matrix information, they are further optimized to sufficient conditions expressed as Riccati-type inequalities by considering the number of nodes in the directed graphs. A semidefinite programming algorithm for achieving consensus in observer-based positive fractional-order multi-agent systems is presented by solving the algebraic Riccati inequalities. Finally, the validity of the results is confirmed through a numerical simulation.

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Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems

Yang,

Si,

Ivanov

2024

Fractal Fract

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This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0<α<1. The objective is to establish the existence of conditions for a linear feedback control law within state constraints and to propose a method for solving the CSRP of DFOLCS. First, based on the decomposition and separation method and coordinate transformation, the DFOLCS can be transformed into an equivalent fractional-order reduced system; hence, the CSRP of the DFOLCS is equivalent to the CSRP of the reduced system. By means of positive invariant sets theory, Lyapunov stability theory, and some mathematical techniques, necessary and sufficient conditions for the polyhedral positive invariant set of the equivalent reduced system are presented. Models and corresponding algorithms for solving the CSRP of a linear feedback controller are also presented by the obtained conditions. Under the condition that the resulting closed system is positive, the given model of the CSRP in this paper for the DFOLCS is formulated as nonlinear programming with a linear objective function and quadratic mixed constraints. Two numerical examples illustrate the proposed method.

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Necessary and Sufficient Conditions on Consensus of General Fractional-Order Multi-Agent Systems Over Directed Networks

Cited by 3 publications

References 32 publications

Analyzing Containment Control Performance for Fractional-Order Multi-Agent Systems via A Delay Margin Perspective

Analyzing Containment Control Performance for Fractional-Order Multi-Agent Systems via A Delay Margin Perspective

Distributed observer-based positive consensus of fractional-order multiagent systems over directed graphs

Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems

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