Optimal control of discrete-time fractional multi-agent systems (Q1748178)

The authors consider optimal control problems for discrete-time multi-agents systems. The systems are described by fractional difference equations in two variants. In the first variant each agent is described by time-dependent consensus parameter and external control strategies. The objective is to minimize control and disagreements among agents. In the second variant each agent is represented by two coordinates representing the time-dependent state and consensus parameters, and the objective is to minimize control inputs together with the distance among agents and discrepancy of the consensus variables to the mean of those variables. The performance indices are quadratic functions of state and control variables. Basing on the theory of extremal smooth-convex problems [\textit{A. D. Ioffe} and \textit{V. M. Tihomirov}, Theory of extremal problems. Translated from the Russian by K. Makowski. New York, Oxford: North-Holland Publishing Company (1979; Zbl 0407.90051)] the authors formulate necessary conditions of optimality for two optimization problems mentioned above. The idea is to convert the optimal control problems into finite dimensional optimization problem and use the relative extremum principle. To illustrate proposed methodology three numerical (academic) examples are presented.