2019/06/16 by Andrea Alessandretti, Alessandretti, Andrea, Sérgio Pequito +5
Engineering · Mathematics · #Advanced Control Systems Design #Extremum Seeking Control Systems #FOS: Mathematics #Fractional Differential Equations Solutions #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1906.06673
openalex publication_date 2019/06/16 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
This paper addresses the design of finite-dimensional feedback control laws\nfor linear discrete-time fractional-order systems with additive state\ndisturbance. A set of sufficient conditions are provided to guarantee\nconvergence of the state trajectories to an ultimate bound around the origin\nwith size increasing with the magnitude of the disturbances. Performing a\nsuitable change of coordinates, the latter result can be used to design a\ncontroller that is able to track reference trajectories that are solutions of\nthe unperturbed fractional-order system. To overcome the challenges associated\nwith the generation of such solutions, we address the practical case where the\nreferences to be tracked are generated as a solution of a specific\nfinite-dimensional approximation of the original fractional-order system. In\nthis case, the tracking error trajectory is driven to an asymptotic bound that\nis increasing with the magnitude of the disturbances and decreases with the\nincrement in the accuracy of the approximation. The proposed controllers are\nfinite-dimensional, in the sense that the computation of the control input only\nrequires a finite number of previous state and input vectors of the system.\nNumerical simulations illustrate the proposed design methods in different\nscenarios.\n