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Distributed controller design and performance optimization for discrete‐time linear systems
Author(s) -
Viegas Daniel,
Batista Pedro,
Oliveira Paulo,
Silvestre Carlos
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2669
Subject(s) - computation , control theory (sociology) , controller (irrigation) , matrix (chemical analysis) , mathematical optimization , discrete time and continuous time , optimization problem , computer science , quadratic equation , mathematics , state (computer science) , constraint (computer aided design) , linear system , algorithm , control (management) , mathematical analysis , statistics , materials science , geometry , artificial intelligence , agronomy , composite material , biology
Summary This article addresses the problem of distributed controller design for linear discrete‐time systems. The problem is posed using the classical framework of state feedback gain optimization over an infinite‐horizon quadratic cost, with an additional sparsity constraint on the gain matrix to model the distributed nature of the controller. An equivalent formulation is derived that consists in the optimization of the steady‐state solution of a matrix difference equation, and two algorithms for distributed gain computation are proposed based on it. The first method consists in a step‐by‐step optimization of said difference matrix equation, and allows for fast computation of stabilizing state feedback gains. The second algorithm optimizes the same matrix equation over a finite time window to approximate asymptotic behavior and thus minimize the infinite‐horizon quadratic cost. To assess the performance of the proposed solutions, simulation results are presented for the problem of distributed control of a quadruple‐tank process, as well as a version of that problem scaled up to 40 interconnected tanks.