Abstract
AbstractThe main contributions of this article are the design of a decentralized controller and state estimator for linear time‐periodic systems with fixed network topologies. The proposed method to tackle both problems consists of reformulating the linear periodic dynamics as a linear time‐invariant system by applying a time‐lifting technique and designing a discrete‐time decentralized controller and state estimator for the time‐lifted formulation. The problem of designing the decentralized estimator is formulated as a discrete‐time Kalman filter subject to sparsity constraints on the gains. Two different algorithms for the computation of steady‐state observer gains are tested and compared. The control problem is posed as a state feedback gain optimization problem over an infinite‐horizon quadratic cost, subject to a sparsity constraint on the gains. An equivalent formulation that consists in the optimization of the steady‐state solution of a matrix difference equation is presented and an algorithm for the computation of the decentralized gain is detailed. Simulation results for the practical cases of the quadruple‐tank process and an extended 40‐tank process are presented that illustrate the performance of the proposed solutions, complemented with numerical simulations using the Monte Carlo method.
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