Decentralized control and state estimation of linear time-periodic systems |
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Authors: | Ivan Andrushka Pedro Batista Paulo Oliveira Carlos Silvestre |
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Affiliation: | 1. Institute for Systems and Robotics, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal;2. IDMEC-Institute of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal;3. Department of Electrical and Computer Engineering, University of Macau, Taipa, Macau |
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Abstract: | The 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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Keywords: | decentralized control decentralized estimation linear time-periodic sparse gains time-lifting |
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