Discrete‐time decentralized linear quadratic control for linear time‐varying systems

• Published in: International journal of robust and nonlinear control Vol. 33; no. 1; pp. 67 - 101
• Main Authors: Pedroso, Leonardo, Batista, Pedro
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.01.2023
• Subjects: Algorithms; Decentralized control; decentralized linear quadratic regulator; decentralized linear quadratic tracker; interconnected systems; Linear quadratic regulator; linear time‐varying systems; System dynamics; Tanks
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5772

This article addresses the problem of designing a decentralized control solution for a network of agents modeled by linear time‐varying (LTV) dynamics, in a discrete‐time framework. A general scheme is proposed, in which the problem is formulated as a classical linear quadratic regulator problem, for the global system, subject to a given sparsity constraint on the gain, which reflects the decentralized nature of the network. A method able to compute a sequence of well‐performing stabilizing regulator gains is presented and validated resorting to simulations of two randomly generated LTV systems, one stable and the other unstable. Moreover, a tracking solution is developed, building on the solution to the regulator problem. Both methods rely on a closed‐form solution, thus they can be computed very rapidly. Similarly to the centralized solution, both the presented methods require that a window of the future system dynamics is known. Both methods are validated resorting to simulations of: (i) a nonlinear network of four interconnected tanks; and (ii) a large‐scale nonlinear network of interconnected tanks. When implemented to a nonlinear network, approximated by an LTV system, the proposed methods are able to compute well‐performing gains that track the desired output. Finally, both algorithms are scalable, being adequate for implementation in large‐scale networks.