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Feedback controller design for nonlinear systems using vector Lyapunov functions and a distributed metaheuristic algorithm
Sergey Ul'yanov, Anton Tolstikhin

Last modified: 2023-06-29


The paper presents a methodology for designing control parameters of nonlinear multicomponent systems using distributed computing and metaheuristic optimization algorithms. The design problem consists of finding feedback gains or other unknown parameters of the system that ensure its optimal or desired quality. The methodology allows the user to formulate the design problem as a multi-objective optimization problem or a single-objective constrained optimization problem with estimates of main dynamic quality indicators (stabilization error, stability region, settling time, etc.) as optimization criteria and constraints. The estimates are computed using specialized algorithms based on sublinear vector Lyapunov functions. To solve the optimization problem, we propose a distributed metaheuristic algorithm that incorporates mechanisms for dividing the area of acceptable values of synthesized parameters into subdomains, their examination, and further refinement of the solutions found. Special procedures that weaken the requirements for the designed controller are applied to accelerate obtaining an initial feasible solution. If it is not possible to obtain a feasible solution, options for changing the requirements for the controller are offered. The efficiency and applicability of the proposed methodology are demonstrated by designing a distributed controller for the multi-robot system.