Algorithms for Synthesis of Adaptive Decentralized Control of Interconnected Systems by The Speed Gradient Method

Sevinov Jasur Usmonovich; Boborayimov Okhunjon Khushmurod ogli

Sevinov Jasur Usmonovich Tashkent State Technical University, Tashkent, Uzbekistan
Boborayimov Okhunjon Khushmurod ogli Tashkent State Technical University, Tashkent, Uzbekistan Address: Universitetskaya-2, 100095 Tashkent City, Republic of Uzbekistan

Keywords: adaptive decentralized control, interconnected systems, speed gradient algorithm, control object, objective function, control action

Abstract

Synthesizing algorithms of decentralized adaptive control for a class of interconnected systems with nonlinear local dynamics and uncertainty are considered, ensuring the stability of isolated subsystems of the entire system, taking into account interactions. When connected to a stable isolated subsystem, the system's stability may be violated and the objective function will cease to be a Lyapunov function for a system with connections. Very strong connections can significantly change the dynamics of the system, and the behavior of subsystems in an isolated state will be radically different from the behavior in a coupled system. Therefore, the law of control of a complex system, which ensures only the stability of isolated subsystems, cannot guarantee the stability of the entire system considering interactions. At the same time, to solve the problem of taking into account the interactions of subsystems, an adaptation algorithm based on the speed gradient method was introduced into the general control law. The results of the numerical analysis confirmed their effectiveness, which allows them to be used in solving applied problems of synthesizing systems for decentralized adaptive control of technological objects.

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