Synthesis of an adaptive control system for unstable and deterministic chaotic processes with m-inputs and n-outputs

Abstract

The paper proposes a method for solving the problem of synthesis of an adaptive control system for unstable and deterministic chaotic processes in the class of ‘dovetail’ catastrophes for objects with m-inputs and n-outputs. The synthesis problem is solved by the gradient-velocity method of Lyapunov vector functions. From the conditions of the aperiodic robust stability of the etalon model with the desired dynamics of the main control loop and the generalised configurable object, the control goal is achieved. One of the most promising ways of solving the problem of managing unstable and deterministic chaotic processes is the synthesis of a control system in the class of ‘swallowtail’ catastrophes and the use of adaptation methods. Selecting and studying a reference model, and employing the gradient-velocity method for a generalised configurable control object ensure robust stability, utilise current information effectively, and achieve desired system quality and management goals.

KEYWORDS:

• Chaos
• model
• adaptive control
• ‘swallowtail’
• vector

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Mamyrbek Beisenbi

Mamyrbek Beisenbi is a Professor at the Department of System Analysis and Control, L.N. Gumilyov Eurasian National University, Astana, Republic of Kazakhstan. The field of research interest is studying methods for detecting, isolating, and accommodating faults in control systems to maintain system performance and reliability in the presence of faults or failures.

Andas Adilbayev

Andas Adilbayev is a Senior Lecturer at the Faculty of Information Technology, M.Kh. Dulaty Taraz Regional University, Taraz, Republic of Kazakhstan. His scientific interests are exploring techniques for controlling nonlinear systems, which may exhibit complex and nonlinear dynamics and developing control strategies that can handle nonlinearities effectively.

Gulzhan Uskenbayeva

Gulzhan Uskenbayeva is a PhD, Head of the Department at the Faculty of Information Technology, L.N. Gumilyov Eurasian National University, Astana, Republic of Kazakhstan. Her research interest is designing adaptive control systems that can adjust their parameters in real-time to handle uncertainties and changing operating conditions.

Saule Akmetova

Saule Akmetova is a Senior Lecturer at the Faculty of Energy, S. Seifullin Kazakh Agrotechnical University, Astana, Republic of Kazakhstan. Her scientific interests are intelligent control, networked control systems, control of autonomous systems, and optimization-based control.