Optimal control of the dynamics of nonlinear oscillating systems using synergetic principles of self-organization

Abstract

This paper analyses the evolution of nonlinear oscillation control methods and presents an innovative approach known as analytical design of aggregated oscillation controllers (ADACO). This method is based on the principles of synergetic control theory and focuses on the integration of self-organization and control processes to synthesize energy-efficient control laws for nonlinear oscillating systems. The authors elaborate on the theoretical foundations of ADACO, which extends the previous analytical design of aggregated controllers (ADAC) method by incorporating energy invariants and integrals of motion into the synthesis of control laws. This approach demonstrates significant advantages over traditional methods, offering a versatile framework for the design of energy-efficient control systems for a wide range of nonlinear oscillating systems in various fields such as aerospace, robotics, vibromechanical systems, and objects with chaotic dynamics. The aim of the paper is to establish a unified approach to the control of nonlinear oscillations, solving both the problems of generation of stable oscillations and suppression of unwanted perturbations. The application of synergetic control principles in the framework of ADACO opens prospects for further development of nonlinear control theory.