Control Systems with Additive Adjustment Based on the Velocity Vector Method
This paper considers the stabilization of a dynamic system with variable uncontrolled perturbations using a controller containing additive adjustment. The variable parameters are perturbations in the form of piecewise continuous functions. The parameters change at arbitrary and unknown times. The adaptive controller and adapter are synthesized using the reference equation method and the velocity vector method, respectively. The closed-loop system has feedback on derivatives of state variables, which leads to different time-scale motions. The stability of the control system is investigated using a common Lyapunov function and the method of separation of motions. The properties of the control system are illustrated by a numerical example.