Control of oscillations of a nonlinear system in the sense of a nonnegative functional
The problem of determining a regulator to generate given oscillatory models in a closed-loop system is considered. One assumes that the control system is described by a nonlinear differential equation and a nonnegative functional is specified on the phase plane of system states. It is required to determine a regulator for a state under consideration such that any solution to a closed-loop system with initial data from a fixed set tends to the zero set of a preset functional. A family of regulators generated by the method of velocity gradient is taken as a set of feedbacks. For this set of generators, one obtains sufficient conditions which globally (locally) guarantee the achievement of the control goal. In the special case where the functional is positive definite, new conditions for global (local) asymptotic stability of the zero state of equilibrium of the nonlinear system are obtained.
scientific article; zbMATH DE number 1557666