Control of oscillations by control of invariants in quasi-polynomial nonlinear systems

An approach to control of invariant sets of quasi-polynomial nonlinear systems in the presence and absence of bounded uncertainty (disturbances) in the model is proposed. The control strategy is based on introduction of an invariant functional for uncontrolled system and posing the control task as achieving the desired value of the invariant functional by means of control. The design is based on the reduction to the multispecies Lotka–Volterra system and employing the speed-gradient control method. Simulation results demonstrate reasonable control accuracy and the presence of the resonance-like behavior of the controlled system under disturbances.