State Feedback Optimal L2-Induced Control of Nonlinear Systems Utilizing Universal Approximation

The paper presents an optimal L2-induced control problem for systems with multiple sector bounded nonlinearities. Sufficient boundedness conditions of the L2-induced norm are derived in terms of a specific system of linear matrix inequalities. Then, based on these conditions, an optimal state feedback control problem is formulated and solved for the considered class of nonlinear systems. A procedure to reduce the conservatism of the derived conditions is also proposed. Further, it is shown that using the universal approximation theorem, the treated optimal control problem can be used for systems with more general types of nonlinearities. These developments are illustrated by a numerical example consisting in the state feedback optimal L2-induced control of a forced Van der Pol oscillator.