Inverse optimal design of input-to-state stabilizing homogeneous controllers for nonlinear homogeneous systems

This work studies the inverse optimality of input-to-state stabilizing controllers with input-output stability guarantees for nonlinear homogeneous systems. We formulate a new inverse optimal control problem, where the cost functional incorporates penalties on the output, in addition to the state, control and disturbance as in current related works. One benefit of penalizing the output is that the resulting inverse optimal controllers can ensure both input-to-state stability and input-output stability. We propose a technique for constructing the corresponding meaningful cost functional by using homogeneity properties, and provide sufficient conditions on solving the inverse optimal gain assignment problem. We show that homogeneous stabilizability of homogeneous systems in the case without disturbance is sufficient for the solvability of inverse optimal gain assignment problem for homogeneous systems.