Nonlinear H∞-control under unilateral constraints

The primary concern of the work is robust control of hybrid mechanical systems under unilateral constraints of co-dimension one. Sufficient conditions for a local solution of the underlying H-infinity control problem to exist are given in terms of the appropriate solvability of Hamilton-Jacobi-Isaacs partial differential inequalities, coupled to an extra condition on the plant reset in the closed loop. Nonlinear H-infinity output feedback synthesis is thus developed in the hybrid setting, covering collision phenomena. Robustness issues of the proposed synthesis are numerically investigated in a benchmark application where the regulation and orbital stabilisation of a simple pendulum, impacting a barrier, illustrate the capability of the proposed approach via position feedback design. Good performance is achieved despite imperfectmeasurements and the presence of both external disturbances, affecting the collision-free motion phase, and uncertainties that occur in the collision phase.