Nonlinear H∞-control under unilateral constraints

ABSTRACT

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 ${\mathcal{H}}_{\infty }$ 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 ${\mathcal{H}}_{\infty }$ 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 imperfect measurements and the presence of both external disturbances, affecting the collision-free motion phase, and uncertainties that occur in the collision phase.

KEYWORDS:

• Robust control
• unilateral constraints
• mechanical systems
• orbital stabilisation
• disturbance attenuation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by CONACYT [grant number 165958].