Nonlinear -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 control problem to exist are given in terms of the appropriate solvability of Hamilton-Jacobi-Isaacs partial d...

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Bibliographic Details
Published in:International journal of control 2016-12, Vol.89 (12), p.2549-2571
Main Authors: Montano, O. E., Orlov, Y., Aoustin, Y.
Format: Article
Language:English
Subjects:
Collision avoidance
disturbance attenuation
Disturbances
Feedback
Mechanical systems
Nonlinearity
orbital stabilisation
Pendulums
Robust control
Synthesis
unilateral constraints
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Summary: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 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 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.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2016.1171400