Tracking Control for Hybrid Systems With State-Triggered Jumps

This paper addresses the tracking problem in which the controller should stabilize time-varying reference trajectories of hybrid systems. Despite the fact that discrete events (or jumps) in hybrid systems can often not be controlled directly, as, e.g., is the case in impacting mechanical systems, th...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2013-04, Vol.58 (4), p.876-890
Main Authors: Biemond, J. J. Benjamin, van de Wouw, N., Heemels, W. P. M. H., Nijmeijer, H.
Format: Article
Language:English
Subjects:
Asymptotic properties
Asymptotic stability
Bouncing
control system analysis
Control systems
Convergence
Design engineering
Hybrid systems
Mechanical systems
Stability analysis
Studies
Time domain analysis
tracking control
Tracking errors
Tracking problem
Trajectories
Trajectory
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Summary:This paper addresses the tracking problem in which the controller should stabilize time-varying reference trajectories of hybrid systems. Despite the fact that discrete events (or jumps) in hybrid systems can often not be controlled directly, as, e.g., is the case in impacting mechanical systems, the controller should still stabilize the desired trajectory. A major complication in the analysis of this hybrid tracking problem is that, in general, the jump times of the plant do not coincide with those of the reference trajectory. Consequently, the conventional Euclidean tracking error does not converge to zero, even if trajectories converge to the reference trajectory in between jumps, and the jump times converge to those of the reference trajectory. Hence, standard control approaches can not be applied. We propose a novel definition of the tracking error that overcomes this problem and formulate Lyapunov-based conditions for the global asymptotic stability of the hybrid reference trajectory. Using these conditions, we design hysteresis-based controllers that solve the hybrid tracking problem for two exemplary systems, including the well-known bouncing ball problem.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2012.2223351