Journal ArticleDOI
Tracking Control for Hybrid Systems With State-Triggered Jumps
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TLDR
A novel definition of the tracking error is proposed that overcomes this problem and Lyapunov-based conditions for the global asymptotic stability of the hybrid reference trajectory are formulated.Abstract:
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.read more
Citations
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System identification in communication with chaotic systems
TL;DR: In this paper, the authors considered communication using chaotic systems from a control point of view and showed that parameter identification methods may be effective in building reconstruction mechanisms, even when a synchronizing system is not available.
Journal ArticleDOI
Hybrid Output Regulation for Linear Systems With Periodic Jumps: Solvability Conditions, Structural Implications and Semi-Classical Solutions
TL;DR: Two semi-classical solutions to the hybrid output regulation problem are introduced and discussed, characterized by the property that the required steady-state input can be generated as a simple linear function of the state of the exosystem (as in the non-hybrid case), although the associated steady- state response has a genuinely hybrid structure.
Journal ArticleDOI
Phase reduction theory for hybrid nonlinear oscillators
TL;DR: A general phase reduction theory for weakly perturbed limit cycles in hybrid dynamical systems that facilitates analysis, control, and optimization of nonlinear oscillators whose smooth models are unavailable or intractable is developed.
Proceedings ArticleDOI
Necessary and sufficient conditions for output regulation in a class of hybrid linear systems
TL;DR: In this paper, the problem of output regulation for a class of hybrid linear systems is considered and necessary and sufficient conditions for its solution are provided, both in the full information and error feedback case, under the additional constraint that the regulator is a hybrid linear time invariant system from the same class.
Journal ArticleDOI
Structural Properties of a Class of Linear Hybrid Systems and Output Feedback Stabilization
Corrado Possieri,Andrew R. Teel +1 more
TL;DR: This paper characterizes the structural properties of a class of linear hybrid systems and establishes duality between control and observation structural properties, necessary and sufficient conditions for the existence of a linear time-invariant output feedback compensator are stated.
References
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