On the existence of executions of hybrid automata

Lygeros, John; Johansson, Karl Henrik; Sastry, S. Shankar; Egerstedt, Magnus

doi:10.1109/cdc.1999.831255

Cited by 68 publications

(74 citation statements)

References 9 publications

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“…To capture the intermediate states, we use the following definition of hybrid time domain [12], [13], which is based on work of [14]: Definition 2.2 (Hybrid trajectory): Let (t n ) n<∞ be an increasing sequence in R + ∪{∞} with t 0 = 0. Then the t n define a hybrid time domain T ⊂ R + × Z + by…”

Section: Hybrid Systemsmentioning

confidence: 99%

Controllability and falsification of hybrid systems

Collins

2009

2009 European Control Conference (ECC)

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Abstract-In this paper we consider the controllability problem for hybrid systems, namely that of determining the set of states which can be driven into a given target set. We show that given a suitable definition of controllability, we can effectively compute arbitrarily accurate under-approximations to the controllable set using Turing machines. However, due to grazing or sliding along guard sets, we see that it may be able to demonstrate that an initial state can be controlled to the target set, without knowing any trajectory which solves the problem.

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Section: Hybrid Systemsmentioning

confidence: 99%

Controllability and falsification of hybrid systems

Collins

2009

2009 European Control Conference (ECC)

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“…For complementarity systems one may develop several solution concepts, which may be similar to the notion of an execution for hybrid automata Lygeros et al, 1999), or to the solution concept for differential inclusions as used for differential equations with discontinuous right-hand sides (Filippov, 1988). A solution concept of the first type can for instance be formulated as follows.…”

Section: Solution Conceptsmentioning

confidence: 99%

Well-Posedness of the Complementarity Class of Hybrid Systems

Heemels

Camlibel

Schaft

et al. 2002

IFAC Proceedings Volumes

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One of the most fundamental properties of any class of dynamical systems is the study of well-posedness, i.e. the existence and uniqueness of a particular type of solution trajectories given an initial state. In case of interaction between continuous dynamics and discrete transitions this issue becomes highly non-trivial. In this survey an overview is given of the well-posedness results for complementarity systems, which form a class of hybrid systems described by the interconnection of differential equations and a specific combination of inequalities and Boolean expressions as appearing in the linear complementarity problem of mathematical programming.

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“…Hence, an infinite loop occurs with τ i = τ i for all i ≥ i 0 for some i 0 in the definition of an execution of the hybrid automaton (livelock). In (Lygeros et al, 1999), it is stated that for an initially well-posedness hybrid automaton "it still remains to be investigated whether executions can be extended over arbitrary time horizons." A first step to a stronger notion is obtained by requiring that a solution exists on some interval [0, ε) with ε > 0; system descriptions for which such solutions exist and are unique are called locally wellposed.…”

Section: Well-posednessmentioning

confidence: 99%