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41
Hybrid systems: Generalized solutions and robust stability
 In IFAC Symposium on Nonliear Control Systems
, 2004
"... Abstract: Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efficient description of the convergence of a sequence of solutions. Graph convergence is used ..."
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Cited by 30 (6 self)
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Abstract: Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efficient description of the convergence of a sequence of solutions. Graph convergence is used. Then a generalized solution definition is given that leads to continuity with respect to initial conditions and perturbations of the system data. This property enables new results on necessary conditions for asymptotic stability in hybrid systems.
Computational Techniques for the Verification and Control of Hybrid Systems
 PROCEEDINGS OF THE IEEE
, 2003
"... Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems which involve the interaction of both discrete state systems, represented by finite automata, and continuous ..."
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Cited by 25 (0 self)
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Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems which involve the interaction of both discrete state systems, represented by finite automata, and continuous state dynamics, represented by differential equations. The embedded autopilot of a modern commercial jet is a prime example of a hybrid system: the autopilot modes correspond to the application of different control laws, and the logic of mode switching is determined by the continuous state dynamics of the aircraft, as well as through interaction with the pilot. Embedded
Results on inputtostate stability for hybrid systems
, 2005
"... We show that, like continuoustime systems, zeroinput locally asymptotically stable hybrid systems are locally inputtostatestable (LISS). We demonstrate by examples that, unlike continuoustime systems, zeroinput locally exponentially stable hybrid systems may not be LISS with linear gain, inpu ..."
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Cited by 19 (2 self)
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We show that, like continuoustime systems, zeroinput locally asymptotically stable hybrid systems are locally inputtostatestable (LISS). We demonstrate by examples that, unlike continuoustime systems, zeroinput locally exponentially stable hybrid systems may not be LISS with linear gain, inputtostate stable (ISS) hybrid systems may not admit any ISS Lyapunov function, and nonuniform ISS hybrid systems may not be (uniformly) ISS. We then provide a strengthened ISS condition as an equivalence to the existence of an ISS Lyapunov function for hybrid systems. This strengthened condition reduces to standard ISS for continuoustime and discretetime systems. Finally under some other assumptions we establish the equivalence among ISS, several asymptotic characterizations of ISS, and the existence of an ISS Lyapunov function for hybrid systems.
Lecture notes on hybrid systems
, 2004
"... The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be hi ..."
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Cited by 16 (0 self)
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The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be highlighted. We will introduce general methods for investigating properties such as existence of solutions, reachability and decidability of hybrid systems. The methods will be demonstrated on the motivating applications. Students who successfully complete the course should be able to appreciate the diversity of phenomena that arise in hybrid systems and how discrete “discrete ” entities and concepts such as automata, decidability and bisimulation can coexist with continuous entities and
Nondeterministic temporal logics for general Flow systems
, 2004
"... In this paper, we use the constructs of branching temporal logic to formalize reasoning about a class of general flow systems, including discretetime transition systems, continuoustime differential inclusions, and hybridtime systems such as hybrid automata. We introduce Full General Flow Logic, ..."
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Cited by 13 (5 self)
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In this paper, we use the constructs of branching temporal logic to formalize reasoning about a class of general flow systems, including discretetime transition systems, continuoustime differential inclusions, and hybridtime systems such as hybrid automata. We introduce Full General Flow Logic, GFL which has essentially the same syntax as the wellknown Full Computation Tree Logic, CTL , but generalizes the semantics to general flow systems over arbitrary timelines. We propose an axiomatic proof system for GFL and establish its soundness w.r.t. the general flow semantics.
Guaranteed Overapproximations of Unsafe Sets for Continuous and Hybrid Systems: Solving the HamiltonJacobi Equation Using Viability Techniques
 IN HYBRID SYSTEMS: COMPUTATION AND CONTROL
, 2002
"... We show how reachable sets of constrained continuous and simple hybrid systems may be computed using the minimum timetoreach function.e pre5N t an algorithm for computing a discre e approximation to the minimum timetore ach function, which we prove to be a conve rgingunde rapproximation to the a ..."
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Cited by 13 (2 self)
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We show how reachable sets of constrained continuous and simple hybrid systems may be computed using the minimum timetoreach function.e pre5N t an algorithm for computing a discre e approximation to the minimum timetore ach function, which we prove to be a conve rgingunde rapproximation to the actual function.e use the discre4 minimum time69re ch function for simple hybrid syste5 to compute ove rapproximations of unsafe zon for aircraft in ase3 or of the Oakland Air Tra#c Control Cete( le ading to the automatic ge516 ation of conflictfree aircraft maneuvers.
Equivalence of Dynamical Systems by Bisimulation
, 2004
"... A general notion of bisimulation is defined for linear inputstateoutput systems, using analogies with the theory of concurrent processes. A characterization of bisimulation and an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation is s ..."
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Cited by 7 (2 self)
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A general notion of bisimulation is defined for linear inputstateoutput systems, using analogies with the theory of concurrent processes. A characterization of bisimulation and an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation is shown to be a notion which unifies the concepts of state–space equivalence and state–space reduction, and which allows to study equivalence of systems with nonminimal state–space dimension. The notion of bisimulation is especially powerful for “nondeterministic ” dynamical systems, and leads in this case to a notion of equivalence which is finer than equality of external behavior. For abstractions of systems it is shown how the results specialize to previously obtained results by other authors. Extensions of the main results to the nonlinear case are provided.
On simulations and bisimulations of general flow systems ⋆
"... Abstract. We introduce a notion of bisimulation equivalence between general flow systems, which include discrete, continuous and hybrid systems, and compare it with similar notions in the literature. The interest in the proposed notion is based on our main result, that the temporal logic GFL ⋆ – an ..."
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Cited by 5 (2 self)
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Abstract. We introduce a notion of bisimulation equivalence between general flow systems, which include discrete, continuous and hybrid systems, and compare it with similar notions in the literature. The interest in the proposed notion is based on our main result, that the temporal logic GFL ⋆ – an extension to general flows of the wellknown computation tree logic CTL ⋆ – is semantically preserved by this equivalence. 1
Robust ReachAvoid Controller Synthesis for Switched Nonlinear Systems
"... Abstract — In this paper, we describe a method to automatically synthesize controllers that provide hard guarantees of safety and target reachability for sampleddata switched systems under bounded continuous disturbances. Techniques from hybrid system verification are used to perform continuous tim ..."
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Cited by 4 (2 self)
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Abstract — In this paper, we describe a method to automatically synthesize controllers that provide hard guarantees of safety and target reachability for sampleddata switched systems under bounded continuous disturbances. Techniques from hybrid system verification are used to perform continuous time differential game calculations on each sampling interval. Iterative procedures are given for computing the set of states for which there exists an admissible control policy so that the closedloop system satisfies the properties of safety and reachability over a finite time horizon. From this computation, we show how to obtain an explicit state feedback policy in the form of multiple reachable sets, and an algorithm is given for using this feedback law in closedloop control of the switched system. A simulation example of automated aerial refueling is used to illustrate the application of our approach. I.