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A classification of symbolic transition systems
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2005
"... We define five increasingly comprehensive classes of infinitestate systems, called STS1STS5, whose state spaces have finitary structure. For four of these classes, we provide examples from hybrid systems.STS1 These are the systems with finite bisimilarity quotients. They can be analyzed symbolica ..."
Abstract

Cited by 44 (5 self)
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We define five increasingly comprehensive classes of infinitestate systems, called STS1STS5, whose state spaces have finitary structure. For four of these classes, we provide examples from hybrid systems.STS1 These are the systems with finite bisimilarity quotients. They can be analyzed symbolically by iteratively applying predecessor and Boolean operations on state sets, starting from a finite number of observable state sets. Any such iteration is guaranteed to terminate in that only a finite number of state sets can be generated. This enables model checking of the μcalculus.STS2 These are the systems with finite similarity quotients. They can be analyzed symbolically by iterating the predecessor and positive Boolean operations. This enables model checking of the existential and universal fragments of the μcalculus.STS3 These are the systems with finite traceequivalence quotients. They can be analyzed symbolically by iterating the predecessor operation and a restricted form of positive Boolean operations (intersection is restricted to intersection with observables). This enables model checking of all ωregular properties, including linear temporal logic.STS4 These are the systems with finite distanceequivalence quotients (two states are equivalent if for every distance d, the same observables can be reached in d transitions). The systems in this class can be analyzed symbolically by iterating the predecessor operation and terminating when no new state sets are generated. This enables model checking of the existential conjunctionfree and universal disjunctionfree fragments of the μcalculus.STS5 These are the systems with finite boundedreachability quotients (two states are equivalent if for every distance d, the same observables can be reached in d or fewer transitions). The systems in this class can be analyzed symbolically by iterating the predecessor operation and terminating when no new states are encountered (this is a weaker termination condition than above). This enables model checking of reachability properties.
Linear time logic control of discretetime linear systems
 IEEE Transactions on Automatic Control
, 2006
"... Abstract. The control of complex systems poses new challenges that fall beyond the traditional methods of control theory. One of these challenges is given by the need to control, coordinate and synchronize the operation of several interacting submodules within a system. The desired objectives are no ..."
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Cited by 21 (3 self)
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Abstract. The control of complex systems poses new challenges that fall beyond the traditional methods of control theory. One of these challenges is given by the need to control, coordinate and synchronize the operation of several interacting submodules within a system. The desired objectives are no longer captured by usual control specifications such as stabilization or output regulation. Instead, we consider specifications given by Linear Temporal Logic (LTL) formulas. We show that existence of controllers for discretetime controllable linear systems and LTL specifications can be decided and that such controllers can be effectively computed. The closedloop system is of hybrid nature, combining the original continuous dynamics with the automatically synthesized switching logic required to enforce the specification. 1.
Model checking LTL over controllable linear systems is decidable
 of Lecture Notes in Computer Science
, 2003
"... Abstract. The use of algorithmic verification and synthesis tools for hybrid systems is currently limited to systems exhibiting simple continuous dynamics such as timed automata or rectangular hybrid systems. In this paper we enlarge the class of systems amenable to algorithmic analysis and synthesi ..."
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Cited by 18 (1 self)
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Abstract. The use of algorithmic verification and synthesis tools for hybrid systems is currently limited to systems exhibiting simple continuous dynamics such as timed automata or rectangular hybrid systems. In this paper we enlarge the class of systems amenable to algorithmic analysis and synthesis by showing decidability of model checking Linear Temporal Logic (LTL) formulas over discrete time, controllable, linear systems. This result follows from the construction of a language equivalent, finite abstraction of a control system based on a set of finite observations which correspond to the atomic propositions appearing in a given LTL formula. Furthermore, the size of this abstraction is shown to be polynomial in the dimension of the control system and the number of observations. These results open the doors for verification and synthesis of continuous and hybrid control systems from LTL specifications. 1
Symbolic Control of Linear Systems Based on Symbolic Subsystems
, 2006
"... This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of ..."
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Cited by 4 (2 self)
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This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem into controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification.
Relaxing Goodness is Still Good
"... Abstract. Polygonal hybrid systems (SPDIs) are planar hybrid systems, whose dynamics are defined in terms of constant differential inclusions, one for each of a number of polygonal regions partitioning the plane. The reachability problem for SPDIs is known to be decidable, but depends on the goodnes ..."
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Cited by 3 (3 self)
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Abstract. Polygonal hybrid systems (SPDIs) are planar hybrid systems, whose dynamics are defined in terms of constant differential inclusions, one for each of a number of polygonal regions partitioning the plane. The reachability problem for SPDIs is known to be decidable, but depends on the goodness assumption — which states that the dynamics do not allow a trajectory to both enter and leave a region through the same edge. In this paper we extend the decidability result to generalised SPDIs (GSPDI), SPDIs not satisfying the goodness property, and give an algorithmic solution to decide reachability of such systems. 1
Symbolic models for control systems
, 2007
"... In this paper we provide a bridge between the infinite state models used in control theory to describe the evolution of continuous physical processes and the finite state models used in computer science to describe software. We identify classes of control systems for which it is possible to constru ..."
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Cited by 3 (2 self)
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In this paper we provide a bridge between the infinite state models used in control theory to describe the evolution of continuous physical processes and the finite state models used in computer science to describe software. We identify classes of control systems for which it is possible to construct equivalent (bisimilar) finite state models. These constructions are based on finite, but otherwise arbitrary, partitions of the set of inputs or outputs of a control system.
Verifying Average Dwell Time of Hybrid Systems
"... Average dwell time (ADT) properties characterize the rate at which a hybrid system performs mode switches. In this paper, we present a set of techniques for verifying ADT properties. The stability of a hybrid system A can be verified by combining these techniques with standard methods for checking s ..."
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Cited by 2 (0 self)
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Average dwell time (ADT) properties characterize the rate at which a hybrid system performs mode switches. In this paper, we present a set of techniques for verifying ADT properties. The stability of a hybrid system A can be verified by combining these techniques with standard methods for checking stability of the individual modes of A. We introduce a new type of simulation relation for hybrid automata—switching simulation— for establishing that a given automaton A switches more rapidly than another automaton B. We show that the question of whether a given hybrid automaton has ADT τa can be answered either by checking an invariant or by solving an optimization problem. For classes of hybrid automata for which invariants can be checked automatically, the invariantbased method yields an automatic method for verifying ADT; for automata that are outside this class, the invariant has to be checked using inductive techniques. The optimizationbased method is automatic and is applicable to a restricted class of initialized hybrid automata. A solution of the optimization problem either gives a counterexample execution that violates the ADT property, or it confirms that the automaton indeed satisfies the property. The optimization and the invariantbased methods can be used in combination to find the unknown ADT of a given hybrid automaton.
A Sense of Life
"... We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure, and computational environment for understanding, experimenting with, manipulating, and modifying a diverse set of fundamental biological processes at multiple scales and spatiotemporal modes. T ..."
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We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure, and computational environment for understanding, experimenting with, manipulating, and modifying a diverse set of fundamental biological processes at multiple scales and spatiotemporal modes. The novelty of our research is based on an approach that (i) requires coevolu # The work reported in this paper was supported by grants from NSF's Qubic program, DARPA, HHMI biomedical support research grant, the US Department of Energy, the US Air Force, National Institutes of Health, and New York State O#ce of Science, Technology & Academic Research.
unknown title
, 2003
"... ABSTRACT We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure and computational environment for understanding, experimenting, manipulating and modifying a diverse set of fundamental biological processes at multiple scales and spatiotemporal modes. ..."
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ABSTRACT We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure and computational environment for understanding, experimenting, manipulating and modifying a diverse set of fundamental biological processes at multiple scales and spatiotemporal modes. The novelty of our research is based on an approach (i) that requires coevolution of experimental science and theoretical techniques and (ii) that exploits certain universality in biology guided by a parsimonious model of evolu
Brief Statement of the Problem:
"... In this thesis, we present a formal framework for modeling and analysis of hybrid systems based on the Hybrid Input/Output Automaton (HIOA) model of Lynch, Segala, and Vaandrager. We add new structure to the HIOA model in order to describe its trajectories using differential and algebraic equations, ..."
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In this thesis, we present a formal framework for modeling and analysis of hybrid systems based on the Hybrid Input/Output Automaton (HIOA) model of Lynch, Segala, and Vaandrager. We add new structure to the HIOA model in order to describe its trajectories using differential and algebraic equations, mode invariants, and stopping conditions. The result is a specialization of the HIOA model, which we call Structured Hybrid I/O Automaton (SHIOA). For modeling probabilistic discrete behavior in hybrid systems we introduce another related model, the Probabilistic Timed I/O Automaton (PTIOA). We define the notions of invariance, stability, and external behavior for these models. For a pair of automata, we formally define what it means for one to be an abstraction of the other, and for the two to be equivalent. We define the composition operation for a pair of automata and prove theorems establishing that abstraction and equivalence relationships are preserved by composition. We present a formal specification language for nonprobabilistic hybrid systems, that is based on the SHIOA model. This language is the basis for the development of a set of software tools, that includes a language front end for checking specifications and a theorem prover interface. For SHIOA and PTIOA, we present methods for proving invariance and stability properties. We also present simulation relation based methods for establishing abstraction and equivalence relationships between