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DiscreteTime Control for Rectangular Hybrid Automata
"... Rectangular hybrid automata model digital control programs of analog plant environments. We study rectangular hybrid automata where the plant state evolves continuously in realnumbered time, and the controller samples the plant state and changes the control state discretely, only at the integer poi ..."
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Cited by 79 (9 self)
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Rectangular hybrid automata model digital control programs of analog plant environments. We study rectangular hybrid automata where the plant state evolves continuously in realnumbered time, and the controller samples the plant state and changes the control state discretely, only at the integer points in time. We prove that rectangular hybrid automata have nite bisimilarity quotients when all control transitions happen at integer times, even if the constraints on the derivatives of the variables vary between control states. This is in contrast with the conventional model where control transitions may happen at any real time, and already the reachability problem is undecidable. Based on the nite bisimilarity quotients, we give an exponential algorithm for the symbolic samplingcontroller synthesis of rectangular automata. We show our algorithm to be optimal by proving the problem to be EXPTIMEhard. We also show that rectangular automata form a maximal class of systems for which the samplingcontroller synthesis problem can be solved algorithmically.
Verification of hybrid systems with linear differential inclusions using ellipsoidal approximations
 In Hybrid Systems : Computation and Control
, 2000
"... Abstract. A general verification algorithm is described. It is then shown how ellipsoidal methods developed by A. B. Kurzhanski and P. Varaiya can be adapted to the algorithm. New numerical algorithms that compute approximations of unions of ellipsoids and intersections of ellipsoids and polyhedra ..."
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Cited by 73 (1 self)
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Abstract. A general verification algorithm is described. It is then shown how ellipsoidal methods developed by A. B. Kurzhanski and P. Varaiya can be adapted to the algorithm. New numerical algorithms that compute approximations of unions of ellipsoids and intersections of ellipsoids and polyhedra were developed. The presented techniques were implemented in the verification tool called VeriSHIFT and some practical results are discussed.
Computational techniques for the verification 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 that involve the interaction of both discrete state systems, represented by finite automata, and continuous sta ..."
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Cited by 72 (9 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 that 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. To understand the behavior of hybrid systems, to simulate, and to control these systems, theoretical advances, analyses, and numerical tools are needed. In this paper, we first present a general model for a hybrid system along with an overview of methods for verifying continuous and hybrid systems. We describe a particular verification
TReX: A Tool for Reachability Analysis of Complex Systems
, 2001
"... Introduction Finitestate modelcheckers such as Smv [13] and Spin [11] do not allow to deal with important aspects that appear in modelling and analysing complex systems, e.g., communication protocols. Among these aspects: realtime constraints, manipulation of unbounded data structures like count ..."
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Cited by 69 (3 self)
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Introduction Finitestate modelcheckers such as Smv [13] and Spin [11] do not allow to deal with important aspects that appear in modelling and analysing complex systems, e.g., communication protocols. Among these aspects: realtime constraints, manipulation of unbounded data structures like counters, communication through unbounded channels, parametric reasoning, etc. The tool we propose, called TReX, allows to analyse automatically automatabased models equipped with variables of different kinds of infinite domain data structures and with parameters (i.e., uninstantiated constants). These models are, at the present time, parametric (continuoustime) timed automata, extended with integer counters and communicating through unbounded lossy FIFO queues. The techniques used in TReX are based on symbolic reachability analysis. Symbolic representation structures are u
Beyond HYTECH: Hybrid systems analysis using interval numerical methods
 in HSCC
, 2000
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The d/dt Tool for Verification of Hybrid System
, 2002
"... In this paper we describe the tool d/dt which provides automatic safety verification of hybrid systems with linear continuous dynamics with uncertain input. The verification procedure is based on a method for overapproximating reachable sets by orthogonal polyhedra. The tool also
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Cited by 64 (8 self)
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In this paper we describe the tool d/dt which provides automatic safety verification of hybrid systems with linear continuous dynamics with uncertain input. The verification procedure is based on a method for overapproximating reachable sets by orthogonal polyhedra. The tool also
Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Deltanotch protein signalling
 Systems Biology
, 2004
"... Hybrid automata are an eminently suitable modelling framework for biological protein regulatory networks, as the protein concentration dynamics inside each biological cell are modelled using linear differential equations; inputs activate or deactivate these continuous dynamics through discrete switc ..."
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Cited by 64 (3 self)
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Hybrid automata are an eminently suitable modelling framework for biological protein regulatory networks, as the protein concentration dynamics inside each biological cell are modelled using linear differential equations; inputs activate or deactivate these continuous dynamics through discrete switches, which themselves are controlled by protein concentrations reaching given thresholds. This paper proposes an iterative refinement algorithm for computing discrete abstractions of a class of hybrid automata with piecewise affine continuous dynamics and forced discrete transitions, defined completely in terms of symbolic variables and parameters. Furthermore, these discrete abstractions are utilized to compute symbolic parametric backward reachable sets from the equilibria of the hybrid automata, that are guaranteed to be exact or conservative underapproximations. The algorithm is then implemented using MATLAB and QEPCAD, to compute reachable sets for the biologically observed equilibria of multiple cell DeltaNotch protein signalling automaton with symbolic parameters. The results are analysed to show that novel, nonintuitive, and biologically interesting properties can be deduced from the reachability computation, thus demonstrating the utility of the algorithm. 1
Relative Completeness of Abstraction Refinement for Software Model Checking
, 2002
"... Automated methods for an undecidable class of verification problems cannot be complete (terminate for every correct program). We therefore consider a new kind of quality measure for such methods, which is completeness relative to a (powerful but unrealistic) oraclebased method. More precisely, we a ..."
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Cited by 63 (4 self)
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Automated methods for an undecidable class of verification problems cannot be complete (terminate for every correct program). We therefore consider a new kind of quality measure for such methods, which is completeness relative to a (powerful but unrealistic) oraclebased method. More precisely, we ask whether an often implemented method known as "software model checking with abstraction refinement" is complete relative to fixpoint iteration with "oracleguided" widening. We show that whenever backward fixpoint iteration with oracleguided widening succeeds in proving a property' (for some sequence of widenings determined by the oracle) then software model checking with a particular form of backward refinement will succeed in proving'. Intuitively, this means that the use of fixpoint iteration over abstractions and a particular backwards refinement of the abstractions has the effect of exploring the entire state space of all possible sequences of widenings.
Automotive engine control and hybrid systems: challenges and opportunities
 PROCEEDINGS OF THE IEEE
, 2000
"... The design of engine control systems has been traditionally carried out using a mix of heuristic techniques validated by simulation and prototyping using approximate averagevalue models. However, the ever increasing demands on passengers ’ comfort, safety, emissions, and fuel consumption imposed by ..."
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Cited by 60 (16 self)
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The design of engine control systems has been traditionally carried out using a mix of heuristic techniques validated by simulation and prototyping using approximate averagevalue models. However, the ever increasing demands on passengers ’ comfort, safety, emissions, and fuel consumption imposed by car manufacturers and regulations call for more robust techniques and the use of cycleaccurate models. We argue that these models must be hybrid because of the combination of timedomain and eventbased behaviors. In this paper, we present a hybrid model of the engine in which both continuous and discrete timedomain as well as eventbased phenomena are modeled in a separate but integrated manner. Based on this model, we formalize the specification of the overall engine control by defining a number of hybrid control problems. To cope with the difficulties arising in the design of hybrid controllers, a design methodology is proposed. This methodology consists of a relaxation
The Theory of Timed I/O Automata
, 2003
"... This paper presents the Timed Input/Output Automaton (TIOA) modeling framework, a basic mathematical framework to support description and analysis of timed systems. An important feature of this model is its support for decomposing timed system descriptions. In particular, the framework includes a no ..."
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Cited by 60 (18 self)
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This paper presents the Timed Input/Output Automaton (TIOA) modeling framework, a basic mathematical framework to support description and analysis of timed systems. An important feature of this model is its support for decomposing timed system descriptions. In particular, the framework includes a notion of external behavior for a timed I/O automaton, which captures its discrete interactions with its environment. The framework also denes what it means for one TIOA to implement another, based on an inclusion relationship between their external behavior sets, and de nes notions of simulations, which provide sucient conditions for demonstrating implementation relationships. The framework includes a composition operation for TIOAs, which respects external behavior, and a notion of receptiveness, which implies that a TIOA does not block the passage of time. The TIOA framework supports the statement and verication of safety and liveness properties for timed systems. It denes what it means for a property to be a safety or a liveness property, includes basic results about safetyliveness classication, and