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Verification of hybrid systems: Formalization and proof rules in PVS
 in PVS. In: ICECCS, IEEE Computer Society
, 2001
"... Combining discrete statemachines with continuous behavior, hybrid systems are a wellestablished mathematical model for discrete systems acting in a continuous environment. As a priori infinite state systems, their computational properties are undecidable in the general model and the main line of r ..."
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Combining discrete statemachines with continuous behavior, hybrid systems are a wellestablished mathematical model for discrete systems acting in a continuous environment. As a priori infinite state systems, their computational properties are undecidable in the general model and the main line of research concentrates on model checking of finite abstractions of restricted subclasses of the general model. In our work, we use deductive methods, falling back upon the generalpurpose theorem prover PVS. To do so we extend the classical approach for the verification of statebased programs by developing an inductive proof method to deal with the parallel composition of hybrid systems. It covers shared variable communication, labelsynchronization, and especially the common continuous activities in the parallel composition of hybrid automata. Besides hybrid systems and their parallel composition, we formalized their operational step semantics and a number of proofrules within PVS, for one of which we give also a rigorous completeness proof. Moreover, the theory is applied to the verification of a number of examples.
Modeling and Verifying a Temperature Control System using Continuous Action Systems
 In Proc. of the 5th Int. Workshop in Formal Methods for Industrial Critical Systems
, 2000
"... . We describe and verify a realtime temperature control system for a nuclear ..."
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. We describe and verify a realtime temperature control system for a nuclear
Proving the correctness of the implementation of a controlcommand algorithm
 In SAS, volume 5673 of LNCS
, 2009
"... Abstract. In this article, we study the interactions between a controlcommand program and its physical environment via sensors and actuators. We are interested in finding invariants on the continuous trajectories of the physical values that the program is supposed to control. The invariants we are l ..."
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Abstract. In this article, we study the interactions between a controlcommand program and its physical environment via sensors and actuators. We are interested in finding invariants on the continuous trajectories of the physical values that the program is supposed to control. The invariants we are looking for are periodic sequences of intervals that are abstractions of the values read by the program. To compute them, we first build octrees that abstract the impact of the program on its environment. Then, we compute a period of the abstract periodic sequence and we finally define the values of this sequence as the fixpoint of a monotone map. We present a prototype analyzer that computes such invariants for C programs using a simple specification language for describing the continuous environment. It shows good results on classical benchmarks for hybrid systems verification. 1 Introduction. The behavior of an embedded, controlcommand program depends on both a
Assertionbased analysis of hybrid systems with PVS
 In Proc. of EuroCAST'2001, LNCS
, 2001
"... Abstract. Hybrid systems are a wellestablished mathematical model for embedded systems. Such systems, which combine discrete and continuous behavior, are increasingly used in safetycritical applications. To guarantee safe functioning, formal verification techniques are crucial. While research in t ..."
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Abstract. Hybrid systems are a wellestablished mathematical model for embedded systems. Such systems, which combine discrete and continuous behavior, are increasingly used in safetycritical applications. To guarantee safe functioning, formal verification techniques are crucial. While research in this area concentrates on model checking, deductive techniques attracted less attention. In this paper we use the general purpose theorem prover PVS for the rigorous formalization and analysis of hybrid systems. To allow for machineassisted proofs, we implement a deductive assertional proof method within PVS. The sound and complete proof system allows modular proofs in that it comprises a proof rule for the parallel composition. Besides hybrid systems and the proof system, a number of examples are formalized within PVS.
Computational Issues in Intelligent Control: DiscreteEvent and Hybrid Systems
 IN: SOFT COMPUTING AND INTELLIGENT SYSTEMS: THEORY AND PRACTICE
, 1999
"... Intelligent control methodologies are being developed to address the control needs of complex systems that exhibit complicated dynamical behaviors. The design, simulation, and verification of intelligent control systems is highly nontrivial and typically involves significant amount of computations. ..."
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Intelligent control methodologies are being developed to address the control needs of complex systems that exhibit complicated dynamical behaviors. The design, simulation, and verification of intelligent control systems is highly nontrivial and typically involves significant amount of computations. In this paper, we identify and discuss several computational issues that are central in intelligent control. In particular, we discuss how the design, simulation, and verification of discreteevent and hybrid systems, which are central in intelligent control, requires the development of computationally efficient algorithms and approaches. Petri net models are used to describe discrete event and hybrid systems. Computational issues of various problems and algorithms concerning the analysis and synthesis of such systems are discussed. In view of hybrid systems, we also review basic computational issues for hybrid automata. Finally, we present a parallel computing architecture for intelligent control systems and we illustrate its advantages by considering parallel discrete event simulations.
Graduate Supervisory Committee:
"... Cyber Physical Systems (CPSs) are systems comprising of computational systems that interact with the physical world to perform sensing, communication, computation and actuation. Common examples of these systems include Body Area Networks (BANs), Autonomous Vehicles (AVs), Power Distribution Systems ..."
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Cyber Physical Systems (CPSs) are systems comprising of computational systems that interact with the physical world to perform sensing, communication, computation and actuation. Common examples of these systems include Body Area Networks (BANs), Autonomous Vehicles (AVs), Power Distribution Systems etc. The close coupling between cyber and physical worlds in a CPS manifests in two types of interactions between computing systems and the physical world: intentional and unintentional. Unintentional interactions result from the physical characteristics of the computing systems and often cause harm to the physical world, if the computing nodes are close to each other, these interactions may overlap thereby increasing the chances of causing a Safety hazard. Similarly, due to mobile nature of computing nodes in a CPS planned and unplanned interactions with the physical world occur. These interactions represent the behavior of a computing node while it is following a planned path and during faulty operations. Both of these interactions change over time due to the dynamics (motion) of the computing node and may overlap thereby causing harm to the physical world. Lack of proper modeling and analysis frameworks for these systems causes system designers to use adhoc techniques thereby further increasing their design and development time. The thesis addresses these problems by taking a holistic approach to model Computational, Physical and Cyber Physical Interactions (CPIs) aspects of a CPS and proposes modeling constructs for them. These constructs are analyzed using a safety analysis algorithm developed as part of the thesis. The algorithm computes the intersection of CPIs for both mobile as well as static computing nodes and determines the safety of the physical system. A framework is developed by extending AADL to support these modeling constructs; the safety analysis algorithm is implemented as OSATE plugin. The applicability of the proposed approach is demonstrated by considering the safety of human tissue during the operations of BAN, and the safety of passengers traveling in an
Computing Flowpipe of Nonlinear Hybrid Systems with Numerical Methods
"... Abstract. Modern controlcommand systems often include controllers that perform nonlinear computations to control a physical system, which can typically be described by an hybrid automaton containing highdimensional systems of nonlinear differential equations. To prove safety of such systems, one mu ..."
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Abstract. Modern controlcommand systems often include controllers that perform nonlinear computations to control a physical system, which can typically be described by an hybrid automaton containing highdimensional systems of nonlinear differential equations. To prove safety of such systems, one must compute all the reachable sets from a given initial position, which might be uncertain (its value is not precisely known). On linear hybrid systems, efficient and precise techniques exist, but they fail to handle nonlinear flows or jump conditions. In this article, we present a new tool name HySon which computes the flowpipes of both linear and nonlinear hybrid systems using guaranteed generalization of classical efficient numerical simulation methods, including with variable integration stepsize. In particular, we present an algorithm for detecting discrete events based on guaranteed interpolation polynomials that turns out to be both precise and efficient. Illustrations of the techniques developed in this article are given on representative examples. 1