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Logics of Dynamical Systems
"... We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded ..."
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Cited by 18 (17 self)
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We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded systems and cyberphysical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. Distributed hybrid systems combine distributed systems with hybrid systems, i.e., they are multiagent hybrid systems that interact through remote communication or physical interaction. Stochastic hybrid systems combine stochastic
Approximate Bisimulation: A Bridge Between Computer Science and Control Theory
 EUROPEAN JOURNAL OF CONTROL (2011)56:568–578
, 2011
"... Fifty years ago, control and computing were part of a broader system science. After a long period of separate development within each discipline, embedded and hybrid systems have challenged us to reunite the, now sophisticated theories of continuous control and discrete computing on a broader syste ..."
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Cited by 12 (0 self)
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Fifty years ago, control and computing were part of a broader system science. After a long period of separate development within each discipline, embedded and hybrid systems have challenged us to reunite the, now sophisticated theories of continuous control and discrete computing on a broader system theoretic basis. In this paper, we present a framework of system approximation that applies to both discrete and continuous systems. We define a hierarchy of approximation metrics between two systems that quantify the quality of the approximation, and capture the established notions in computer science as zero sections. The central notions in this framework are that of approximate simulation and bisimulation relations and their functional characterizations called simulation and bisimulation functions and defined by Lyapunovtype inequalities. In particular, these functions can provide computable upperbounds on the approximation metrics by solving a static game. Our approximation framework will be illustrated by showing some of its applications in various problems such as reachability analysis of continuous systems and hybrid systems, approximation of continuous and hybrid systems by discrete systems, hierarchical control design, and simulationbased approaches to verification of continuous and hybrid systems.
Enclosing temporal evolution of dynamical systems using numerical methods. under submission
 In RSP. IEEE
, 2012
"... Abstract. Numerical methods are necessary to understand the behaviors of complex hybrid systems used to design controlcommand systems. Especially, numerical integration methods are heavily used in simulation to compute approximations of the solution of differential equations, including nonlinear a ..."
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Cited by 7 (2 self)
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Abstract. Numerical methods are necessary to understand the behaviors of complex hybrid systems used to design controlcommand systems. Especially, numerical integration methods are heavily used in simulation to compute approximations of the solution of differential equations, including nonlinear and stiff solutions. Nevertheless, these methods only produce approximate results and they should not be used in formal verification methods as is. We propose a systematic way to make explicit RungeKutta integration method safe with respect to the mathematical solution. As side effect, we can hence compare different integration schemes in order to pick the right one in different situations. 1
System Level Formal Verification via Model Checking Driven Simulation
"... Abstract. We show how by combining Explicit Model Checking techniques and simulation it is possible to effectively carry out (bounded) System Level Formal Verification of large Hybrid Systems such as those defined using modelbased tools like Simulink. We use an explicit model checker (namely, CMurp ..."
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Cited by 6 (4 self)
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Abstract. We show how by combining Explicit Model Checking techniques and simulation it is possible to effectively carry out (bounded) System Level Formal Verification of large Hybrid Systems such as those defined using modelbased tools like Simulink. We use an explicit model checker (namely, CMurphi) to generate all possible (finite horizon) simulation scenarios and then optimise the simulation of such scenarios by exploiting the ability of simulators to save and restore visited states. We show feasibility of our approach by presenting experimental results on the verification of the fuel control system example in the Simulink distribution. To the best of our knowledge this is the first time that (exhaustive) verification has been carried out for hybrid systems of such a size. 1
Formal modelling, analysis and verification of hybrid systems
 In Unifying Theories of Programming and Formal Engineering Methods, volume 8050 of LNCS
, 2013
"... Abstract. Hybrid systems is a mathematical model of embedded systems, and has been widely used in the design of complex embedded systems. In this chapter, we will introduce our systematic approach to formal modelling, analysis and verification of hybrid systems. In our framework, a hybrid system i ..."
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Cited by 6 (5 self)
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Abstract. Hybrid systems is a mathematical model of embedded systems, and has been widely used in the design of complex embedded systems. In this chapter, we will introduce our systematic approach to formal modelling, analysis and verification of hybrid systems. In our framework, a hybrid system is modelled using Hybird CSP (HCSP), and specified and reasoned about by Hybrid Hoare Logic (HHL), which is an extension of Hoare logic to hybrid systems. For deductive verification of hybrid systems, a complete approach to generating polynomial invariants for polynomial hybrid systems is proposed; meanwhile, a theorem prover for HHL that can provide tool support for the verification has been implemented. We give some case studies from realtime world, for instance, Chinese HighSpeed Train Control System at Level 3 (CTCS3). In addition, based on our invariant generation approach, we consider how to synthesize a switching logic for a considered hybrid system by reduction to constraint solving, to meet a given safety, liveness, optimality requirement, or any of their combinations. We also discuss other issues of hybrid systems, e.g., stability analysis.
δComplete Analysis for Bounded Reachability of Hybrid Systems
, 2014
"... We present the framework of δcomplete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving δdecision problems over the reals. The techniques take into account of robustness properties of the systems under numerical perturbat ..."
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Cited by 5 (1 self)
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We present the framework of δcomplete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving δdecision problems over the reals. The techniques take into account of robustness properties of the systems under numerical perturbations. We prove that the verification problems become much more mathematically tractable in this new framework. Our implementation of the techniques, an opensource tool dReach, scales well on several highly nonlinear hybrid system models that arise in biomedical and robotics applications.
A Vision of Collaborative VerificationDriven Engineering of Hybrid Systems
"... Abstract. Hybrid systems with both discrete and continuous dynamics are an important model for realworld physical systems. The key challenge is how to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be modeldriven engineering to develop hy ..."
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Cited by 4 (3 self)
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Abstract. Hybrid systems with both discrete and continuous dynamics are an important model for realworld physical systems. The key challenge is how to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be modeldriven engineering to develop hybrid systems in a welldefined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verificationdriven engineering. Despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires significant human guidance, since hybrid systems verification tools solve undecidable problems. It is thus not uncommon for verification teams to consist of many players with diverse expertise. This paper introduces a verificationdriven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) modeling hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle largescale verification tasks. 1
TimeAware Relational Abstractions for Hybrid Systems
"... Hybrid Systems model both discrete switches and continuous dynamics and are suitable to represent embedded systems where discrete controllers interact with a physical plant. Relational abstraction is a new approach for verifying hybrid systems. In relational abstraction, the continuous dynamics in e ..."
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Cited by 4 (1 self)
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Hybrid Systems model both discrete switches and continuous dynamics and are suitable to represent embedded systems where discrete controllers interact with a physical plant. Relational abstraction is a new approach for verifying hybrid systems. In relational abstraction, the continuous dynamics in each location of the hybrid system is abstracted by a binary relation that relates the current value of the continuous variables with all future values of the variables that are reachable after a time elapse (continuous) transition. The abstract system is an infinitestate system, which can be verified using kinduction or abstract interpretation. Existing techniques for computing relational abstractions are timeagnostic: they do not construct any relationship between the state variables and the time elapsed during the continuous evolution. Timeagnostic abstractions cannot verify timing properties. We present a technique to compute a timeaware relational abstraction for verifying (timingrelated) safety properties of cyberphysical systems. We show the effectiveness of the new abstraction on several case studies on which the previous techniques fail.
System Level Formal Verification via Distributed MultiCore Hardware in the Loop Simulation
"... Abstract—The goal of System Level Formal Verification (SLFV) is to show system correctness notwithstanding uncontrollable events (such as: faults, variation in system parameters, external inputs, etc). Hardware In the Loop Simulation (HILS) based SLFV attains such a goal by considering exhaustively ..."
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Cited by 3 (2 self)
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Abstract—The goal of System Level Formal Verification (SLFV) is to show system correctness notwithstanding uncontrollable events (such as: faults, variation in system parameters, external inputs, etc). Hardware In the Loop Simulation (HILS) based SLFV attains such a goal by considering exhaustively all relevant simulation scenarios. We present a distributed multicore algorithm for HILSbased SLFV. Our experimental results on the Fuel Control System example in the Simulink distribution show that by using 64 machines with an 8 core processor each we can complete the SLFV activity in about 27 hours whereas a sequential approach would require more than 200 days. To the best of our knowledge this is the first time that a distributed multicore algorithm for HILSbased SLFV is presented.
Synthesizing switching controllers for hybrid systems by continuous invariant generation
 CORR ABS/1304.0825
, 2013
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