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Synthesizing Switching Logic using Constraint Solving
"... A new approach based on constraint solving techniques was recently proposed for verification of hybrid systems. This approach works by searching for inductive invariants of a given form. In this paper, we extend that work to automatic synthesis of safe hybrid systems. Starting with a multi-modal d ..."
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Cited by 19 (11 self)
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A new approach based on constraint solving techniques was recently proposed for verification of hybrid systems. This approach works by searching for inductive invariants of a given form. In this paper, we extend that work to automatic synthesis of safe hybrid systems. Starting with a multi-modal dynamical system and a safety property, we present a sound technique for synthesizing a switching logic for changing modes so as to preserve the safety property. By construction, the synthesized hybrid system is well-formed and is guaranteed safe. Our approach is based on synthesizing a controlled invariant that is sufficient to prove safety. The generation of the controlled invariant is cast as a constraint solving problem. When the system, the safety property, and the controlled invariant are all expressed only using polynomials, the generated constraint is an ∃ ∀ formula in the theory of reals, which we solve using SMT solvers. The generated controlled invariant is then used to arrive at the maximally liberal switching logic.
Verification and synthesis using real quantifier elimination
, 2011
"... We present the application of real quantifier elimination to formal verification and synthesis of continuous and switched dynamical systems. Through a series of case studies, we show how first-order formulas over the reals arise when formally analyzing models of complex control systems. Existing off ..."
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Cited by 13 (3 self)
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We present the application of real quantifier elimination to formal verification and synthesis of continuous and switched dynamical systems. Through a series of case studies, we show how first-order formulas over the reals arise when formally analyzing models of complex control systems. Existing off-the-shelf quantifier elimination procedures are not successful in eliminating quantifiers from many of our benchmarks. We therefore automatically combine three established software components: virtual subtitution based quantifier elimination in Reduce/Redlog, cylindrical algebraic decomposition implemented in Qepcad, and the simplifier Slfq implemented on top of Qepcad. We use this combination to successfully analyze various models of systems including adaptive cruise control in automobiles, adaptive flight control system, and the classical inverted pendulum problem studied in control theory.
Switching Logic Synthesis for Reachability
, 2010
"... We consider the problem of driving a system from some initial configuration to a desired configuration while avoiding some unsafe configurations. The system to be controlled is a dynamical system that can operate in different modes. The goal is to synthesize the logic for switching between the modes ..."
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Cited by 13 (6 self)
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We consider the problem of driving a system from some initial configuration to a desired configuration while avoiding some unsafe configurations. The system to be controlled is a dynamical system that can operate in different modes. The goal is to synthesize the logic for switching between the modes so that the desired reachability property holds. In this paper, we first present a sound and complete inference rule for proving reachability properties of single mode continuous dynamical systems. Next, we present an inference rule for proving controlled reachability in multi-modal continuous dynamical systems. From a constructive proof of controlled reachability, we show how to synthesize the desired switching logic. We show that our synthesis procedure is sound and produces only non-zeno hybrid systems. In practice, we perform a constructive proof of controlled reachability by solving an Exists-Forall formula in the theory of reals. We present an approach for solving such formulas that combines symbolic and numeric solvers. We demonstrate our approach on some examples. All results extend naturally to the case when, instead of reachability, interest is in until properties.
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 sys-tems, and has been widely used in the design of complex embedded sys-tems. 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 sys-tems, and has been widely used in the design of complex embedded sys-tems. 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 exten-sion of Hoare logic to hybrid systems. For deductive verification of hy-brid 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 im-plemented. We give some case studies from real-time world, for instance, Chinese High-Speed Train Control System at Level 3 (CTCS-3). In ad-dition, 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 require-ment, or any of their combinations. We also discuss other issues of hybrid systems, e.g., stability analysis.
M.: Exponential-condition-based barrier certificate generation for safety verification of hybrid systems
- In: CAV’13
, 2013
"... Abstract. A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system. Safety veri-fication based on barrier certificate has the benefit of avoiding explicit computation of the exact reachable set which is usually intractable for nonlinea ..."
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Cited by 4 (0 self)
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Abstract. A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system. Safety veri-fication based on barrier certificate has the benefit of avoiding explicit computation of the exact reachable set which is usually intractable for nonlinear hybrid systems. In this paper, we propose a new barrier cer-tificate condition, called Exponential Condition, for the safety verifica-tion of semi-algebraic hybrid systems. The most important benefit of Exponential Condition is that it has a lower conservativeness than the existing convex condition and meanwhile it possesses the property of convexity. On the one hand, a less conservative barrier certificate forms a tighter over-approximation for the reachable set and hence is able to verify critical safety properties. On the other hand, the property of con-vexity guarantees its solvability by semidefinite programming method. Some examples are presented to illustrate the effectiveness and practi-cality of our method.
Synthesizing switching controllers for hybrid systems by continuous invariant generation
- CORR ABS/1304.0825
, 2013
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Research Statement
"... I am broadly interested in the applications of programming language theory, logic and formal methods to various real-world problems pertaining to web security, system security and verification. My research employs a two-pronged approach: (i) mathematically modeling real-world systems in order to rig ..."
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I am broadly interested in the applications of programming language theory, logic and formal methods to various real-world problems pertaining to web security, system security and verification. My research employs a two-pronged approach: (i) mathematically modeling real-world systems in order to rigorously formulate properties of interest in them, and (ii) developing analysis techniques for proving and disproving these properties. For instance, in [7], in order to verify that a JavaScript API confines security-critical resources, I rigorously formulated the confinement problem as a points-to analysis problem and then solved it by adapting off-theshelf program analysis techniques. For many problems where classical techniques are insufficient, I have also developed new principled techniques. For instance, in order to verify safety properties of polynomial continuous dynamical systems, I developed a novel provably sound and complete deductive verification rule, as all existing rules were either unsound or incomplete. 1 Research Accomplishments Over the last four years, I have worked on applying programming language techniques for improving the security of JavaScript web applications (thesis research), developing deductive verification techniques for hybrid and continuous dynamical systems, and developing constraint-solving techniques for synthesizing symbolic instruction encodings for processor instruction sets. What follows is a brief summary of my research in these areas.
Synthesizing Switching Controllers for Hybrid Systems by Generating Invariants
, 2013
"... We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating invariants with a qualitative approach for predefining tem ..."
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We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating invariants with a qualitative approach for predefining templates. Our synthesis method is relatively complete with regard to a given family of predefined templates. Using qualitative analysis, we discuss heuristics to reduce the numbers of parameters appearing in the templates. To avoid too much human interaction in choosing templates as well as the high computational complexity caused by QE, we further investigate applications of the SOS (sum-of-squares) relaxation approach and the template polyhedra approach in invariant generation, which are both supported by modern numerical solvers.
