Results 1  10
of
11
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 multimodal d ..."
Abstract

Cited by 19 (11 self)
 Add to MetaCart
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 multimodal 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 wellformed 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 firstorder formulas over the reals arise when formally analyzing models of complex control systems. Existing off ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
(Show Context)
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 firstorder formulas over the reals arise when formally analyzing models of complex control systems. Existing offtheshelf 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 ..."
Abstract

Cited by 13 (6 self)
 Add to MetaCart
(Show Context)
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 multimodal 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 nonzeno hybrid systems. In practice, we perform a constructive proof of controlled reachability by solving an ExistsForall 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 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 ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
(Show Context)
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.
M.: Exponentialconditionbased 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 verification based on barrier certificate has the benefit of avoiding explicit computation of the exact reachable set which is usually intractable for nonlinea ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Abstract. A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system. Safety verification 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 certificate condition, called Exponential Condition, for the safety verification of semialgebraic 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 overapproximation for the reachable set and hence is able to verify critical safety properties. On the other hand, the property of convexity guarantees its solvability by semidefinite programming method. Some examples are presented to illustrate the effectiveness and practicality of our method.
Synthesizing switching controllers for hybrid systems by continuous invariant generation
 CORR ABS/1304.0825
, 2013
"... ..."
(Show Context)
Research Statement
"... I am broadly interested in the applications of programming language theory, logic and formal methods to various realworld problems pertaining to web security, system security and verification. My research employs a twopronged approach: (i) mathematically modeling realworld systems in order to rig ..."
Abstract
 Add to MetaCart
(Show Context)
I am broadly interested in the applications of programming language theory, logic and formal methods to various realworld problems pertaining to web security, system security and verification. My research employs a twopronged approach: (i) mathematically modeling realworld 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 securitycritical resources, I rigorously formulated the confinement problem as a pointsto analysis problem and then solved it by adapting offtheshelf 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 constraintsolving 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 templatebased approach for synthesizing switching controllers for semialgebraic 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 ..."
Abstract
 Add to MetaCart
(Show Context)
We extend a templatebased approach for synthesizing switching controllers for semialgebraic 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 (sumofsquares) relaxation approach and the template polyhedra approach in invariant generation, which are both supported by modern numerical solvers.