Hybridization for stability verification of nonlinear switched systems

We propose a novel hybridization method for stability analysis that over-approximates nonlinear dynamical systems by switched systems with linear inclusion dynamics. We observe that existing hybridization techniques for safety analysis that over-approximate nonlinear dynamical systems by switched affine inclusion dynamics and provide fixed approximation error, do not suffice for stability analysis. Hence, we propose a hybridization method that provides a state-dependent error which converges to zero as the state tends to the equilibrium point. The crux of our hybridization computation is an elegant recursive algorithm that uses partial derivatives of a given function to obtain upper and lower bound matrices for the over-approximating linear inclusion. We illustrate our method on some examples to demonstrate the application of the theory for stability analysis. In particular, our method is able to establish stability of a nonlinear system which does not admit a polynomial Lyapunov function

Hybridization based CEGAR for Hybrid Automata with Affine Dynamics

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Patching task-level robot controllers based on a local µ-calculus formula

We present a method for mending strategies for GR(1) specifications. Given the addition or removal of edges from the game graph describing a problem (essentially transition rules in a GR(1) specification), we apply a µ-calculus formula to a neighborhood of states to obtain a “local strategy” that navigates around the invalidated parts of an original synthesized strategy. Our method may thus avoid global resynthesis while recovering correctness with respect to the new specification. We illustrate the results both in simulation and on physical hardware for a planar robot surveillance task

Relating Syntactic and Semantic Perturbations of Hybrid Automata

We investigate how the semantics of a hybrid automaton deviates with respect to syntactic perturbations on the hybrid automaton. We consider syntactic perturbations of a hybrid automaton, wherein the syntactic representations of its elements, namely, initial sets, invariants, guards, and flows, in some logic are perturbed. Our main result establishes a continuity like property that states that small perturbations in the syntax lead to small perturbations in the semantics. More precisely, we show that for every real number epsilon>0 and natural number k, there is a real number delta>0 such that H^delta, the delta syntactic perturbation of a hybrid automaton H, is epsilon-simulation equivalent to H up to k transition steps. As a byproduct, we obtain a proof that a bounded safety verification tool such as dReach will eventually prove the safety of a safe hybrid automaton design (when only non-strict inequalities are used in all constraints) if dReach iteratively reduces the syntactic parameter delta that is used in checking approximate satisfiability. This has an immediate application in counter-example validation in a CEGAR framework, namely, when a counter-example is spurious, then we have a complete procedure for deducing the same

Bayesian Statistical Model-Checking of Continuous Stochastic Logic

Master of ScienceDepartment of StatisticsChristopher VahlAutonomous systems are transforming the society by enabling sophisticated technologies such as robotic surgery and driverless cars. On one hand, increased automation through removal of the human-in-the-loop promises enhanced efficiency, while, on the other hand, the highly uncertain and safety critical environments, such as, varying weather and road conditions, and the presence of pedestrians on the road, pose challenge to the design of reliable autonomous systems. Hence, there is an immediate need for a robust framework for certifying the correctness of autonomous systems. In this report, we explore verifying the correctness of uncertain autonomous systems modeled as discrete-time Markov chains (DTMCs) against correctness criteria provided as continuous stochastic logic (CSL) formulae. Statistical model-checking (SMC) is a paradigm for verification based on formulating the verification problem as a hypothesis testing prob- lem. We propose a novel statistical model-checking algorithm based on Bayesian hypothesis testing. While Bayesian approaches for simpler logics without nested probabilistic operators and Frequentist approaches for nested logic have been previously explored, the Bayesian ap- proach for CSL that has nested probabilistic operators has not been addressed. The challenge in the nested case arises from the fact that unlike in probabilistic model-checking (PMC), where we obtain a definitive answer for the model-checking problem for the sub-formulae, we only obtain a correct answer with a certain confidence, which needs to be factored into the recursive SMC algorithm. We have implemented our algorithm in a Python Toolbox, and present our evaluation on some benchmark examples. We observe that while both the Bayesian and frequentist SMC perform well in terms of inference, Bayesian SMC is more efficient in terms of the number of samples. On several examples, it even beats the state-of- the-art probabilistic model-checker PRISM

Formal synthesis of stabilizing controllers for periodically controlled linear switched systems

In this paper, we address the problem of synthesizing periodic switching controllers for stabilizing a family of linear systems. Our broad approach consists of constructing a finite game graph based on the family of linear systems such that every winning strategy on the game graph corresponds to a stabilizing switching controller for the family of linear systems. The construction of a (finite) game graph, the synthesis of a winning strategy and the extraction of a stabilizing controller are all computationally feasible. We illustrate our method on an example

STORMED hybrid systems

Abstract. We introduce STORMED hybrid systems, a decidable class which is similar to o-minimal hybrid automata in that the continuous dynamics and constraints are described in an o-minimal theory. However, unlike o-minimal hybrid automata, the variables are not initialized in a memoryless fashion at discrete steps. STORMED hybrid systems require flows which are monotonic with respect to some vector in the continuous space and can be characterised as bounded-horizon systems in terms of their discrete transitions. We demonstrate that such systems admit a finite bisimulation, which can be effectively constructed provided the o-minimal theory used to describe the system is decidable. As a consequence, many verification problems for such systems have effective decision algorithms

Specifications for decidable hybrid games

Abstract We introduce STORMED hybrid games (SHG), a generalization of STORMED Hybrid System