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17
Robustness of Temporal Logic Specifications for ContinuousTime Signals
, 2009
"... In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with nontrivial metrics, for example continuous or hybrid, robustness is not only na ..."
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Cited by 43 (18 self)
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In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with nontrivial metrics, for example continuous or hybrid, robustness is not only natural, but also a critical measure of system performance. Thus, we propose multivalued semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, ε, from unsatisfiability. We prove that any other signal that remains εclose to the initial one also satisfies the same MTL specification under the usual Boolean semantics. Finally, our framework is applied to the problem of testing formulas of two fragments of MTL, namely Metric Interval Temporal Logic (MITL) and closed Metric Temporal Logic (clMTL), over continuoustime signals using only discretetime analysis. The motivating idea behind our approach is that if the continuoustime signal fulfills certain conditions and the discrete time signal robustly satisfies the temporal logic specification, then the corresponding continuoustime signal should also satisfy the same temporal logic specification.
Cost approximation: A unified framework of descent algorithms for nonlinear programs
 SIAM Journal on Optimization
, 1994
"... . The paper describes and analyzes the cost approximation algorithm. This class of iterative descent algorithms for nonlinear programs and variational inequalities places a large number of algorithms within a common framework and provides a means for analyzing relationships among seemingly unrelated ..."
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Cited by 18 (4 self)
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. The paper describes and analyzes the cost approximation algorithm. This class of iterative descent algorithms for nonlinear programs and variational inequalities places a large number of algorithms within a common framework and provides a means for analyzing relationships among seemingly unrelated methods. A common property of the methods included in the framework is that their subproblems may be characterized by monotone mappings, which replace an additive part of the original cost mapping in an iterative manner; alternately, a step is taken in the direction obtained in order to reduce the value of a merit function for the original problem. The generality of the framework is illustrated through examples, and the convergence characteristics of the algorithm are analyzed for applications to nondifferentiable optimization. The convergence results are applied to some example methods, demonstrating the strength of the analysis compared to existing results. Key Words. Nondifferentiable o...
Robust sampling for MITL specifications
 In Proc. of FORMATS’07, volume 4763 of LNCS
, 2007
"... Abstract. Realtime temporal logic reasoning about trajectories of physical systems necessitates models of time which are continuous. However, discrete time temporal logic reasoning is computationally more efficient than continuous time. Moreover, in a number of engineering applications only discret ..."
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Cited by 12 (1 self)
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Abstract. Realtime temporal logic reasoning about trajectories of physical systems necessitates models of time which are continuous. However, discrete time temporal logic reasoning is computationally more efficient than continuous time. Moreover, in a number of engineering applications only discrete time models are available for analysis. In this paper, we introduce a framework for testing MITL specifications on continuous time signals using only discrete time analysis. The motivating idea behind our approach is that if the dynamics of the signal fulfills certain conditions and the discrete time signal robustly satisfies the MITL specification, then the corresponding continuous time signal should also satisfy the same MITL specification. 1
Proofs from simulations and modular annotations
 In In 17th International Conference on Hybrid Systems: Computation and Control
"... We present a modular technique for simulationbased bounded verification for nonlinear dynamical systems. We introduce the notion of inputtostate discrepancy of each subsystem Ai in a larger nonlinear dynamical system A which bounds the distance between two (possibly diverging) trajectories of Ai ..."
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Cited by 3 (2 self)
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We present a modular technique for simulationbased bounded verification for nonlinear dynamical systems. We introduce the notion of inputtostate discrepancy of each subsystem Ai in a larger nonlinear dynamical system A which bounds the distance between two (possibly diverging) trajectories of Ai in terms of their initial states and inputs. Using the IS discrepancy functions, we construct a low dimensional deterministic dynamical system M(δ). For any two trajectories of A starting δ distance apart, we show that one of them bloated by a factor determined by the trajectory of M contains the other. Further, by choosing appropriately small δ’s the overapproximations computed by the above method can be made arbitrarily precise. Using the above results we develop a sound and relatively complete algorithm for bounded safety verification of nonlinear ODEs. Our preliminary experiments with a prototype implementation of the algorithm show that the approach can be effective for verification of nonlinear models.
Length scale for characterising continuous optimization problems
 in Proc. PPSN XII, 2012, LNCS 7491
"... Abstract. In metaheuristic optimization, understanding the relationship between problems and algorithms is important but nontrivial. There has been a growing interest in the literature on techniques for analysing problems, however previous work has mainly been developed for discrete problems. In t ..."
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Cited by 2 (2 self)
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Abstract. In metaheuristic optimization, understanding the relationship between problems and algorithms is important but nontrivial. There has been a growing interest in the literature on techniques for analysing problems, however previous work has mainly been developed for discrete problems. In this paper, we develop a novel framework for characterising continuous optimization problems based on the concept of length scale. We argue that length scale is an important property for the characterisation of continuous problems that is not captured by existing techniques. Intuitively, length scale measures the ratio of changes in the objective function value to steps between points in the search space. The concept is simple, makes few assumptions and can be calculated or estimated based only on the information available in blackbox optimization (objective function values and search points). Some fundamental properties of length scale and its distribution are described. Experimental results show the potential use of length scale and directions to develop the framework further are discussed.
Temporal Precedence Checking for Switched Models and its Application to a Parallel Landing Protocol
"... Abstract. We present an algorithm for checking temporal precedence properties of nonlinear switched systems. This class of properties subsume bounded safety and capture requirements about visiting a sequence of predicates within given time intervals. Our algorithm handles nonlinear predicates that ..."
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Abstract. We present an algorithm for checking temporal precedence properties of nonlinear switched systems. This class of properties subsume bounded safety and capture requirements about visiting a sequence of predicates within given time intervals. Our algorithm handles nonlinear predicates that arise from dynamicsbased predictions used in alerting protocols for stateoftheart transportation systems. It is sound and relatively complete for nonlinear switch systems that robustly satisfy the given property. The algorithm is implemented in our Compare Execute Check Engine (C2E2) using validated simulations. As a case study, we consider NASA’s Adjacent Landing Alerting System (ALAS), which is an alerting protocol for closely spaced parallel runways. Using our approach, we study the performance of the ALAS protocol with respect to false and missed alerts for different operating conditions such as initial velocities, bank angles, initial longitudinal separation, and runway configurations. 1
A new exclusion test for finding the global minimum �
, 2006
"... www.elsevier.com/locate/cam Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a minimization condition that can be applied to each cell in the domain. ..."
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Cited by 1 (1 self)
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www.elsevier.com/locate/cam Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a minimization condition that can be applied to each cell in the domain. In this paper, we consider Lipschitz functions of order � and give a new minimization condition for the exclusion algorithm. Furthermore, convergence and complexity results are presented for such algorithm.
Verification of Annotated Models from Executions
"... Simulations can help enhance confidence in system designs but they provide almost no formal guarantees. In this paper, we present a simulationbased verification framework for embedded systems described by nonlinear, switched systems. In our framework, users are required to annotate the dynamics ..."
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Simulations can help enhance confidence in system designs but they provide almost no formal guarantees. In this paper, we present a simulationbased verification framework for embedded systems described by nonlinear, switched systems. In our framework, users are required to annotate the dynamics in each control mode of switched system by something we call a discrepancy function that formally measures the nature of trajectory convergence/divergence of the system. Discrepancy functions generalize other measures of trajectory convergence and divergence like Contraction Metrics and Incremental Lyapunov functions. Exploiting such annotations, we present a sound and relatively complete verification procedure for robustly safe/unsafe systems. We have built a tool based on the framework that is integrated into the popular Simulink/Stateflow modeling environment. Experiments with our prototype tool shows that the approach (a) outperforms other verification tools on standard linear and nonlinear benchmarks, (b) scales reasonably to larger dimensional systems and to longer time horizons, and (c) applies to models with diverging trajectories and unknown parameters. 1.
Technological sciences, informatics engineering (07T)
"... The license to conduct the doctoral studies was granted by the resolution No. 457 of the Government of Lithuania dated 14/04/1998. The doctoral committee: The main supervisor Prof. Dr. Habil. (technological sciences, informatics engineering, 07T) ..."
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The license to conduct the doctoral studies was granted by the resolution No. 457 of the Government of Lithuania dated 14/04/1998. The doctoral committee: The main supervisor Prof. Dr. Habil. (technological sciences, informatics engineering, 07T)