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33
B.H.: Reachable set computation for uncertain timevarying linear systems
 In: Hybrid Systems: Computation and Control
, 2011
"... This paper presents a method for using setbased approximations to the PeanoBaker series to compute overapproximations of reachable sets for linear systems with uncertain, timevarying parameters and inputs. Alternative representations for sets of uncertain system matrices are considered, includ ..."
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Cited by 14 (10 self)
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This paper presents a method for using setbased approximations to the PeanoBaker series to compute overapproximations of reachable sets for linear systems with uncertain, timevarying parameters and inputs. Alternative representations for sets of uncertain system matrices are considered, including matrix polytopes, matrix zonotopes, and interval matrices. For each representation, the computational efficiency and resulting approximation error for reachable set computations are evaluated analytically and empirically. As an application, reachable sets are computed for a truck with hybrid dynamics due to a gainscheduled yaw controller. As an alternative to computing reachable sets for the hybrid model, for which switching introduces an additional overapproximation error, the gainscheduled controller is approximated with uncertain timevarying parameters, which leads to more efficient and more accurate reachable set computations.
Modelbased probabilistic collision detection in autonomous driving
 IEEE Transactions on Intelligent Transportation Systems
, 2009
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Computing Reachable States for Nonlinear Biological Models
"... Abstract. In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We then develop a novel algorithm for computing reachable states for nonlinear systems and report experimental res ..."
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Cited by 13 (5 self)
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Abstract. In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We then develop a novel algorithm for computing reachable states for nonlinear systems and report experimental results obtained using a prototype implementation. We believe these results constitute a promising contribution to the analysis of complex models of biological systems. 1
Mining requirements from closedloop control models
 in Hybrid Systems: Computation and Control (HSCC
, 2013
"... A significant challenge to the formal validation of softwarebased industrial control systems is that system requirements are often imprecise, nonmodular, evolving, or even simply unknown. We propose a framework for mining requirements from the closedloop model of an industrialscale control system ..."
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Cited by 12 (5 self)
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A significant challenge to the formal validation of softwarebased industrial control systems is that system requirements are often imprecise, nonmodular, evolving, or even simply unknown. We propose a framework for mining requirements from the closedloop model of an industrialscale control system, such as one specified in the Simulink modeling language. The input to our algorithm is a requirement template expressed in Parametric Signal Temporal Logic — a formalism to express temporal formulas in which concrete signal or time values are replaced by parameters. Our algorithm is an instance of counterexampleguided inductive synthesis: an intermediate candidate requirement is synthesized from simulation traces of the system, which is refined using counterexamples to the candidate obtained with the help of a falsification tool. The algorithm terminates when no counterexample is found. Mining has many usage scenarios: mined requirements can be used to validate future modifications of the model, they can be used to enhance understanding of legacy models, and can also guide the process of bugfinding through simulations. We present two case studies for requirement mining: a simple automobile transmission controller and an industrial airpath control model for an engine.
Computing Reachable Sets of Hybrid Systems Using a Combination of Zonotopes and Polytopes
, 2009
"... The computation of reachable sets for hybrid systems with linear continuous dynamics is addressed. Zonotopes are used for the representation of reachable sets, resulting in an algorithm with low computational complexity with respect to the dimension of the considered system. However, zonotopes have ..."
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Cited by 12 (3 self)
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The computation of reachable sets for hybrid systems with linear continuous dynamics is addressed. Zonotopes are used for the representation of reachable sets, resulting in an algorithm with low computational complexity with respect to the dimension of the considered system. However, zonotopes have drawbacks when being intersected with transition guards which determine the discrete behavior of the hybrid system. For this reason, in the proposed approach, reachable sets are represented by polytopes within guard sets as an intermediate step in order to enclose them by zonotopes afterwards. Different methods for the conservative conversion from zonotopes to polytopes and vice versa are proposed and numerically evaluated.
Avoiding geometric intersection operations in reachability analysis of hybrid systems
 In Hybrid Systems: Computation and Control
, 2012
"... Although a growing number of dynamical systems studied in various fields are hybrid in nature, the verification of properties, such as stability, safety, etc., is still a challenging problem. Reachability analysis is one of the promising methods for hybrid system verification, which together with ..."
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Cited by 11 (6 self)
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Although a growing number of dynamical systems studied in various fields are hybrid in nature, the verification of properties, such as stability, safety, etc., is still a challenging problem. Reachability analysis is one of the promising methods for hybrid system verification, which together with all other verification techniques faces the challenge of making the analysis scale with respect to the number of continuous state variables. The bottleneck of many reachability analysis techniques for hybrid systems is the geometrically computed intersection with guard sets. In this work, we replace the intersection operation by a nonlinear mapping onto the guard, which is not only numerically stable, but also scalable, making it possible to verify systems which were previously out of reach. The approach can be applied to the fairly common class of hybrid systems with piecewise continuous solutions, guard sets modeled as halfspaces, and urgent semantics, i.e. discrete transitions are immediately taken when enabled by guard sets. We demonstrate the usefulness of the new approach by a mechanical system with backlash which has 101 continuous state variables.
Safety Verification of Autonomous Vehicles for Coordinated Evasive Maneuvers
"... Abstract — The verification of evasive maneuvers for autonomous vehicles driving with constant velocity is considered. Modeling uncertainties, uncertain measurements, and disturbances can cause substantial deviations from an initially planned evasive maneuver. From this follows that the maneuver, wh ..."
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Cited by 10 (1 self)
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Abstract — The verification of evasive maneuvers for autonomous vehicles driving with constant velocity is considered. Modeling uncertainties, uncertain measurements, and disturbances can cause substantial deviations from an initially planned evasive maneuver. From this follows that the maneuver, which is safe under perfect conditions, might become unsafe. In this work, the possible set of deviations is computed with methods from reachability analysis, which allows to verify evasive maneuvers under consideration of the mentioned uncertainties. Since the presented approach has a short response time, it can be applied for real time safety decisions. The methods are presented for a numerical example where two autonomous cars plan a coordinated evasive maneuver in order to prevent a collision with a wrongway driver. I.
Powertrain Control Verification Benchmark
 In Proc. of Hybrid Systems: Computation and Control
, 2014
"... Industrial control systems are often hybrid systems that are required to satisfy strict performance requirements. Verifying designs against requirements is a difficult task, and there is a lack of suitable open benchmark models to assess, evaluate, and compare tools and techniques. Benchmark mode ..."
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Cited by 9 (4 self)
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Industrial control systems are often hybrid systems that are required to satisfy strict performance requirements. Verifying designs against requirements is a difficult task, and there is a lack of suitable open benchmark models to assess, evaluate, and compare tools and techniques. Benchmark models can be valuable for the hybrid systems research community, as they can communicate the nature and complexity of the problems facing industrial practitioners. We present a collection of benchmark problems from the automotive powertrain control domain that are focused on verification for hybrid systems; the problems are intended to challenge the research community while maintaining a manageable scale. We present three models of a fuel control system, each with a unique level of complexity, along with representative requirements in signal temporal logic (STL). We provide results obtained by applying a state of the art analysis tool to these models, and finally, we discuss challenge problems for the research community.
Hybridization Domain Construction using Curvature Estimation ∗ ABSTRACT
"... This paper is concerned with the reachability computation for nonlinear systems using hybridization. The main idea of hybridization is to approximate a nonlinear vector field by a piecewiseaffine one. The piecewiseaffine vector field is defined by building around the set of current states of the ..."
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Cited by 7 (2 self)
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This paper is concerned with the reachability computation for nonlinear systems using hybridization. The main idea of hybridization is to approximate a nonlinear vector field by a piecewiseaffine one. The piecewiseaffine vector field is defined by building around the set of current states of the system a simplicial domain and using linear interpolation over its vertices. To achieve a good timeefficiency and accuracy of the reachability computation on the approximate system, it is important to find a simplicial domain which, on one hand, is as large as possible and, on the other hand, guarantees a small interpolation error. In our previous work [8], we proposed a method for constructing hybridization domains based on the curvature of the dynamics and showed how the method can be applied to quadratic systems. In this paper we pursue this work further and present two main results. First, we prove an optimality property of the domain construction method for a class of quadratic systems. Second, we propose an algorithm of curvature estimation for more general nonlinear systems with nonconstant Hessian matrices. This estimation can then be used to determine efficient hybridization domains. We also describe some experimental results to illustrate the main ideas of the algorithm as well as its performance. 1.
SetBased Computation of Vehicle Behaviors for the Online Verification of Autonomous Vehicles
"... Abstract — We compute the set of all possible behaviors of an autonomous vehicle using reachability analysis. A reachable set is the set of states a system can possibly reach for a given set of initial states, disturbances, and sensor noise values. We consider autonomous vehicles which plan trajecto ..."
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Cited by 6 (5 self)
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Abstract — We compute the set of all possible behaviors of an autonomous vehicle using reachability analysis. A reachable set is the set of states a system can possibly reach for a given set of initial states, disturbances, and sensor noise values. We consider autonomous vehicles which plan trajectories for a certain lookahead horizon which are followed using feedback control. While a perfectly followed trajectory might not violate specified safety properties (e.g. lane departures or vehicle collisions), there might exist a violating deviation from the planned trajectory. Given the mathematical model of the controlled vehicle and bounds on uncertainty, our approach detects any possible violation. In addition, the approach provides results faster than real time such that maneuvers of vehicles can be checked before they are fully executed. I.