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Reachability Analysis of Nonlinear Systems with Uncertain Parameters using Conservative Linearization
"... Abstract — Given an initial set of a nonlinear system with uncertain parameters and inputs, the set of states that can possibly be reached is computed. The approach is based on local linearizations of the nonlinear system, while linearization errors are considered by Lagrange remainders. These error ..."
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Cited by 33 (15 self)
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Abstract — Given an initial set of a nonlinear system with uncertain parameters and inputs, the set of states that can possibly be reached is computed. The approach is based on local linearizations of the nonlinear system, while linearization errors are considered by Lagrange remainders. These errors are added as uncertain inputs, such that the reachable set of the locally linearized system encloses the one of the original system. The linearization error is controlled by splitting of reachable sets. Reachable sets are represented by zonotopes, allowing an efficient computation in relatively highdimensional space. I.
Breach: A Toolbox for Verification and Parameter Synthesis of Hybrid Systems
 In ComputerAided Verification
, 2010
"... Abstract. We describe Breach, a Matlab toolbox providing a coherent set of simulationbased techniques aimed at the analysis of deterministic models of hybrid dynamical systems. The primary feature of Breach is to facilitate the computation and the property investigation of large sets of trajectorie ..."
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Cited by 20 (2 self)
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Abstract. We describe Breach, a Matlab toolbox providing a coherent set of simulationbased techniques aimed at the analysis of deterministic models of hybrid dynamical systems. The primary feature of Breach is to facilitate the computation and the property investigation of large sets of trajectories. It relies on an efficient numerical solver of ordinary differential equations that can also provide information about sensitivity with respect to parameters variation. The latter is used to perform approximate reachability analysis and parameter synthesis. A major novel feature is the robust monitoring of metric interval temporal logic (MITL) formulas. The application domain of Breach ranges from embedded systems design using Simulink to the analysis of complex nonlinear models from systems biology. 1
Modelbased probabilistic collision detection in autonomous driving
 IEEE Transactions on Intelligent Transportation Systems
, 2009
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Sensitive StateSpace Exploration
"... Abstract — In this paper, we describe a simulationbased approach to the verification of high dimensional nonlinear systems subject to disturbances and uncertainty in the initial conditions. Standard simulation can only sample finitely many initial states and disturbance signals and cannot verify co ..."
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Cited by 14 (1 self)
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Abstract — In this paper, we describe a simulationbased approach to the verification of high dimensional nonlinear systems subject to disturbances and uncertainty in the initial conditions. Standard simulation can only sample finitely many initial states and disturbance signals and cannot verify correctness in an exhaustive manner. The alternative approach of computing all the reachable states of the system using setbased simulation, can provide, in principle, correctness proofs but is computationally expensive especially for high dimensional and nonlinear systems. In this paper we propose an approach that provides a good compromise between setbased computation and simulation by combining guided random exploration of the state space together with sensitivity analysis. The exploration technique is used to choose input signals that guarantee good coverage of the reachable set, while sensitivity information is used to create neighborhoods around explored behaviors that cover the trajectories generated by neighboring input signals. I.
Reachability analysis of linear systems with uncertain parameters and inputs
 In Proc. of the 46th IEEE Conference on Decision and Control
, 2007
"... Abstract — For a dynamic system with given initial state set, the reachable state set contains the states along all possible trajectories defined over (in)finite time. This paper presents a method for computing conservative approximations of reachable sets for linear systems with uncertain system m ..."
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Cited by 10 (7 self)
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Abstract — For a dynamic system with given initial state set, the reachable state set contains the states along all possible trajectories defined over (in)finite time. This paper presents a method for computing conservative approximations of reachable sets for linear systems with uncertain system matrices and bounded inputs. Over and underapproximations are computed for exponentials of system matrices with entries specified as bounded intervals. It is shown that reachable sets represented by sequences of zonotopes can be computed up to a dimension of 100 within a few seconds. I.
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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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.
Parameter Synthesis for Hybrid Systems with an Application to Simulink Models
"... Abstract. This paper addresses a parameter synthesis problem for nonlinear hybrid systems. Considering a set of uncertain parameters and a safety property, we give an algorithm that returns a partition of the set of parameters into subsets classified as safe, unsafe, or uncertain, depending on wheth ..."
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Cited by 9 (1 self)
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Abstract. This paper addresses a parameter synthesis problem for nonlinear hybrid systems. Considering a set of uncertain parameters and a safety property, we give an algorithm that returns a partition of the set of parameters into subsets classified as safe, unsafe, or uncertain, depending on whether respectively all, none, or some of their behaviors satisfy the safety property. We make use of sensitivity analysis to compute approximations of reachable sets and an error control mechanism to determine the size of the partition elements in order to obtain the desired precision. We apply the technique to Simulink models by combining generated code with a numerical solver that can compute sensitivities to parameter variations. We present experimental results on a nontrivial Simulink model of a quadrotor helicopter. 1
Formal Verification of PhaseLocked Loops Using Reachability Analysis and Continuization
"... Wepresentanapproachfor verifyinglockingofchargepump phaselocked loops by performing reachability analysis on a behavioral model of the circuit. Bounded uncertain parameters in the behavioral model make it possible to represent all possible behaviors of more detailed models. The dynamics of the beh ..."
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Cited by 8 (3 self)
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Wepresentanapproachfor verifyinglockingofchargepump phaselocked loops by performing reachability analysis on a behavioral model of the circuit. Bounded uncertain parameters in the behavioral model make it possible to represent all possible behaviors of more detailed models. The dynamics of the behavioral model is hybrid (i.e., discrete and continuous) due to the switching of charge pumps that drive the analog control circuits. A unique feature of phaselocked loops compared to most other hybrid systems is that they require thousands of switchings in the continuous dynamics to converge sufficiently close to a limit cycle. This makes reachability analysis a challenging task since switches in the dynamics are expensive to compute and result in conservative overapproximations. We solve this problem by overapproximating the effects of the switching conditions with uncertain parameters inlinear continuousmodels, amethodwe call continuization. Using efficient reachability algorithms for discretetime linear systems, locking is verified over the complete range of possible initial states of a chargepump PLL designed in 32nm CMOS SOI technology in comparable time required for Monte Carlo simulations of the same behavioral model. 1.
Navigating Dynamic Environments Using Trajectory Deformation
 IEEERSJ INT. CONF. ON INTELLIGENT ROBOTS AND SYSTEMS, NICE: FRANCE
, 2008
"... Path deformation is a technique that was introduced to generate robot motion wherein a path, that has been computed beforehand, is continuously deformed online in response to unforeseen obstacles. In an effort to improve path deformation, this paper presents a trajectory deformation scheme. The ma ..."
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Cited by 8 (2 self)
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Path deformation is a technique that was introduced to generate robot motion wherein a path, that has been computed beforehand, is continuously deformed online in response to unforeseen obstacles. In an effort to improve path deformation, this paper presents a trajectory deformation scheme. The main idea is that by incorporating the time dimension and hence information on the obstacles ’ future behaviour, quite a number of situations where path deformation would fail can be handled. The trajectory represented as a spacetime curve is subject to deformation forces both external (to avoid collision with the obstacles) and internal (to maintain trajectory feasibility and connectivity). The trajectory deformation scheme has been tested successfully on a planar robot with double integrator dynamics and a carlike vehicle.
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.