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24
Approximate Reachability Analysis of PiecewiseLinear Dynamical Systems
, 2000
"... . In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much small ..."
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Cited by 138 (32 self)
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. In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much smaller than in previouslyused methods. The d=dt system can, so far, treat nontrivial continuous systems, hybrid systems, convex differential inclusions and controller synthesis problems. 1 Introduction The problem of calculating reachable states for continuous and hybrid systems has emerged as one of the major problems in hybrid systems research [G96,GM98,DM98,KV97,V98,GM99,CK99,PSK99,HHMW99]. It constitutes a prerequisite for exporting algorithmic verification methodology outside discrete systems or hybrid systems with piecewisetrivial dynamics. For computer scientists it poses new challenges in treating continuous functions and their approximations and in applying computational geometry...
Effective Synthesis of Switching Controllers for Linear Systems
, 2000
"... In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the sys ..."
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Cited by 108 (8 self)
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In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the system from one "mode" to another in order to avoid a set of bad states, and propose an abstract algorithm which solves the problem by an iterative computation of reachable states. We have implemented a concrete version of the algorithm, which uses a new approximation scheme for reachability analysis of linear systems.
Reachability Analysis Using Polygonal Projections
 IN HYBRID SYSTEMS: COMPUTATION AND CONTROL
, 1999
"... Coho is a reachability analysis tool for systems modeled by nonlinear, ordinary differential equations. Coho represents highdimensional objects using projections onto planes corresponding to pairs of variables. This representation is compact and allows efficient algorithms from computational geome ..."
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Cited by 58 (5 self)
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Coho is a reachability analysis tool for systems modeled by nonlinear, ordinary differential equations. Coho represents highdimensional objects using projections onto planes corresponding to pairs of variables. This representation is compact and allows efficient algorithms from computational geometry to be exploited while also capturing dependencies in the behaviour of related variables. Reachability is performed by integration where methods from linear programming and linear systems theory are used to bound trajectories emanating from each face of the object. This paper has two contributions: first, we describe the implementation of Coho and, second, we present analysis results obtained by using Coho on several simple models.
Integrating Projections
 IN
, 1998
"... This paper describes three techniques for reachability analysis for systems modeled by ordinary differential equations (ODEs). First, linear models with regions modeled by convex polyhedra are considered, and an exact algorithm is presented. Next, nonconvex polyhedra are considered, and techniq ..."
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Cited by 46 (6 self)
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This paper describes three techniques for reachability analysis for systems modeled by ordinary differential equations (ODEs). First, linear models with regions modeled by convex polyhedra are considered, and an exact algorithm is presented. Next, nonconvex polyhedra are considered, and techniques are presented for representing a polyhedron by its projection onto twodimensional subspaces. This approach yields a compact representation, and allows efficient algorithms from computational geometry to be employed. Within this context, an approximation technique for reducing nonlinear ODE models to linear nonhomogeneous models is presented. This
Orthogonal polyhedra: Representation and computation
 Schuppen (Eds.), Hybrid Systems: Computation and Control, LNCS 1569
, 1999
"... Abstract. In this paper we investigate orthogonal polyhedra, i.e. polyhedra which are finite unions of fulldimensional hyperrectangles. We define representation schemes for these polyhedra based on their vertices, and show that these compact representation schemes are canonical for all (convex and ..."
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Cited by 42 (4 self)
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Abstract. In this paper we investigate orthogonal polyhedra, i.e. polyhedra which are finite unions of fulldimensional hyperrectangles. We define representation schemes for these polyhedra based on their vertices, and show that these compact representation schemes are canonical for all (convex and nonconvex) polyhedra in any dimension. We then develop efficient algorithms for membership, facedetection and Boolean operations for these representations. 1
Efficient computation of reachable sets of linear timeinvariant systems with inputs
 in HSCC’06, vol. 3927 in LNCS
, 2006
"... Abstract. This work is concerned with the problem of computing the set of reachable states for linear timeinvariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over ..."
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Cited by 37 (7 self)
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Abstract. This work is concerned with the problem of computing the set of reachable states for linear timeinvariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and underapproximations of the reachable sets are proposed as well. These algorithms are not subject to the wrapping effect and therefore our approximations are tight. We show that these approximations are useful in the context of hybrid systems verification and control synthesis. The performance of a prototype implementation of the algorithm confirms its qualities and gives hope for scaling up verification technology for continuous and hybrid systems. 1
Some lessons from the HyTech experience
 In Proceedings of the 40th Annual Conference on Decision and Control
, 2001
"... We provide an overview of the current status of the tool HyTech, and re ect on some of the lessons learned from our experiences with the tool. HyTech is a symbolic model checker for mixed discretecontinuous systems that are modeled as automata with piecewiseconstant polyhedral di erential inclusio ..."
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Cited by 26 (0 self)
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We provide an overview of the current status of the tool HyTech, and re ect on some of the lessons learned from our experiences with the tool. HyTech is a symbolic model checker for mixed discretecontinuous systems that are modeled as automata with piecewiseconstant polyhedral di erential inclusions. The use of a formal input language and automated procedures for statespace traversal lay the foundation for formally verifying properties of hybrid dynamical systems. We describe some recent experiences analyzing three hybrid systems. We point out the successes and limitations of the tool. The analysis procedure has been extended in a number of ways to address some of the tool's shortcomings. We evaluate these extensions, and conclude with some desiderata for veri cation tools for hybrid systems. 1
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
CircuitLevel Verification of a HighSpeed Toggle
 IEEE International Conference on Formal Methods in ComputerAided Design
, 2007
"... ..."
A Smooth Dynamical System that Counts in Binary
, 1997
"... This paper presents a smooth dynamical system that implements a toggle flipflop. The flipflop is described as a system of smooth, nonlinear ODE's. We identify a period2, invariant set of this system, and show that this corresponds to the discrete state transitions of a discrete model. We sh ..."
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Cited by 3 (1 self)
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This paper presents a smooth dynamical system that implements a toggle flipflop. The flipflop is described as a system of smooth, nonlinear ODE's. We identify a period2, invariant set of this system, and show that this corresponds to the discrete state transitions of a discrete model. We show that this behaviour is robust for a large class of inputs and that these toggle elements can be composed to implement a binary counter of any number of bits. I.