Results 11  20
of
62
Nonlinear Systems: Approximating Reach Sets
, 2004
"... We describe techniques to generate useful reachability information for nonlinear dynamical systems. These techniques can be automated for polynomial systems using algorithms from computational algebraic geometry. The generated information can be incorporated into other approaches for doing reachab ..."
Abstract

Cited by 39 (6 self)
 Add to MetaCart
We describe techniques to generate useful reachability information for nonlinear dynamical systems. These techniques can be automated for polynomial systems using algorithms from computational algebraic geometry. The generated information can be incorporated into other approaches for doing reachability computation. It can also be used when abstracting hybrid systems that contain modes with nonlinear dynamics. These techniques are most naturally embedded in the hybrid qualitative abstraction approach proposed by the authors previously. They also show that the formal qualitative abstraction approach is well suited for dealing with nonlinear systems.
Progress on Reachability Analysis of Hybrid Systems Using Predicate Abstraction
 in Hybrid Systems: Computation and Control, LNCS 2623
, 2003
"... Predicate abstraction has emerged to be a powerful technique for extracting nitestate models from in nitestate systems, and has been recently shown to enhance the eectiveness of the reachability computation techniques for hybrid systems. Given a hybrid system with linear dynamics and a set o ..."
Abstract

Cited by 39 (5 self)
 Add to MetaCart
(Show Context)
Predicate abstraction has emerged to be a powerful technique for extracting nitestate models from in nitestate systems, and has been recently shown to enhance the eectiveness of the reachability computation techniques for hybrid systems. Given a hybrid system with linear dynamics and a set of linear predicates, the veri er performs an onthey search of the nite discrete quotient whose states correspond to the truth assignments to the input predicates. To compute the transitions out of an abstract state, the tool needs to compute the set of discrete and continuous successors, and nd out all the abstract states that this set intersects with. The complexity of this computation grows exponentially with the number of abstraction predicates. In this paper we present various optimizations that are aimed at speeding up the search in the abstract statespace, and demonstrate their bene ts via case studies.
Automated Symbolic Reachability Analysis; with Application to DeltaNotch Signaling Automata
 Lecture Notes in Computer Science
, 2003
"... This paper describes the implementation of predicate abstraction techniques to automatically compute symbolic backward reachable sets of high dimensional piecewise a#ne hybrid automata, used to model DeltaNotch biological cell signaling networks. These automata are analyzed by creating an abstr ..."
Abstract

Cited by 38 (2 self)
 Add to MetaCart
(Show Context)
This paper describes the implementation of predicate abstraction techniques to automatically compute symbolic backward reachable sets of high dimensional piecewise a#ne hybrid automata, used to model DeltaNotch biological cell signaling networks. These automata are analyzed by creating an abstraction of the hybrid model, which is a finite state discrete transition system, and then performing the computation on the abstracted system. All the steps, from model generation to the simplification of the reachable set, have been automated using a variety of decision procedure and theoremproving tools. The concluding example computes the reach set for a four cell network with 8 continuous and 256 discrete states. This demonstrates the feasibility of using these tools to compute on high dimensional hybrid automata, to provide deeper insight into realistic biological systems.
M.: Verification of hybrid systems based on counterexampleguided abstraction refinement. In: Technical Report. (2002) Downloadable from http://www.cs.cmu.edu
 In: HSCC. LNCS 1569
, 1999
"... Abstract. Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finitestate abstraction. Model checking can be inconclusive, however, in which ..."
Abstract

Cited by 38 (6 self)
 Add to MetaCart
(Show Context)
Abstract. Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finitestate abstraction. Model checking can be inconclusive, however, in which case the abstraction must be refined. This paper presents a new procedure to perform this refinement operation for abstractions of infinitestate systems, in particular of hybrid systems. Following an approach originally developed for finitestate systems [1, 2], the refinement procedure constructs a new abstraction that eliminates a counterexample generated by the model checker. For hybrid systems, analysis of the counterexample requires the computation of sets of reachable states in the continuous state space. We show how such reachability computations with varying degrees of complexity can be used to refine hybrid system abstractions efficiently. A detailed example illustrates our counterexampleguided refinement procedure. Experimental results for a prototype implementation of the procedure indicate its advantages over existing methods. 1
Reachability analysis of multiaffine systems
 In Hybrid Systems: Computation and Control, LNCS 3927
, 2006
"... Abstract We present a computationally attractive technique to study the reachability of rectangular regions by trajectories of continuous multiaffine systems. The method is iterative. At each step, finer partitions and finite quotients that overapproximate the reachability properties of the initi ..."
Abstract

Cited by 31 (4 self)
 Add to MetaCart
(Show Context)
Abstract We present a computationally attractive technique to study the reachability of rectangular regions by trajectories of continuous multiaffine systems. The method is iterative. At each step, finer partitions and finite quotients that overapproximate the reachability properties of the initial system are produced. We exploit some convexity properties of multiaffine functions on rectangles to show that the construction of the quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. This methodology can be used for formal analysis of biochemical networks, aircraft and underwater vehicles, where multiaffine models are widely used.
Recent progress in continuous and hybrid reachability analysis
 In Proc. IEEE International Symposium on ComputerAided Control Systems Design. IEEE Computer
, 2006
"... Abstract — Setbased reachability analysis computes all possible states a system may attain, and in this sense provides knowledge about the system with a completeness, or coverage, that a finite number of simulation runs can not deliver. Due to its inherent complexity, the application of reachabilit ..."
Abstract

Cited by 30 (1 self)
 Add to MetaCart
(Show Context)
Abstract — Setbased reachability analysis computes all possible states a system may attain, and in this sense provides knowledge about the system with a completeness, or coverage, that a finite number of simulation runs can not deliver. Due to its inherent complexity, the application of reachability analysis has been limited so far to simple systems, both in the continuous and the hybrid domain. In this paper we present recent advances that, in combination, significantly improve this applicability, and allow us to find better balance between computational cost and accuracy. The presentation covers, in a unified manner, a variety of methods handling increasingly complex types of continuous dynamics (constant derivative, linear, nonlinear). The improvements include new geometrical objects for representing sets, new approximation schemes, and more flexible combinations of graphsearch algorithm and partition refinement. We report briefly some preliminary experiments that have enabled the analysis of systems previously beyond reach. I.
Dealing with nondeterminism in symbolic control,”
 in Proc HSCC, ser. LNCS.
, 2008
"... Abstract. Abstractions (also called symbolic models) are simple descriptions of continuous and hybrid systems that can be used in analysis and control. They are usually constructed in the form of transition systems with finitely many states. Such abstractions offer a very attractive approach to dea ..."
Abstract

Cited by 19 (12 self)
 Add to MetaCart
(Show Context)
Abstract. Abstractions (also called symbolic models) are simple descriptions of continuous and hybrid systems that can be used in analysis and control. They are usually constructed in the form of transition systems with finitely many states. Such abstractions offer a very attractive approach to deal with complexity, while at the same time allowing for rich specification languages. Recent results show that, through the abstraction process, the resulting transition systems can be nondeterministic (i.e., if an input is applied in a state, several next states are possible). However, the problem of controlling a nondeterministic transition system from a rich specification such as a temporal logic formula is not well understood. In this paper, we develop a control strategy for a nondeterministic transition system from a specification given as a Linear Temporal Logic formula with a deterministic Büchi generator. Our solution is inspired by LTL games on graphs, is complete, and scales polynomially with the size of the Büchi automaton. An example of controlling a linear system from a specification given as a temporal logic formula over the regions of its triangulated state space is included for illustration.
Approximate bisimulation relations for constrained linear systems
 AUTOMATICA
, 2007
"... In this paper, we define the notion of approximate bisimulation relation between two systems, extending the well established exact bisimulation relations for discrete and continuous systems. Exact bisimulation requires that the observations of two systems are and remain identical, approximate bisi ..."
Abstract

Cited by 18 (5 self)
 Add to MetaCart
In this paper, we define the notion of approximate bisimulation relation between two systems, extending the well established exact bisimulation relations for discrete and continuous systems. Exact bisimulation requires that the observations of two systems are and remain identical, approximate bisimulation allows the observation to be different provided they are and remain arbitrarily close. Approximate bisimulation relations are conveniently defined as level sets of a function called bisimulation function. For the class of linear systems with constrained initial states and constrained inputs, we develop effective characterizations for bisimulation functions that can be interpreted in terms of linear matrix inequalities, set inclusion and games. We derive a computationally effective algorithm to evaluate the precision of the approximate bisimulation between a constrained linear system and its projection. This algorithm has been implemented in a MATLAB toolbox: MATISSE. Two examples of use of the toolbox in the context of safety verification are shown.
Verification of a Cruise Control System Using CounterexampleGuided Search
, 2003
"... Formal verification has been identified by the research community as a useful step in logic controller design since it reveals algorithmically whether the controller in conjunction with the controlled plant satisfies given design specifications. If it is necessary, however, to model the continuous/h ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
Formal verification has been identified by the research community as a useful step in logic controller design since it reveals algorithmically whether the controller in conjunction with the controlled plant satisfies given design specifications. If it is necessary, however, to model the continuous/hybrid behavior of the plant, the verification is a computationally expensive task, thus limiting its applicability to rather small systems. This paper shows for the example of a cruise control system that the recently proposed approach of counterexampleguided verification can reduce the computational costs considerably. The method generates a sequence of abstractions, for which those behaviors (the counterexamples) are identified that potentially violate the specifications. The paper presents a tailormade sequence of validation methods that aim at checking the existence of these behaviors for the hybrid model of the controlled plant with as small computational costs as possible. As is shown for the cruise control system, the iteration consisting of counterexample generation, validation, and model refinement checks the specification while computing only a relatively small portion of the continuous reachable set. Since determining reachable sets is the most costly step in existing approaches, the overall e#ort is found to be much smaller in many cases.