We present necessary and sufficient conditions for reachable sets of discrete-time systems x(k+1) = F (k, x(k)) to be convex. In particular, the set of states reachable at a given time from a sufficiently small ellipsoid of initial states is always convex if F is smooth enough, and we provide explicit bounds on the size of those ellipsoids. Our results imply that outer discrete approximations w...

This paper presents an approach to compute conservative approximations to the set of reachable states and outputs for affine systems using -decomposition techniques. Instead of performing reachability analysis on the full-order system model, the method presented in this paper first applies -decomposition to obtain a number of -coupled subsystem models, and then performs reachability analysis on...

We present a necessary and sufficient condition for the reachable set, i.e., the set of states reachable from a ball of initial states at some time, of an ordinary differential equation to be convex. In particular, convexity is guaranteed if the ball of initial states is sufficiently small, and we provide an upper bound on the radius of that ball, which can be directly obtained from the right h...

When rewriting a regular language with a left-linear term rewriting system, if the set of reachable terms is regular, we show that equational tree automata completion can compute it. This was known to be true for some known TRS classes preserving regularity, but was still an open question in the general case. The proof is not constructive: it assumes that the set of reachable terms is regular, ...

As the key step in verifying hybrid systems, the computation of reachable sets largely determines the complexity and thus the applicability of a verification approach. Most existing methods compute the reachable set without considering the specification to be verified. This paper presents an approach that identifies for abstractions of the hybrid model those behaviors that potentially violate t...

Set sharing is an abstract domain in which each concrete object is represented by the set of local variables from which it might be reachable. It is a useful abstraction to detect parallelism opportunities, since it contains definite information about which variables do not share in memory, i.e., about when the memory regions reachable from those variables are disjoint. Set sharing is a more pr...

Amethod for thenumerical computation of reachable sets for hybrid systems is presented andapplied to thedesign and safety analysis of autoland systems. It is shown to be applicable to specific phases of landing: descent, flare, and touchdown. The method is based on optimal control and level set methods; it simultaneously computes a maximal controlled invariant set and a set-valued control law g...

Timed reachability analysis of gate-level circuits is important in several applications. In this paper, we present techniques for efficient approximate symbolic reachability of circuits assuming discrete delays of gates. We exploit local interactions among gates to develop a highly scalable algorithm for over-approximating the set of timed reachable states. We present a scheme of successive ove...

This paper presents the analysis method of quasi-LPV models, comparing the ellipsoid set which contains the reachable set of a nonlinear system to de ne which quasi-LPV model is less conservative to represent the nonlinear dynamics. Three quasi-LPV models are constructed from a nonlinear model using three di erent methods, to facilitate synthesis of an LPV controller for the nonlinear system. T...

Abstract: We present a set of methods for the verification and control of continuous and hybrid systems, based on the use of individual trajectories. In the first part, we specify the class of the systems considered and their properties. We start from continuous systems governed by ordinary differential equations to which we add inputs and discrete events, thus constituting a class of hybrid dy...