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- Goran Frehse, Colas Le Guernic, +7 authors Oded Maler
- CAV
- 2011

We present a scalable reachability algorithm for hybrid systems with piecewise affine, non-deterministic dynamics. It combines poly-hedra and support function representations of continuous sets to compute an over-approximation of the reachable states. The algorithm improves over previous work by using variable time steps to guarantee a given local error… (More)

- Antoine Girard, George J. Pappas
- IEEE Trans. Automat. Contr.
- 2007

Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In this paper, we develop the first framework of system… (More)

- Antoine Girard
- HSCC
- 2005

We present a method for the computation of reachable sets of uncertain linear systems. The main innovation of the method consists in the use of zonotopes for reachable set representation. Zonotopes are special polytopes with several interesting properties : they can be encoded efficiently, they are closed under linear transformations and Minkowski sum. The… (More)

- Georgios E. Fainekos, Antoine Girard, Hadas Kress-Gazit, George J. Pappas
- Automatica
- 2009

In this paper, we address the temporal logic motion planning problem for mobile robots that are modeled by second order dynamics. Temporal logic specifications can capture the usual control specifications such as reachability and invariance as well as more complex specifications like sequencing and obstacle avoidance. Our approach consists of three basic… (More)

- Antoine Girard, George J. Pappas
- Automatica
- 2009

In this paper, we present a new approach for hierarchical control based on the recent notions of approximate simulation and simulation functions, a quantitative version of the simulation relations. Given a complex system that needs to be controlled and a simpler abstraction, we show how the knowledge of a simulation function allows us to synthesize… (More)

- Antoine Girard, Giordano Pola, Paulo Tabuada
- HSCC
- 2008

Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make similar progress with respect to different , and perhaps… (More)

- Giordano Pola, Antoine Girard, Paulo Tabuada
- Automatica
- 2008

Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they are less suitable to describe software and hardware interfacing the physical world. For this reason there is a growing… (More)

- Antoine Girard, George J. Pappas
- 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 bisimulation allows the observation to be different provided they… (More)

- Antoine Girard, Colas Le Guernic, Oded Maler
- HSCC
- 2006

This work is concerned with the problem of computing the set of reachable states for linear time-invariant 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 under-approximations of the reachable sets are proposed as well.… (More)

- Antoine Girard, George J. Pappas
- HSCC
- 2006

Verification and simulation have always been complementary , if not competing, approaches to system design. In this paper, we present a novel method for so-called metric transition systems that bridges the gap between verification and simulation, enabling system verification using a finite number of simulations. The existence of metrics on the system state… (More)