Abstract-In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems.

This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing over-approximation result based on the sign-stability of the sensitivity matrices and a discrete-time approach relying on a mixed-monotonicity property. We then present a new overapproximation result which scales at worst linearly with the state dimension and is applicable to any continuous-time system with bounded sensitivity. Finally, we provide a simulationbased approach to estimate these bounds through sampling and falsification. The results are illustrated with numerical examples on traffic networks and satellite orbits.

This paper presents TIRA, a Matlab library gathering several methods for the computation of interval over-approximations of the reachable sets for both continuous-and discrete-time nonlinear systems. Unlike other existing tools, the main strength of intervalbased reachability analysis is its simplicity and scalability, rather than the accuracy of the over-approximations. The current implementation of TIRA contains four reachability methods covering wide classes of nonlinear systems, handled with recent results relying on contraction/growth bounds and monotonicity concepts. TIRA's architecture features a central function working as a hub between the user-defined reachability problem and the library of available reachability methods. This design choice offers increased extensibility of the library, where users can define their own method in a separate function and add the function call in the hub function.

This paper deals with the control synthesis problem for a continuous nonlinear dynamical system under a Linear Temporal Logic (LTL) formula. The proposed solution is a topdown hierarchical decomposition of the control problem involving three abstraction layers of the problem, iteratively solved from the coarsest to the finest. The LTL planning is first solved on a small transition system only describing the regions of interest involved in the LTL formula. For each pair of consecutive regions of interest in the resulting accepting path satisfying the LTL formula, a discrete plan is then constructed in the partitioned workspace to connect these two regions while avoiding unsafe regions. Finally, an abstraction refinement approach is applied to synthesize a controller for the dynamical system to follow each discrete plan. The second main contribution, used in the third abstraction layer, is a new monotonicity-based method to overapproximate the finite-time reachable set of any continuously differentiable system. The proposed framework is demonstrated in simulation for a motion planning problem of a mobile robot modeled as a disturbed unicycle.

International audienceThe problem considered is the temperature control in a building equipped with UnderFloor Air Distribution (UFAD). Its 0-D model is derived from the energy and mass conservation in each room, and also presents discrete components to describe the disturbances from heat sources and doors opening. Using the monotonicity of this model, we can characterize two concepts of robust control, the Robust Controllability and the Robust Controlled Invariance introduced in this paper, and determine their limits for control design objectives. The validity of these results is then illustrated in a simulation of a two-room example