Compositional abstraction and safety synthesis using overlapping symbolic models

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

Approximately Optimal Controllers for Quantitative Two-Phase Reach-Avoid Problems on Nonlinear Systems

The present work deals with quantitative two-phase reach-avoid problems on nonlinear control systems. This class of optimal control problem requires the plant's state to visit two (rather than one) target sets in succession while minimizing a prescribed cost functional. As we illustrate, the naive approach, which subdivides the problem into the two evident classical reach-avoid tasks, usually does not result in an optimal solution. In contrast, we prove that an optimal controller is obtained by consecutively solving two special quantitative reach-avoid problems. In addition, we present a fully-automated method based on Symbolic Optimal Control to practically synthesize for the considered problem class approximately optimal controllers for sampled-data nonlinear plants. Experimental results on parcel delivery and on an aircraft routing mission confirm the practicality of our method.Comment: 14 pages, 7 figure