10 research outputs found
Symbolic models for nonlinear control systems without stability assumptions
Finite-state models of control systems were proposed by several researchers
as a convenient mechanism to synthesize controllers enforcing complex
specifications. Most techniques for the construction of such symbolic models
have two main drawbacks: either they can only be applied to restrictive classes
of systems, or they require the exact computation of reachable sets. In this
paper, we propose a new abstraction technique that is applicable to any smooth
control system as long as we are only interested in its behavior in a compact
set. Moreover, the exact computation of reachable sets is not required. The
effectiveness of the proposed results is illustrated by synthesizing a
controller to steer a vehicle.Comment: 11 pages, 2 figures, journa
Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach
In this paper, we present some preliminary results for compositional analysis
of heterogeneous systems containing both discrete state models and continuous
systems using consistent notions of dissipativity and passivity. We study the
following problem: given a physical plant model and a continuous feedback
controller designed using traditional control techniques, how is the
closed-loop passivity affected when the continuous controller is replaced by a
discrete (i.e., symbolic) implementation within this framework? Specifically,
we give quantitative results on performance degradation when the discrete
control implementation is approximately bisimilar to the continuous controller,
and based on them, we provide conditions that guarantee the boundedness
property of the closed-loop system.Comment: This is an extended version of our IEEE CDC 2015 paper to appear in
Japa
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
Formal Controller Synthesis from Specifications Given by Discrete-Time Hybrid Automata
This paper deals with formal controller synthesis for discrete-time dynamical systems. For a specification under the form of a discrete-time hybrid automaton, we aim at synthesizing controllers such that the trajectories of the closed-loop system are also trajectories of the hybrid automaton. We first show that the existence of an alternating simulation relation from the specification to the open-loop system is a necessary and sufficient condition for the existence of such controllers. Then, we propose an approach based on the use of symbolic (i.e. finite-state) abstractions of both the system and the specification. Effective computations are discussed for systems that are monotone and for specifications given by piecewise affine hybrid automata. We extend our approach to handle specifications with additional safety or reachability requirements. Finally, we illustrate our approach with examples from autonomous vehicle control