Feedback Refinement Relations for the Synthesis of Symbolic Controllers
Reads0
Chats0
TLDR
This work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances.Abstract:
We present an abstraction and refinement methodology for the automated controller synthesis to enforce general predefined specifications. The designed controllers require quantized (or symbolic) state information only and can be interfaced with the system via a static quantizer. Both features are particularly important with regard to any practical implementation of the designed controllers and, as we prove, are characterized by the existence of a feedback refinement relation between plant and abstraction. Feedback refinement relations are a novel concept introduced in this paper. Our work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances. We identify a class of abstractions that is canonical in a well-defined sense, and provide a method to efficiently compute canonical abstractions. We demonstrate the practicality of our approach on two examples.read more
Citations
More filters
Proceedings ArticleDOI
SCOTS: A Tool for the Synthesis of Symbolic Controllers
Matthias Rungger,Majid Zamani +1 more
TL;DR: SCOTS a software tool for the automatic controller synthesis for nonlinear control systems based on symbolic models, also known as discrete abstractions, which natively provides algorithms to synthesize controllers with respect to invariance and reachability specifications.
Journal ArticleDOI
Compositional Abstraction and Safety Synthesis Using Overlapping Symbolic Models
TL;DR: In this article, a compositional approach to abstraction and safety synthesis for a general class of discrete-time nonlinear systems is presented, which makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they share some common state variables.
Proceedings ArticleDOI
Multi-Layered Abstraction-Based Controller Synthesis for Continuous-Time Systems
TL;DR: It is empirically demonstrate that multi-layered synthesis can outperform standard (single-layer) ABCS algorithms on a number of examples, despite the additional cost of constructing multiple abstract systems.
Journal ArticleDOI
Compositional Synthesis of Finite-State Abstractions
TL;DR: It is shown how networks of incrementally input-to-state stable, nonlinear, continuous-time control systems can be abstracted compositionally, so that all local abstractions are simultaneously disturbance bisimilar to their continuous counterparts.
Journal ArticleDOI
Formal Methods for Control of Traffic Flow: Automated Control Synthesis from Finite-State Transition Models
TL;DR: This work states that the next generation of transportation systems will include connected vehicles, connected infrastructure, and increased automation, and these advances must coexist with legacy technology into the foreseeable future.
References
More filters
Proceedings ArticleDOI
Approximately bisimilar abstractions of incrementally stable finite or infinite dimensional systems
TL;DR: The first result states that the sampled dynamics of an incrementally stable dynamical system is approximately bisimilar to a family of finite dimensional systems; this is of particular interest for infinite dimensional dynamical systems.
Proceedings ArticleDOI
Monotonic reach control on polytopes
TL;DR: It is shown that, generically,solvability via arbitrary triangulations is equivalent to monotonic solvability, and this provides an avenue for reach control on polytopes that does not depend on the choice of triangulation of the polytope.
Proceedings ArticleDOI
On the construction of in-block controllable covers of nonlinear systems on polytopes
Mohamed K. Helwa,Peter E. Caines +1 more
TL;DR: This paper studies how to systematically construct polytopic covers of the given polytope such that the affine systems, resulting from the linearization of the nonlinear system inside the polytopic regions of the cover, are in-block controllable.
Journal ArticleDOI
Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems
Alexander Weber,Gunther Reissig +1 more
TL;DR: In this article, sufficient and necessary conditions for convexity and strong convexness of connected sublevel sets that are defined by finitely many real-valued maps are presented.
Journal ArticleDOI
Abstraction-Based Control for Not Necessarily Closed Behaviours
TL;DR: In this paper, the authors address abstraction-based supervisory control for plant and specification behaviours that are not necessarily ω-closed and identify a controllability condition for the plant, that ensures a nonblocking closed-loop behaviour with a controller that has been obtained for a plant abstraction.