A Symbolic Approach to the Self-Triggered Design for Networked Control Systems

Abstract

In this paper, we investigate novel self-triggered controllers for nonlinear control systems with reachability and safety specifications. To synthesize the self-triggered controller, we leverage the notion of symbolic models, or abstractions, which represent abstracted expressions of control systems. The symbolic models will be constructed through the concepts of approximate alternating simulation relations, based on which, and by employing a reachability game, the self-triggered controller is synthesized. We illustrate the effectiveness of the proposed approach through numerical simulations.

Fast Synthesis for Symbolic Self-triggered Control under Right-recursive LTL Specifications

“…Self-triggered control has been increasingly attracting attention from academia and has proven to be a practical control approach, especially for networked control systems [1], [2], [3], [4]. Unlike conventional periodic control schemes, self-triggered control is a proactive control paradigm with a triggering mechanism that prescribes a time when the control signal has to be updated.…”

“…However, previous self-triggered control studies focus on stability [1], [5], consensus [4], and reachability or safety [2] problems. To extend self-triggered control to complex specifications such as temporal logic, we consider symbolic control, which is an abstraction-based control approach that constructs a discrete abstraction of the continuous system, then synthesises a discrete controller that can be refined to a controller for the original system in a sound way [6], [7], [8], [9], [10].…”

“…The first symbolic self-triggered control approach was introduced in [2] for discrete-time deterministic nonlinear systems under reach-avoid specifications. It was developed in the symbolic control framework for nonlinear systems without stability assumptions proposed in [6].…”

“…It was developed in the symbolic control framework for nonlinear systems without stability assumptions proposed in [6]. Our previous work in [11] extended the concept in [2] to the control of continuous-time non-deterministic nonlinear systems for 2-LTL specifications: a subclass of Linear Temporal Logic (LTL) specifications that is strictly more expressive than reach-avoid. Our control objective is to: 1) control the system to satisfy the given 2-LTL formula and 2) restrict the limit average control-signal length to stay above a given threshold.…”

“…Dealing with Until heavily increases non-determinism in the mean-payoff parity game. Moreover, unlike previous self-triggered control works that consider constant control signals of different lengths in a sample-and-hold manner [1], [2], we consider piecewiseconstant control signals, resulting in a far larger set of control signals choices. For these reasons, we develop a heuristic pruning method to speed up the computation.…”