Resilient and Effort-Optimal Controller Synthesis under Temporal Logic Specifications

TL;DR

This paper develops methods for synthesizing controllers that optimize resilience and effort for systems satisfying temporal logic specifications, balancing robustness and input constraints.

Contribution

It introduces a new effort metric and formulates a robust optimization framework for controller synthesis considering resilience and effort trade-offs.

Findings

Exact solutions for linear systems with polytopic specifications.

Probabilistic guarantees for nonlinear systems using scenario optimization.

Case studies demonstrating theoretical results.

Abstract

In this paper, we consider the notions of effort and resilience of a dynamical control system defined by the maximum disturbance the system can withstand while satisfying given finite temporal logic specifications. Given a dynamical system and a specification, the objective is to synthesize the controller such that the system satisfies the specification while maximizing its resilience, taking into account input constraints. In addition, we introduce a new metric, called the effort metric, which characterizes the minimal input bound necessary to satisfy a given specification for a perturbed system. The problem for both metrics is formulated as a robust optimization program where the objective is to compute the maximum resilience for the system with input constraints or the minimal effort while simultaneously synthesizing the corresponding controller parameters. Moreover, we study the trade-off between resilience and effort, where we seek to maximize resilience and minimize the control effort. For linear systems and linear controllers, exact solutions are provided for the class of time-varying polytopic specifications for the closed-loop and open-loop systems. For the case of nonlinear systems, nonlinear controllers, and more general specifications, we leverage tools from the scenario optimization approach, offering a probabilistic guarantee of the solution as well as computational feasibility. Different case studies are presented to illustrate the theoretical results.