Decentralized Control Barrier Functions for Coupled Multi-Agent Systems under Signal Temporal Logic Tasks

Abstract

We study the problem of controlling multi-agent systems under a set of signal temporal logic tasks. Signal temporal logic is a formalism that is used to express time and space constraints for dynamical systems. Recent methods to solve the control synthesis problem for single-agent systems under signal temporal logic tasks are, however, subject to a high computational complexity. Methods for multi-agent systems scale at least linearly with the number of agents and induce even higher computational burdens. We propose a computationallyefficient control strategy to solve the multi-agent control synthesis problem that results in a robust satisfaction of a set of signal temporal logic tasks. In particular, a decentralized feedback control law is proposed that is based on time-varying control barrier functions. The obtained control law is discontinuous and formal guarantees are provided by nonsmooth analysis. Simulations show the efficacy of the presented method.

Disturbance Bounds for Signal Temporal Logic Task Satisfaction: A Dynamics Perspective

“…Over 1000 simulated Segway runs where disturbances are sampled randomly from within our prescribed norm-bound, we show that the Segway-controller pair rejects disturbances within our identified bound and achieves its Signal Temporal Logic task. For context, the subset of STL tasks studied in the sequel is consistent with prior works in the controls literature [9], [10], [24]. Organization: Section II details some background material in Subsection II-A, motivates our problem in Subsection II-B, and formally states our problem in Subsection II-C. Then, Section III details our main contributions -the optimization problems determining two-norm disturbance-bounds rejectable by a system's controller.…”

“…Here, we note that our restriction to this specific subclass of STL specifications aligns with prior work coupling Signal Temporal Logic and control barrier functions (see the examples in [9]- [11], [24]). We will also make one fairness assumption -that the intervals of existence for solutions to either system (CL) or (CL-d) are sufficiently large enough to permit analysis as to whether they satisfy their STL specification.…”

Adversarial Resilience for Sampled-Data Systems Under High-Relative-Degree Safety Constraints

“…When all agents behave normally, methods exist for agents to locally solve for appropriate local control inputs that together satisfy the condition in (3) (e.g. [29]).…”

“…Theorem 2. Consider the system (1) with sampling times described by (29). If at sampling time t k i for k ≥ 0, i ∈ N it holds that x ki ∈ S, then for any…”

“…Proof. Choose any i ∈ N and consider the time interval (29) and the definition of δ max . In particular, this implies…”