Prescribed performance control for signal temporal logic specifications

Abstract

Motivated by the recent interest in formal methods-based control for dynamic robots, we discuss the applicability of prescribed performance control to nonlinear systems subject to signal temporal logic specifications. Prescribed performance control imposes a desired transient behavior on the system trajectories that is leveraged to satisfy atomic signal temporal logic specifications. A hybrid control strategy is then used to satisfy a finite set of these atomic specifications. Simulations of a multi-agent system, using consensus dynamics, show that a wide range of specifications, i.e., formation, sequencing, and dispersion, can be robustly satisfied.y := H(y, t) with y(0) := y 0 ∈ Ω y ,

Time-constrained multi-agent task scheduling based on prescribed performance control

“…That is to say, ξ i (t), ∀i ∈ I k and ξ i j (t), ∀(i, j) ∈ E will evolve within the regions (14) and (15) for all t ≥ t k 0 . Since ξ i (t), ξ i j (t) ∈ 0, S −1 1 2V 1 (t k 0 ) , one has that ∇S 1 (ξ i ) is bounded for all i ∈ I k and ∇S 1 (ξ i j ) is bounded for all (i, j) ∈ E .…”

Decentralized Robust Control of Coupled Multi-Agent Systems under Local Signal Temporal Logic Tasks

“…To the best of our knowledge, this is the first approach not making use of such discretization in the context of formal methods-based multiagent control. This paper extends our work on single-agent systems [7] to multi-agent systems.…”

Prescribed Performance Control Guided Policy Improvement for Satisfying Signal Temporal Logic Tasks

“…Note, however, that knowledge of the term f (x) in the system dynamics (1) is not required to evaluate u φ (x, t)! In order to compute the derivative ∂ρ ψ (x)/∂x in the control law (5), [9] uses a differentiable under-approximation of the robustness associated with the conjunction of propositions: ρ ψ1∧ψ2 (x, t) ≈ − ln e −ρ ψ 1 (x,t) + e −ρ ψ 2 (x,t) . This preserves the property that a positive robustness measure ρ ψ implies satisfaction of the corresponding formula ψ.…”

“…STL task specifications have lately been studied from a control perspective in the sense of how to ensure their satisfaction. Proposed approaches for controller synthesis include model predictive control (MPC) [6], [7], barrier function- [8], and prescribed performance control (PPC)based methods [9]. These methods rely heavily on knowledge of system dynamics and exhibit a trade-off between their computational complexity and the range of system dynamics and STL task fragments they can handle.…”