Funnel control for fully actuated systems under a fragment of signal temporal logic specifications

Abstract

Temporal logics have lately proven to be a valuable tool for various control applications by providing a rich specification language. Existing temporal logic-based control strategies discretize the underlying dynamical system in space and/or time. We will not use such an abstraction and consider continuous-time systems under a fragment of signal temporal logic specifications by using the associated robust semantics. In particular, this paper provides computationally-efficient funnel-based feedback control laws for a class of systems that are, in a sense, feedback equivalent to single integrator systems, but where the dynamics are partially unknown for the control design so that some degree of robustness is obtained. We first leverage the transient properties of a funnel-based feedback control strategy to maximize the robust semantics of some atomic temporal logic formulas. We then guarantee the satisfaction for specifications consisting of conjunctions of such atomic temporal logic formulas with overlapping time intervals by a suitable switched control system. The result is a framework that satisfies temporal logic specifications with a user-defined robustness when the specification is satisfiable. When the specification is not satisfiable, a least violating solution can be found. The theoretical findings are demonstrated in simulations of the nonlinear Lotka–Volterra equations for predator–prey models.