Robust and Abstraction-free Control of Dynamical Systems under Signal Temporal Logic Tasks

Abstract: Dynamical systems that provably satisfy given specifications have become increasingly important in many engineering areas. For instance, safety-critical systems such as human-robot networks or autonomous driving systems are required to be safe and to also satisfy some complex specifications that may include timing constraints, i.e., when or in which order some tasks should be accomplished. Temporal logics have recently proven to be a valuable tool for these control systems by providing a rich specification language. Existing temporal logic-based control approaches discretize the underlying dynamical system in space and/or time, which is commonly referred to as the abstraction process. In other words, the continuous dynamical system is abstracted into a finite system representation, e.g., into a finite state automaton. Such approaches may lead to high computational burdens due to the curse of dimensionality, which makes it hard to use them in practice. Especially with respect to multi-agent systems, these methods do not scale computationally when the number of agents increases. We will address this open research question by deriving abstraction-free control methods for single- and multi-agent systems under signal temporal logic tasks. Another aim of this research is to consider robustness, which is partly taken care of by the robust semantics admitted by signal temporal logic as well as by the robustness properties of the derived control methods. In this work, we propose computationally-efficient frameworks that deal with the aforementioned problems for single- and multi-agent systems by using feedback control strategies such as optimization-based techniques, prescribed performance control, and control barrier functions in combination with hybrid systems theory that allows us to model some higher level decision-making. In each of these approaches, the temporal properties of the employed control methods are used to impose a temporal behavior on the closed-loop system dynamics, which eventually results in the satisfaction of the signal temporal logic task. With respect to the multi-agent case, we consider a bottom-up approach where each agent is subject to a local (individual) task. These tasks may depend on the behavior of other agents. Hence, the multi-agent system is subject to couplings induced on the task level as well as on the dynamical level. The main challenge then is to deal with these couplings and derive control methods that can still satisfy the given tasks or alternatively result in least violating solutions. The efficacy of the theoretical findings is demonstrated in simulations of single- and multi-agent systems under complex specifications.