Skip to main content

Control of Dynamical Systems subject to Spatio-Temporal Constraints

Time: Fri 2022-04-01 10.00

Location: Q2, Malvinas väg 10, Stockholm

Video link: link for online defense

Language: English

Subject area: Electrical Engineering

Doctoral student: Maria Charitidou , Reglerteknik

Opponent: Professor Christian Ebenbauer,

Supervisor: Dimos V. Dimarogonas, Reglerteknik

QC 20220311


Over the last decades, autonomous robots have been considered in a variety of applications such  as persistent monitoring, package delivery and cooperative transportation. These applications often require the satisfaction of a set of complex tasks that need to be possibly performed in a timely manner. For example, in search and rescue missions, UAVs are expected to cover a set of regions within predetermined time intervals in order to increase the probability of identifying the victims of an accident. Spatio-temporal tasks of this form can be easily expressed in Signal Temporal Logic (STL), a predicate language that allow us to formally introduce time-constrained tasks such as visit area A between 0 and 5 min or robot 1 should move in a formation with robot 2 until robot 1 reaches region B between 5 and 20 sec.

Existing approaches in control under spatio-temporal tasks encode the STL constraints using mixed-integer expressions. In the majority of these works, receding horizon schemes are designed and long planning horizons are considered that depend on the temporal constraints of the STL tasks. As a result, the complexity of these problems may increase with the number of the tasks or the length of the time interval within which a STL task needs to be satisfied. Other approaches, consider a limited STL fragment and propose computationally efficient feedback controllers that ensure the satisfaction of the STL task with a minimum, desired robustness. Nevertheless, these approaches do not consider actuation limitations that are always present in real-world systems and thus, yield controllers of arbitrarily large magnitude. 

In this thesis, we consider the control problem under spatio-temporal constraints for systems that are subject to actuation limitations. In the first part, receding horizon control schemes (RHS) are proposed that ensure the satisfaction or minimal violation of a given set of STL tasks. Contrary to existing approaches, the planning horizon of the RHS scheme can be chosen independent of the STL task and hence, arbitrarily small, given the initial feasibility of the problem. Combining the advantages of the RHS and feedback strategies, we encode the STL tasks using control barrier functions that are designed either online or offline and design controllers that aim at maximizing the robustness of the STL task. The recursive feasibility property of the framework is established and a lower bound on the violation of the STL formula is derived.

In the next part, we consider a multi-agent system that is subject to a STL task whose satisfaction may involve a large number of agents in the team. Then, the goal is to decompose the global task into local ones the satisfaction of each one of which  depends only on a given sub-team of agents. The proposed decomposition method enables the design of decentralized controllers under local STL tasks avoiding unnecessary communication among agents.  In the last part of the thesis, the coordination problem of multiple platoons is considered and related tasks such as splitting, merging and distance maintenance are expressed as Signal Temporal Logic tasks. Then, feedback control techniques are employed ensuring the satisfaction the STL formula, or alternatively minimal violation in presence of actuation limitations.