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Distributed Control for Spatio-Temporally Constrained Systems

Time: Thu 2023-06-08 15.00

Location: Harry Nyquist, Malvinas väg 10, Stockholm

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Language: English

Doctoral student: Adrian Wiltz , Reglerteknik

Opponent: Professor Matthias Müller, Leibniz Universität Hannover

Supervisor: Dimos V. Dimarogonas, Reglerteknik; Jonas Mårtensson, Reglerteknik

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QC 20230520


In this thesis, we develop methods leading towards the distributed control of spatio-temporally constrained systems. Overall, we focus on two different approaches: a model predictive control approach and an approach based on ensuring set-invariance via control barrier functions. Developing a distributed control framework for spatio-temporally constrained systems is challenging since multiple subsystems are interconnected via time-varying state constraints. Often, such constraints are only implicitly given as logic formulas, for example in Signal Temporal Logic (STL).

Our approach to dealing with spatio-temporal constraints is as follows. We aim at combining the computational efficiency of low-level feedback controllers with planning algorithms. Low-level feedback controllers shall ensure the satisfaction of parts of spatio-temporal constraints such as coupling state constraints or short term time-constraints. In contrast, planning algorithms account for those parts that require computationally intense planning operations. Powerful low-level controllers can simplify the planning task significantly. For this reason, the focus of this thesis is on the development of low level feedback controllers. 

In the first part, we focus on handling coupling state constraints using a model predictive control (MPC) approach. Commonly, the distributed handling of coupling state constraints requires a sequential or iterative MPC scheme which however is computationally time-intense. We address this issue by employing consistency constraints to develop a parallelized distributed model predictive controller (DMPC). By using consistency constraints, each subsystem guarantees to its neighbors that its states stay within a particular neighborhood around a reference trajectory. Furthermore, we propose extensions to robust and iterative schemes. Building up on this, also systems with bounded dynamic couplings can be controlled.

In the second part, we focus on methods for ensuring set-invariance. In particular, we focus on control barrier functions (CBF). We show how spatio-temporal constraints that comprise disjunctions (logic OR) can be encoded in non-smooth time-varying control barrier functions and how subgradients can be used to synthesize an efficient gradient-based controller. For these results, controllability assumptions must be invoked. To extend the results to systems with weaker controllability properties, we investigate the connection between controllability properties and the construction of CBFs. As a result, we propose a construction method for CBFs based on finite horizon predictions. The constructed CBF exhibits favorable properties for the extension of the previous results on encoding spatio-temporal constraints in CBFs to systems with weaker controllability properties. At last, we investigate with a case study how set-invariance methods can be used to implicitly coordinate systems subject to coupled state constraints. Our proposed method is fully decentralized and subsystems coordinate themselves purely via their actions and the adjustment of their individual constraints.

In the end, we draw a conclusion and outline how the presented results contribute to the development of a distributed control framework for spatio-temporally constrained systems.