Ensuring constraint satisfaction in large-scale systems with hard constraints is vital in many safety critical systems. The challenge is to design controllers that are efficiently synthesized offline, easily implementable online, and provide formal correctness guarantees. We take a divide and conquer approach to design controllers for reachability and infinite-time/finite-time constraint satisfaction control problems given large-scale interconnected linear systems with polyhedral constraints on states, controls, and disturbances. Such systems are made of small subsystems with coupled dynamics. Our goals are to design controllers that are i) fully compositional and ii) decentralized, such that online implementation requires only local state information.
We treat the couplings among the subsystems as additional disturbances and use assume-guarantee (AG) contracts to characterize these disturbance sets. For each subsystem, we design and implement a robust controller locally, subject to its own constraints and contracts. Our main contribution is a method to derive the contracts via a novel parameterization, and a corresponding potential function that characterizes the distance to the correct composition of controllers and contracts, where all contracts are held. We show that the potential function is convex in the contract parameters. This enables the subsystems to negotiate the contracts with the gradient information from the dual of their local synthesis optimization problems in a distributed way, facilitating compositional control synthesis that scales to large systems.
We then incorporate Signal Temporal Logic (STL) specifications into our formulation. We develop a decentralized control method for a network of perturbed linear systems with dynamical couplings subject to STL specifications. We first transform the STL requirements into set containment problems, then we develop controllers to solve these problems. The set containment requirements and parameterized contracts are added to the subsystems’ constraints. We introduce a centralized optimization problem to derive the contracts, reachability tubes, and decentralized closed-loop control laws. We show that, when the STL formula is separable with respect to the subsystems, the centralized optimization problem can be solved in a distributed way, which scales to large systems. We present formal theoretical guarantees on robustness of STL satisfaction.
We present numerical examples, including scalability studies on systems with tens of thousands of dimensions, and case studies on applying our method to a distributed Model Predictive Control (MPC) problem in a power system. / 2024-01-16T00:00:00Z
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/45468 |
| Date | 17 January 2023 |
| Creators | Ghasemi, Kasra |
| Contributors | Belta, Calin A. |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
| Rights | Attribution 4.0 International, http://creativecommons.org/licenses/by/4.0/ |
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