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Compositional Synthesis for Linear Systems via Convex Optimization of Assume-Guarantee Contracts
We take a divide and conquer approach to design controllers for reachability
problems given large-scale linear systems with polyhedral constraints on
states, controls, and disturbances. Such systems are made of small subsystems
with coupled dynamics. We treat the couplings 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. The main contribution of this paper 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
present numerical examples, including a scalability study on a system with tens
of thousands of dimensions, and a case study on applying our method to a
distributed Model Predictive Control (MPC) problem in a power system
Compositional Synthesis via a Convex Parameterization of Assume-Guarantee Contracts
We develop an assume-guarantee framework for control of large scale linear
(time-varying) systems from finite-time reach and avoid or infinite-time
invariance specifications. The contracts describe the admissible set of states
and controls for individual subsystems. A set of contracts compose correctly if
mutual assumptions and guarantees match in a way that we formalize. We propose
a rich parameterization of contracts such that the set of parameters that
compose correctly is convex. Moreover, we design a potential function of
parameters that describes the distance of contracts from a correct composition.
Thus, the verification and synthesis for the aggregate system are broken to
solving small convex programs for individual subsystems, where correctness is
ultimately achieved in a compositional way. Illustrative examples demonstrate
the scalability of our method
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