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Controller Synthesis for Interconnected Systems using Parametric Assume-Guarantee Contracts
Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts
This paper presents an assume-guarantee reasoning approach to the computation
of robust invariant sets for network systems. Parameterized signal temporal
logic (pSTL) is used to formally describe the behaviors of the subsystems,
which we use as the template for the contract. We show that set invariance can
be proved with a valid assume-guarantee contract by reasoning about individual
subsystems. If a valid assume-guarantee contract with monotonic pSTL template
is known, it can be further refined by value iteration. When such a contract is
not known, an epigraph method is proposed to solve for a contract that is
valid, ---an approach that has linear complexity for a sparse network. A
microgrid example is used to demonstrate the proposed method. The simulation
result shows that together with control barrier functions, the states of all
the subsystems can be bounded inside the individual robust invariant sets.Comment: Submitted to 2019 American Control Conferenc
Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts
This paper presents an assume-guarantee reasoning approach to the computation of robust invariant sets for network systems. Parameterized signal temporal logic (pSTL) is used to formally describe the behaviors of the subsystems, which we use as the template for the contract. We show that set invariance can be proved with a valid assume-guarantee contract by reasoning about individual subsystems. If a valid assume-guarantee contract with monotonic pSTL template is known, it can be further refined by value iteration. When such a contract is not known, an epigraph method is proposed to solve for a contract that is valid, -an approach that has linear complexity for a sparse network. A microgrid example is used to demonstrate the proposed method. The simulation result shows that together with control barrier functions, the states of all the subsystems can be bounded inside the individual robust invariant sets
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
Behavioural assume-guarantee contracts for linear dynamical systems
Motivated by the growing requirements on theoperation of complex engineering systems, we present con-tracts as specifications for continuous-time linear dynamicalsystems with inputs and outputs. A contract is defined asa pair of assumptions and guarantees, both characterized ina behavioural framework. The assumptions encapsulate theavailable information about the dynamic behaviour of theenvironment in which the system is supposed to operate, whilethe guarantees express the desired dynamic behaviour of thesystem when interconnected with relevant environments. Inaddition to defining contracts, we characterize contract imple-mentation, and we find necessary conditions for the existence ofan implementation. We also characterize contract refinement,which is used to characterize contract conjunction in two specialcases. These concepts are then illustrated by an example of avehicle following 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
Safety-Critical Control Synthesis for network systems with Control Barrier Functions and Assume-Guarantee Contracts
This paper presents a contract based framework for safety-critical control synthesis for network systems. To handle the large state dimension of such systems, an assume-guarantee contract is used to break the large synthesis problem into smaller subproblems. Parameterized signal temporal logic (pSTL) is used to formally describe the behaviors of the subsystems, which we use as the template for the contract. We show that robust control invariant sets (RCIs) for the subsystems can be composed to form a robust control invariant set for the whole network system under a valid assume-guarantee contract. An epigraph algorithm is proposed to solve for a contract that is valid, ---an approach that has linear complexity for a sparse network, which leads to a robust control invariant set for the whole network. Implemented with control barrier function (CBF), the state of each subsystem is guaranteed to stay within the safe set. Furthermore, we propose a contingency tube Model Predictive Control (MPC) approach based on the robust control invariant set, which is capable of handling severe contingencies, including topology changes of the network. A power grid example is used to demonstrate the proposed method. The simulation result includes both set point control and contingency recovery, and the safety constraint is always satisfied
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