6,623 research outputs found
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
Contracts as specifications for dynamical systems in driving variable form
This paper introduces assume/guarantee contracts on continuous-time control
systems, hereby extending contract theories for discrete systems to certain new
model classes and specifications. Contracts are regarded as formal
characterizations of control specifications, providing an alternative to
specifications in terms of dissipativity properties or set-invariance. The
framework has the potential to capture a richer class of specifications more
suitable for complex engineering systems. The proposed contracts are supported
by results that enable the verification of contract implementation and the
comparison of contracts. These results are illustrated by an example of a
vehicle following system.Comment: 8 pages, 2 figures; minor changes in the final version, as accepted
for publication in the Proceedings of the 2019 European Control Conference,
Naples, Ital
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
Risk modeling concepts relating to the design and rating of agricultural insurance contracts
The authors identify the key issues and concerns that arise in the design and rating of crop yield insurance plans, with a particular emphasis on production risk modeling. The authors show how the availability of data shapes the insurance scheme and the ratemaking procedures. Relying on the U.S. experience and recent developments in statistics and econometrics, they review risk modeling concepts and provide technical guidelines in the development of crop insurance plans. Finally, they show how these risk modeling techniques can be extended to price risk in order to develop crop revenue insurance schemes.Health Economics&Finance,Insurance Law,Environmental Economics&Policies,Insurance&Risk Mitigation,Labor Policies,Insurance&Risk Mitigation,Crops&Crop Management Systems,Health Economics&Finance,Insurance Law,Environmental Economics&Policies
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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Insurance with multiple insurers: A game-theoretic approach
This paper studies the set of Pareto optimal insurance contracts and the core of an insurance game. Our setting allows multiple insurers with translation invariant preferences. We characterise the Pareto optimal contracts, which determines the shape of the indemnities. Closed-form and numerical solutions are found for various preferences that the insurance players might have. Determining associated premiums with any given optimal Pareto contract is another problem for which economic-based arguments are further discussed. We also explain how one may link the recent fast growing literature on risk-based optimality criteria to the Pareto optimality criterion and we show that the latter is much more general than the former one, which according to our knowledge, has not been pointed out by now. Further, we extend some of our results when model risk is included, i.e. there is some uncertainty with the risk model and/or the insurance players make decisions based on divergent beliefs about the underlying risk. These robust optimal contracts are investigated and we show how one may find robust and Pareto efficient contracts, which is a key decision-making problem under uncertainty
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
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