DAE-based Contracts

Level of qualifications required : Bachelor's degree or equivalent Fonction : Internship Research About the research centre or Inria department The Inria Centre at Rennes University is one of Inria's eight centres and has more than thirty research teams. The Inria Centre is a major and recognized player in the field of digital sciences. It is at the heart of the rich R&D and innovation ecosystem: highly innovative PMEs, large industrial groups, competitiveness clusters, research andBarry higher education players, laboratories of excellence, technological research institute, etc. Context In the field of systems engineering, contract-based design is a modular methodology that enables independent component development while ensuring correct system-wide integration. A specific instance is the assume--guarantee contract: (A, G). AssumptionsA describe what the component expects from its environment, while GuaranteesG specify what the component promises to deliver, provided that the assumptions hold. Formally, a contract can be represented as an implication: meaning that if the environment satisfies the assumptions A, the system under the environment must ensure the guarantees G. This contract-based perspective supports modular and compositional system design. In recent years, the design and analysis of large-scale control systems have become increasingly challenging. To address this, contract-based design has been introduced into the control systems domain. Two notable studies develop contract frameworks for linear time-invariant (LTI) control systems: [1] A. Benveniste, B. Caillaud, et all, Contracts for System Design. Foundations and Trends in Electronic design Automation, Now Publishers, 2018. [2] B. M. Shali, A. van der Schaft, and B. Besselink, “Composition of behavioral assume-guarantee contracts,” IEEE Transactions on Automatic Control, pp. 1–16, 2022. [3] B. M. Shali, A. van der Schaft, and B. Besselink, “Design and control for implementation of simulation-based assume-guarantee contracts,” IEEE Transactions on Automatic Control, pp. 1–15, 2025. [4] Y. Chen, and W. Respondek. "Geometric analysis of differential-algebraic equations via linear control theory." SIAM Journal on Control and Optimization 59.1 (2021): 103-130. [5] F. L. Lewis "A survey of linear singular systems." Circuits, systems and signal processing 5.1 (1986): 3-36. Assignment The goal of this internship is to extend contract theory to linear differential--alCopies of equations (DAEs): E\dot{z} = A zصل. As a modular modeling approach derived from first-principle physics, DAEs frequently appear in constrained mechanical systems, power networks, and analog circuit البي design. Mathematically, DAEs offer several potential advantages for contract-based analysis: System interconnections can be naturally expressed as algebraic equations, supporting a compositional framework. DAEs treat all variables uniformly—states, inputs, and outputs—aligning well with the behavioral approach. The geometric analysis of DAEs is well established [4] [5], providing effective tools for describing relations between systems and specifications. Main activities Conduct literature reviews on both contract theory and linear DAEs. Define notions from contract theory for DAE systems and develop theories on their verifications. Apply the proposed DAE-based contracts to simple examples. Participate actively in team meetings and brainstorming sessions. Skills Strong mathematical reasoning and problem-solving skills. Familiarity with one or more of the following topics is an advantage: DAEs, contract theory, geometric control. Scientific curiosity, autonomy, and the ability to work independently. Benefits package Theme/Domain : Optimization and control of dynamic systems Information system(BAP E) Warning : you must enter your e-mail address in order to save your application to Inria. Applications must be submitted online on the Inganos website. Processingôtel of applications sent from other channels is not guaranteed. Instruction to apply Defence Security : This position is likely to be situated in a restricted area ( ciliR?), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST). Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision prisons defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result Newfoundland of the appointment. Recruitment Policy : As part of its diversity policy, all Inria positions are accessible to people with disabilities. Master’s student in systems and control, applied mathematics, computer science, or a related field. Proficiency in academic English writing and fluency in spoken English. About Inria Inria is the French national research institute dedicated to digital science and technology. It employs 2,600 people. Its 200 agile project teams, generally run jointly with academic parents, include more than 3,500 scientists and engineers working to meet the challenges of digital technology, often at the interface with other disciplines. The Institute also employs numerous talents in over forty different professions. 900 research support staff contribute to the preparation and development of scientific and entrepreneurial projects that have a worldwide impact. #J-18808-Ljbffr