Postdoc in formal methods for control systems

Missions

The recruited postdoctoral researcher will contribute to the ANR/NSF CAFEE project, an international collaboration aiming at bridging the gap between control theory and formal verification at code level . The project targets end-to-end guarantees , from high-level control design to embedded software implementation, with applications in safety-critical systems (e.g., aerospace, robotics).

The postdoctoral researcher will be primarily involved in the design, implementation, and evaluation of formal verification methods for control software , with a particular focus on optimization-based control algorithms and their implementation.

Main scientific objectives

• Develop formal and exhaustive verification techniques for control system software at code level.
• Bridge high-level control guarantees (e.g., stability, performance, convergence) with low-level implementation semantics (finite precision arithmetic, C code).
• Contribute to the development of an end-to-end verification toolchain , integrating modeling, proof generation, and code-level validation.

Core Research activities

Formal verification of control algorithms at code level

• Design static analysis and deductive verification techniques to prove system-level properties (stability, robustness, performance).
• Develop methods to express control-theoretic properties (e.g., Lyapunov invariants) as program invariants.
• Apply and extend tools such as Frama-C, SMT solvers, and theorem provers.

Verification of optimization-based control algorithms

• Formalize and verify convex optimization algorithms embedded in control loops.
• Prove termination and convergence guarantees , including finite-time convergence .
• Analyze numerical aspects such as discretization, linearization, and solver correctness.

Handling numerical precision and implementation effects

• Model and verify the impact of floating-point and fixed-point arithmetic on system behavior.
• Develop methods to ensure correctness under finite-precision computation .

Contribution to an end-to-end verification toolchain

• Participate in the extension of toolchains such as CocoSim for combined modeling, code generation, and verification.

Experimental validation and case studies

• Apply developed methods to realistic control systems (e.g., UAVs, embedded controllers, trajectory planning).
• Evaluate scalability and applicability on representative benchmarks.

Collaboration and dissemination

• Collaborate closely with project partners at ENAC and the University of Michigan.
• Contribute to joint publications in top-tier venues in formal methods, control, and programming languages.
• Participate in project meetings, workshops, and international research exchanges.
• Optionally contribute to supervision of PhD students and teaching-related activities.

Profil

We are seeking a highly motivated candidate with a strong interdisciplinary background at the interface of control theory and formal methods .

PhD degree

• Control Theory
• Computer Science (Formal Methods, Programming Languages, Verification)
• Applied Mathematics (with strong relevance to the topic)

Technical expertise

• Strong background in control systems theory, including:
  • Lyapunov theory (especially for discrete-time systems)
  • Stability and robustness analysis
  • Familiarity with optimization-based control is a strong plus
• Solid knowledge of formal methods, including:
  • Deductive verification and/or static analysis
  • Experience with tools such as Frama-C, SMT solvers, or proof assistants
  • Understanding of program semantics and verification at code level
• Familiarity with at least some of the following topics is highly desirable:
  • Integral Quadratic Constraints (IQC)
  • Convex optimization and numerical algorithms
  • Floating-point or fixed-point arithmetic verification
  • Hybrid systems and cyber-physical systems
  • Signal Temporal Logic (STL) or temporal logics
• Strong programming experience in C/C++ , Python, or similar languages
• Experience with formal verification tools or scientific computing environments

Research profile

• Proven ability to conduct independent research
• Strong publication record in top-tier conferences and/or journals in relevant fields (formal methods, control, programming languages, embedded systems)

Language and communication

• Fluency in English (spoken and written)
• Ability to work in an international and interdisciplinary research environment

Personnal skills

• Strong analytical and problem-solving abilities
• Ability to collaborate across disciplines (control theory and computer science)
• Autonomy, initiative, and scientific curiosity