Set-Theoretic Estimation and Control for Safety-Critical Cyber-Physical Systems

Recent research in safety control has leveraged the availability of accurate models to detect impending safety violations and to intervene accordingly. However, there is often a mismatch between the models that are used for algorithm design and the real systems. Moreover, control designs typically assume the availability of full state information that is error-free and trustworthy. These modeling discrepancies, sensing/estimation errors and the possibility of compromised/spoofed signals, if not proactively considered, will jeopardize safety guarantees, leading to serious damage to safety-critical systems, including autonomous vehicles and power systems, and to loss of trust in these technologies. This talk presents some of our contributions to safety-critical cyber-physical systems under uncertainty from the perspective of set-theoretic estimation and control. 

The first part of the talk will focus on set-membership/set-valued estimation methods for dynamic systems with bounded process and measurement noise under various forms of set uncertainties, including unknown models, unknown inputs/attacks and missing/delayed data. Specifically, we consider various set representations and derive robust and resilient estimators/observers with provable accuracy guarantees. Then, in the second part of the talk, we will consider correct-by-design safety control problems under similar set uncertainties and set-valued estimation errors based on the derivation/synthesis of (controlled) invariant sets. Finally, the presentation will be closed with a brief discussion about some ongoing work and future opportunities, including set-membership learning, for designing and applying set-theoretic methods to safety-critical systems.