Computing Safety Margins of Parameterized Nonlinear Systems for Vulnerability Assessment via Trajectory Sensitivities
Physical systems experience nonlinear disturbances which have the potential to disrupt desired behavior. For a particular disturbance, whether or not the system recovers from the disturbance to a desired stable equilibrium point depends on system parameter values, which are typically uncertain and time-varying. Therefore, to quantify proximity to vulnerability we define the safety margin to be the smallest change in parameter values from a nominal value such that the system will no longer be able to recover from the disturbance. Safety margins are valuable but challenging to compute as related methods, such as those for robust region of attraction estimation, are often either overly conservative or computationally intractable for high dimensional systems. Recently, we developed algorithms to compute safety margins efficiently and non-conservatively by exploiting the large sensitivity of the system trajectory near the region of attraction boundary to small perturbations. Although these algorithms have enjoyed empirical success, they lack theoretical guarantees that would ensure their generalizability. This work develops a novel characterization of safety margins in terms of trajectory sensitivities, and uses this to derive well-posedness and convergence guarantees for these algorithms, enabling their generalizability and successful application to a large class of nonlinear systems.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Correct-by-Design Control of Parametric Stochastic Systems
This paper addresses the problem of computing controllers that are correct by design for safety-critical systems and can provably satisfy (complex) functional requirements. We develop new methods for models of systems su…
Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes
While reinforcement learning produces very promising results for many applications, its main disadvantage is the lack of safety guarantees, which prevents its use in safety-critical systems. In this work, we address this…
reinforcement-learningReinforcement LearningReinforcement Learning (RL)Safe Reinforcement LearningSafety-Critical Protective Systems and Margins of Safety
The design and operation of protective systems is an essential engineering responsibility. Ensuring public safety, while essential, must be accomplished at a feasible cost and within government regulation. Hence, protect…
Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions
Recent developments in autonomous driving and robotics underscore the necessity of safety-critical controllers. Control barrier functions (CBFs) are a popular method for appending safety guarantees to a general control f…
Autonomous DrivingCollision AvoidanceConformal PredictionDetermining Disturbance Recovery Conditions by Inverse Sensitivity Minimization
Power systems naturally experience disturbances, some of which can damage equipment and disrupt consumers. It is important to quickly assess the likely consequences of credible disturbances and take preventive action, if…
Sensitivity