Finite-time regional verification of stochastic non-linear systems

By Jacob Steinhardt, Russ Tedrake. 2011

118 citations recorded by the source corpus.

Recent trends pushing robots into unstructured environments with limited sensors have motivated considerable work on planning under uncertainty and stochastic optimal control, but these methods typically do not provide guaranteed performance. Here we consider the problem of bounding the probability of failure (defined as leaving a finite region of state space) over a finite time for stochastic non-linear systems with continuous state. Our approach searches for exponential barrier functions that provide bounds using a variant of the classical supermartingale result. We provide a relaxation of this search to a semidefinite program, yielding an efficient algorithm that provides rigorous upper bounds on the probability of failure for the original non-linear system. We give a number of numerical examples in both discrete and continuous time that demonstrate the effectiveness of the approach.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering

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Citations in the corpus

Stability of Controllers for Gaussian Process Forward Models (2016, methodology): “Relaxing the supermartingale criterion allows for stability statements for a finite time horizon, cf. (Kushner, 1966; Steinhardt & Tedrake, 2012).”