Approximate Stochastic Reachability for High Dimensional Systems
| Autor: | Meeko M. K. Oishi, Adam J. Thorpe, Vignesh Sivaramakrishnan |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
Markov kernel Dynamical systems theory Computer science 010102 general mathematics Systems and Control (eess.SY) 02 engineering and technology Conditional probability distribution Electrical Engineering and Systems Science - Systems and Control 01 natural sciences Nonlinear system Double integrator 020901 industrial engineering & automation Optimization and Control (math.OC) Reachability FOS: Electrical engineering electronic engineering information engineering FOS: Mathematics 0101 mathematics Mathematics - Optimization and Control Algorithm Reproducing kernel Hilbert space Curse of dimensionality |
| Zdroj: | ACC |
| DOI: | 10.23919/acc50511.2021.9483404 |
| Popis: | We present a method to compute the stochastic reachability safety probabilities for high-dimensional stochastic dynamical systems. Our approach takes advantage of a nonparametric learning technique known as conditional distribution embeddings to model the stochastic kernel using a data-driven approach. By embedding the dynamics and uncertainty within a reproducing kernel Hilbert space, it becomes possible to compute the safety probabilities for stochastic reachability problems as simple matrix operations and inner products. We employ a convergent approximation technique, random Fourier features, in order to alleviate the increased computational requirements for high-dimensional systems. This technique avoids the curse of dimensionality, and enables the computation of safety probabilities for high-dimensional systems without prior knowledge of the structure of the dynamics or uncertainty. We validate this approach on a double integrator system, and demonstrate its capabilities on a million-dimensional, nonlinear, non-Gaussian, repeated planar quadrotor system. |
| Databáze: | OpenAIRE |
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