On robust stability of fully probabilistic control with respect to data-driven model uncertainties

We investigate robust stability of the fully probabilistic control with respect to data-driven model uncertainties. This scheme attempts to control a system modeled via a probability density function (pdf) and does so by computing a probabilistic control policy that is optimal in the Kullback-Leibler sense. The results are illustrated via simulations.

[1]  Shie Mannor,et al.  Bayesian Reinforcement Learning: A Survey , 2015, Found. Trends Mach. Learn..

[2]  Miroslav Kárný,et al.  Towards fully probabilistic control design , 1996, Autom..

[3]  Michael E. Henderson,et al.  Multiple Parameter Continuation: Computing Implicitly Defined k-Manifolds , 2002, Int. J. Bifurc. Chaos.

[4]  J. Berger Statistical Decision Theory and Bayesian Analysis , 1988 .

[5]  Francesco Borrelli,et al.  Learning Model Predictive Control for Iterative Tasks. A Data-Driven Control Framework , 2016, IEEE Transactions on Automatic Control.

[6]  Torsten Koller,et al.  Learning-based Model Predictive Control for Safe Exploration and Reinforcement Learning , 2019, ArXiv.

[7]  Miroslav Karny Optimized Bayesian Dynamic Advising: Theory and Algorithms (Advanced Information and Knowledge Processing) , 2005 .

[8]  Tatiana V. Guy,et al.  Mixture‐based adaptive probabilistic control , 2003 .

[9]  Andreas Krause,et al.  Safe Model-based Reinforcement Learning with Stability Guarantees , 2017, NIPS.

[10]  Benjamin Recht,et al.  A Tour of Reinforcement Learning: The View from Continuous Control , 2018, Annu. Rev. Control. Robotics Auton. Syst..

[11]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[12]  Tatiana V. Guy,et al.  Fully probabilistic control design , 2006, Syst. Control. Lett..

[13]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[14]  Randa Herzallah,et al.  Fully probabilistic control for stochastic nonlinear control systems with input dependent noise , 2015, Neural Networks.

[15]  K. Åström Introduction to Stochastic Control Theory , 1970 .