Stochastic algorithms for robustness of control performances.

*(English)*Zbl 1166.93387Summary: In recent years, there has been a growing interest in developing statistical learning methods to provide approximate solutions to “difficult” control problems. In particular, randomized algorithms have become a very popular tool used for stability and performance analysis as well as for design of control systems. However, as randomized algorithms provide an efficient solution procedure to the “intractable” problems, stochastic methods bring closer to understanding the properties of the real systems. The topic of this paper is the use of stochastic methods in order to solve the problem of control robustness: the case of parametric stochastic uncertainty is considered. Necessary concepts regarding stochastic control theory and stochastic differential equations are introduced. Then a convergence analysis is provided by means of the Chernoff bounds, which guarantees robustness in mean and in probability. As an illustration, the robustness of control performances of example control systems is computed.

##### MSC:

93E35 | Stochastic learning and adaptive control |

93E15 | Stochastic stability in control theory |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

##### Keywords:

control system; robustness; randomized algorithms; stochastic algorithms; stochastic differential equations##### Software:

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\textit{B. Piccoli} et al., Automatica 45, No. 6, 1407--1414 (2009; Zbl 1166.93387)

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