Intractable problems in control theory
SIAM Journal on Control and Optimization
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
A Monte Carlo approach to the analysis of control system robustness
Automatica (Journal of IFAC) - Special issue on robust control
Robust Control: The Parametric Approach
Robust Control: The Parametric Approach
Some Problems of Robust Control of a Stochastic Object
Automation and Remote Control
A survey of randomized algorithms for control synthesis and performance verification
Journal of Complexity
Automatica (Journal of IFAC)
Robust H∞ filtering for nonlinear stochastic systems
IEEE Transactions on Signal Processing
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
Brief Filtering on nonlinear time-delay stochastic systems
Automatica (Journal of IFAC)
| Hi-index | 22.14 |
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.