Brief paper: Feedback and invariance under uncertainty via set-iterates
Automatica (Journal of IFAC)
Set-Theoretic Methods in Control
Set-Theoretic Methods in Control
Constrained Control and Estimation: An Optimisation Approach
Constrained Control and Estimation: An Optimisation Approach
Survey paper: Research on probabilistic methods for control system design
Automatica (Journal of IFAC)
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
| Hi-index | 22.14 |
The notions of invariant sets and ultimate bounds are important concepts in the analysis of dynamical systems and very useful tools for the design of control systems. Several approaches have been reported for the characterisation of these sets, including constructive methods for their computation and procedures to obtain different approximations. However, there are shortcomings in those concepts, in the sense that no general probability distributions can be considered for the disturbances affecting the system (which, for example, precludes the assumption of Gaussian distributions insofar as they are not bounded). Motivated by those shortcomings, we propose in this paper the novel concepts of probabilistic ultimate bounds and probabilistic invariant sets, which extend the notions of invariant sets and ultimate bounds to consider 'containment in probability', and have the important feature of allowing stochastic noises with more general distributions, including the ubiquitous Gaussian distribution, to be considered. We introduce some key definitions for these sets, establish their main properties and develop methods for their computation. A numerical example illustrates the main ideas.