Non-Asymptotic estimation for on-line systems: Finite-time algorithms and applications

International audienceFinite-time estimation is a way to perform real-time control and achieve specified time performance. The Inria project-team Non-A is focusing on designing such "non-asymptotic" algorithms: there, mathematics (algebra, homogeneity) are combined with real-time applications (robotics, energy, environment)… For engineers, a wide variety of information is not directly obtained through measurement. Some parameters (constants of an electrical actuator, time delay in communication, etc.) or internal variables (torques applied to a robot arm, posture and localization of a mobile, detection of impact of angles in biped walk, etc.) are unknown or are not measured. Similarly, more often than not, signals from sensors are distorted and tainted by measurement noises. To control such processes, and to extract information conveyed by the signals, one often has to estimate parameters or variables. Estimation can concern parameters (identification), states (observation), derivatives (differentiation), inputs (left inversion) or noisy data (filtering). It means a nearly infinite number of results have already been produced in this area, concerning either control or signal processing… However, unlike traditional methods, the majority of which pertain to asymptotic statistics, the particularity of Non-A is to develop algorithms which converge after a finite-time. This is summarized in the project's name: "Non-Asymptotic estimation for online systems"