NON-A Research team

Non-Asymptotic estimation for online systems

Team presentation

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 (robot's posture, torques applied to a robot, localization of a mobile, 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 identify a system and estimate parameters or variables. In the fields of control and signal processing, estimating non-measured variables or identifying the parameters of a model are common problems, normally processed within the context of optimization. The team Non-A is developing an algebraic approach that provides either explicit formulae or finite-time estimates. This non-asymptotic character is a significant advantage for real-time applications. Non-A has been created in January 2011 in the continuity of a previous ALIEN project leaded by Michel Fliess who published with H.Sira-Ramirez in 2003 a breaking, seminal result: ''An algebraic framework for linear identification'', ESAIM Control Optim. Calc. Variat., 9, 2003, 151-168.

Research themes

The team Non-A is developing an estimation theory, built around differential algebra and operational calculation on the one hand, and high gain algorithms (such as sliding mode, etc.) on the other hand. Both approaches allow for estimating in finite-time the derivatives of noisy signals, which opens a lot of prospects in control and signal processing. It has resulted in relatively simple, rapid algorithms. Solutions are provided by explicit formulae, with straightforward implementation, using standard tools from computational mathematics. Unlike traditional methods, the majority of which pertain to asymptotic statistics, the Non-A estimators are ''non-asymptotic''. In many application sectors, the response time parameter is crucial. Using this approach, computations are performed as the application is running: the ''real-time'' computing is targeted, as opposed to processing that occurs after the event. Non-A is focusses on non-asymptotic estimation for on-line systems. It is structured by three main challenges: the definition of annihilators of perturbations; numerical differentiation in finite time; the model-free control (based on the output signals). Application fields for this development are plentiful: today, the team is working on the control of NCS (networked control systems, including Wireless Networks of Sensors and Robots), as well as very high precision systems such as micro or nano-machining. Our ''model-free control'' also attracts various industrial contracts.

International and industrial relations

International: InterReg SYSIASS: Autonomous and Intelligent Healthcare System - http://www.sysiass.eu FP7 HYCON2: Highly-complex and networked control systems - http://www.hycon2.eu European GDR: Time Delay Systems PHC Volubilis PHC Galileo National: ANR CHASLIM: Sliding Modes - http://chaslim.gforge.inria.fr ADT SENSROB: Robotics and Wireless Sensor and Actuator Networks - http://sensas.gforge.inria.fr

Keywords: Finite-time Estimation Numerical differentiation Control

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