Bounded Error Identification of Systems With Time-Varying Parameters

This note presents a new approach to guaranteed system identification for time-varying parameterized discrete-time systems. A bounded description of noise in the measurement is considered. The main result is an algorithm to compute a set that contains the parameters consistent with the measured output and the given bound of the noise. This set is represented by a zonotope, that is, an affine map of a unitary hypercube. A recursive procedure minimizes the size of the zonotope with each noise corrupted measurement. The zonotopes take into account the time-varying nature of the parameters in a nonconservative way. An example has been provided to clarify the algorithm

Indirect M-MRAC for Systems with Time Varying Parameters and Bounded Disturbances

The paper presents a prediction-identification model based adaptive control method for uncertain systems with time varying parameters in the presence of bounded external disturbances. The method guarantees desired tracking performance for the system s state and input signals. This is achieved by feeding back the state prediction error to the identification model. It is shown that the desired closed-loop properties are obtained with fast adaptation when the error feedback gain is selected proportional to the square root of the adaptation rate. The theoretical findings are confirmed via a simulation example

Identifiability of slowly varying systems

A system is conceived of as being slowly varying if it changes slowly enough to permit identification to within a specified error. A generic model is developed to study the identifiability and identification of slowly varying systems. The model is suitable for a large variety of nonlinear, time-varying, causal, bounded memory systems; it has finitely many parameters and is linear in its parameters. Results are obtained with the use of this general model that give guaranteed accuracy of identification as a function of the prior knowledge of the unknown system, the maximum rate of time variation of the system, and the characteristics of output observation noise. To derive these results, a recursive estimation procedure is developed for time-discrete linear dynamical system structures in which the observation noise is statistical but the dynamic equation noise is nonstatistical and is known only to be bounded.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21640/1/0000024.pd

Modeling and identification of a quadrotor using LPV techniques

The aim of this project is to modelize a LPV model and to compare different identification methods. In order to accomplish that, first of all a white box model of the quadrotor has been provided. This model has been used to find a LPV description that can be used in this case. With this data various identification procedures has been tested. This project is focused in the use of particle filters to identify the parameters of the system

Connections Between Adaptive Control and Optimization in Machine Learning

This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are examined. Concepts in stability, performance, and learning, common to both fields are then discussed. Building on the similarities in update laws and common concepts, new intersections and opportunities for improved algorithm analysis are provided. In particular, a specific problem related to higher order learning is solved through insights obtained from these intersections.Comment: 18 page