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Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation

Marina L. Kleptsyna, Alain Le Breton, Michel Viot (2008)

ESAIM: Probability and Statistics

In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we show that a separation principle holds, i.e., the optimal control separates into two stages based on optimal...

Simultaneous state and parameter estimation based actuator fault detection and diagnosis for an unmanned helicopter

Chong Wu, Juntong Qi, Dalei Song, Xin Qi, Jianda Han (2015)

International Journal of Applied Mathematics and Computer Science

Simultaneous state and parameter estimation based actuator fault detection and diagnosis (FDD) for single-rotor unmanned helicopters (UHs) is investigated in this paper. A literature review of actuator FDD for UHs is given firstly. Based on actuator healthy coefficients (AHCs), which are introduced to represent actuator faults, a combined dynamic model is established with the augmented state containing both the flight state and AHCs. Then the actuator fault detection and diagnosis problem is transformed...

SMAC-FDI: A single model active fault detection and isolation system for unmanned aircraft

Guillaume J.J. Ducard (2015)

International Journal of Applied Mathematics and Computer Science

This article presents a single model active fault detection and isolation system (SMAC-FDI) which is designed to efficiently detect and isolate a faulty actuator in a system, such as a small (unmanned) aircraft. This FDI system is based on a single and simple aerodynamic model of an aircraft in order to generate some residuals, as soon as an actuator fault occurs. These residuals are used to trigger an active strategy based on artificial exciting signals that searches within the residuals for the...

State estimation under non-Gaussian Lévy noise: A modified Kalman filtering method

Xu Sun, Jinqiao Duan, Xiaofan Li, Xiangjun Wang (2015)

Banach Center Publications

The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems with non-Gaussian Lévy noise is devised. It works effectively with reasonable computational cost. Simulation results are presented to illustrate this non-Gaussian filtering method.

Straight-lines modelling using planar information for monocular SLAM

André M. Santana, Adelardo A.D. Medeiros (2012)

International Journal of Applied Mathematics and Computer Science

This work proposes a SLAM (Simultaneous Localization And Mapping) solution based on an Extended Kalman Filter (EKF) in order to enable a robot to navigate along the environment using information from odometry and pre-existing lines on the floor. These lines are recognized by a Hough transform and are mapped into world measurements using a homography matrix. The prediction phase of the EKF is developed using an odometry model of the robot, and the updating makes use of the line parameters in Kalman...

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