Fault tolerant control for bimodal piecewise affine systems

This thesis addresses the design of fault-tolerant controllers and a fault identification technique for bimodal piecewise affine systems. A new fault-tolerant control methodology is presented. Fault-tolerant, state feedback controllers are synthesized for piecewise-affine (PWA) systems while minimizing an upper bound on the expected value of a quadratic cost function. The controllers are designed to deal with partial loss of control authority in the closed loop PWA system. The proposed controller design technique stabilizes and satisfies performance bounds for both the nominal and faulty systems. Another contribution is the development of a fault identification technique for bimodal piecewise affine (PWA) systems. A Luenberger-based observer structure is applied to estimate partial loss of control authority in PWA systems. More specifically, the unknown value of the fault parameter is estimated by an observer equation obtained from a Lyapunov function. The design procedure is formulated as a set of linear matrix inequalities (LMIs) and guarantees asymptotic stability of the estimation error, provided the norm of the input is upper and lower bounded by positive constants. The new PWA identification method is illustrated in a numerical example. Asa third contribution, an active fault-tolerant controller structure is proposed for bimodal PWA systems. The new active fault-tolerant controller structure is illustrated in a numerical example

Optimal Control and Estimation Strategies for Nonlinear and Switched Systems

This dissertation includes two main parts. In the first part, the main contribution is to use an inverse optimality approach to analytically solve the Hamilton-Jacobi-Bellman equation of a third order nonlinear optimal control problem for which the dynamics are affine and the cost is quadratic in the input. One special advantage of this work is that the solution is directly obtained for the control input without finding a value function first. However, the value function can be obtained after one solves for the control input and it is shown to be at least a local Lyapunov function. Furthermore, the developed controller is combined with a Continuous-Discrete Extended Kalman Filter (CDEKF) as an approach to deal with noisy measurements and provide an estimate of the states for feedback. The proposed technique is illustrated by its application to a path following problem of a Wheeled Mobile Robot (WMR). The main contribution of the second part of this thesis is the development of two recursive state estimation algorithms for discrete-time piecewise affine (PWA) singular systems with simulation evidence that the idea works for both uncorrelated and correlated process and measurement noise. The proposed algorithms are derived based on successive QR decompositions and Maximum Likelihood (ML) estimation theory. Numerical examples are presented for the case of a PWA system with an unknown input, transformed to a PWA singular system

Mathematical modeling, analysis, and control of hybrid dynamical systems

EditorialPeng Shi, Hamid Reza Karimi, Rongni Yang, and Xiaojie S

Image Segmentation using PDE, Variational, Morphological and Probabilistic Methods

The research in this dissertation has focused upon image segmentation and its related areas, using the techniques of partial differential equations, variational methods, mathematical morphological methods and probabilistic methods. An integrated segmentation method using both curve evolution and anisotropic diffusion is presented that utilizes both gradient and region information in images. A bottom-up image segmentation method is proposed to minimize the Mumford-Shah functional. Preferential image segmentation methods are presented that are based on the tree of shapes in mathematical morphologies and the Kullback-Leibler distance in information theory. A thorough evaluation of the morphological preferential image segmentation method is provided, and a web interface is described. A probabilistic model is presented that is based on particle filters for image segmentation. These methods may be incorporated as components of an integrated image processed system. The system utilizes Internet Protocol (IP) cameras for data acquisition. It utilizes image databases to provide prior information and store image processing results. Image preprocessing, image segmentation and object recognition are integrated in one stage in the system, using various methods developed in several areas. Interactions between data acquisition, integrated image processing and image databases are handled smoothly. A framework of the integrated system is implemented using Perl, C++, MySQL and CGI. The integrated system works for various applications such as video tracking, medical image processing and facial image processing. Experimental results on this applications are provided in the dissertation. Efficient computations such as multi-scale computing and parallel computing using graphic processors are also presented

Systems and control : 21th Benelux meeting, 2002, March 19-21, Veldhoven, The Netherlands

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