Vision based target tracking using robust linear filtering

The use of perspective projection in tracking a target from a video stream involves nonlinear observations. The target dynamics, however, are modeled in Cartesian coordinates and result in a linear system. In this paper we provide a robust version of a linear Kalman filter and perform a measurement conversion technique on the nonlinear optical measurements. We show that our linear robust filter significantly outperforms the Extended Kalman Filter. Moreover, we prove that the state estimation error is bounded in a probabilistic sense.

Design of reduced-order state/unknown input observers: a descriptor system approach

This paper addresses the problem of estimating simultaneously a linear function of both the state and unknown input of linear system with unknown inputs. By adopting the descriptor system approach, the problem can be conveniently solved. Observers proposed in this paper are of low-order and do not include the derivatives of the outputs. New conditions for the existence of reduced-order observers are derived. A design procedure for the determination of the observer parameters can also be easily derived based on the derived existence conditions

An algebraic approach for delay-independent and delay-dependent stability of linear time-delay systems

This paper addresses the problem of asymptotic stability of a linear system with many delay units. A novel algebraic test is proposed for the delay-independent stability of the system, based on the root distribution of the system's characteristic equation. If the system is only stable dependent of delay, the whole stable regions of the system can be perfectly obtained. Two algorithms are derived to examine the delay-independent stability, and to compute the whole stable regions if the system is of delay-dependent stability. These algorithms are computationally efficient and applicable to both certain and uncertain systems. Some illustrative examples demonstrate the validity of the approach.

A generalized data windowing scheme for adaptive conjugate gradient algorithms

The performance of the modified adaptive conjugate gradient (CG) algorithms based on the iterative CG method for adaptive filtering is highly related to the ways of estimating the correlation matrix and the cross-correlation vector. The existing approaches of implementing the CG algorithms using the data windows of exponential form or sliding form result in either loss of convergence or increase in misadjustment. This paper presents and analyzes a new approach to the implementation of the CG algorithms for adaptive filtering by using a generalized data windowing scheme. For the new modified CG algorithms, we show that the convergence speed is accelerated, the misadjustment and tracking capability comparable to those of the recursive least squares (RLS) algorithm are achieved. Computer simulations demonstrated in the framework of linear system modeling problem show the improvements of the new modifications.

Vision-based target tracking and surveillance with robust set-valued state estimation

Tracking a target from a video stream (or a sequence of image frames) involves nonlinear measurements in Cartesian coordinates. However, the target dynamics, modeled in Cartesian coordinates, result in a linear system. We present a robust linear filter based on an analytical nonlinear to linear measurement conversion algorithm. Using ideas from robust control theory, a rigorous theoretical analysis is given which guarantees that the state estimation error for the filter is bounded, i.e., a measure against filter divergence is obtained. In fact, an ellipsoidal set-valued estimate is obtained which is guaranteed to contain the true target location with an arbitrarily high probability. The algorithm is particularly suited to visual surveillance and tracking applications involving targets moving on a plane.

A method for stereo-vision-based tracking for robotic applications

Vision-based tracking of an object using perspective projection inherently results in non-linear measurement equations in the Cartesian coordinates. The underlying object kinematics can be modelled by a linear system. In this paper we introduce a measurement conversion technique that analytically transforms the non-linear measurement equations obtained from a stereo-vision system into a system of linear measurement equations.We then design a robust linear filter around the converted measurement system. The state estimation error of the proposed filter is bounded and we provide a rigorous theoretical analysis of this result. The performance of the robust filter developed in this paper is demonstrated via computer simulation and via practical experimentation using a robotic manipulator as a target. The proposed filter is shown to outperform the extended Kalman filter (EKF).

A new design of sliding mode control systems

A new sliding mode control technique for a class of SISO dynamic systems is presented in this chapter. It is seen that the stability status of the closed-loop system is first checked, based on the approximation of the most recent information of the first-order derivative of the Lyapunov function of the closed-loop system, an intelligent sliding mode controller can then be designed with the following intelligent features: (i) If the closed-loop system is stable, the correction term in the controller will continuously adjust control signal to drive the closed-loop trajectory to reach the sliding mode surface in a finite time and the desired closed-loop dynamics with the zero-error convergence can then be achieved on the sliding mode surface. (ii) If, however, the closed-loop system is unstable, the correction term is capable of modifying the control signal to continuously reduce the value of the derivative of the Lyapunov function from the positive to the negative and then drives the closed-loop trajectory to reach the sliding mode surface and ensures that the desired closed-loop dynamics can be obtained on the sliding mode surface. The main advantages of this new sliding mode control technique over the conventional one are that no chattering occurs in the sliding mode control system because of the recursive learning control structure; the system uncertainties are embedded in the Lipschitz-like condition and thus, no priori information on the upper and/or the lower bounds of the unknown system parameters and uncertain system dynamics is required for the controller design; the zero-error convergence can be achieved after the closed-loop dynamics reaches the sliding mode surface and remains on it. The performance for controlling a third-order linear system is evaluated in the simulation section to show the effectiveness and efficiency of the new sliding mode control technique.

Fast cross-validation of kernel fisher discriminant classifiers

Given n training examples, the training of a Kernel Fisher Discriminant (KFD) classifier corresponds to solving a linear system of dimension n. In cross-validating KFD, the training examples are split into 2 distinct subsets for a number of times (L) wherein a subset of m examples is used for validation and the other subset of(n - m) examples is used for training the classifier. In this case L linear systems of dimension (n - m) need to be solved. We propose a novel method for cross-validation of KFD in which instead of solving L linear systems of dimension (n - m), we compute the inverse of an n × n matrix and solve L linear systems of dimension 2m, thereby reducing the complexity when L is large and/or m is small. For typical 10-fold and leave-one-out cross-validations, the proposed algorithm is approximately 4 and (^4/9n) times respectively as efficient as the naive implementations. Simulations are provided to demonstrate the efficiency of the proposed algorithms.

Nonlinear DSTATCOM controller design for distribution network with distributed generation to enhance voltage stability

This paper presents a nonlinear controller design for a DSTATCOM connected to a distribution network with distributed generation (DG) to regulate the line voltage by providing reactive power compensation.The controller is designed based on the partial feedback linearization which transforms the nonlinear system into a reduced-order linear system and an autonomous system whose dynamics are known as internal dynamics of the system. This paper also investigates the stability of internal dynamics of a DSTATCOM as it is a basic requirement to design partial feedback linearizing controllers. The performance of the proposed controller is evaluated in terms reactive power compensation to enhance the voltage stability of distribution with DG.

A novel approach to exponential stability of continuous-time Roesser systems with directional time-varying delays

This paper addresses the problem of exponential stability analysis of two-dimensional (2D) linearcontinuous-time systems with directional time-varying delays. An abstract Lyapunov-like theorem whichensures that a 2D linear system with delays is exponentially stable for a prescribed decay rate is exploitedfor the first time. In light of the abstract theorem, and by utilizing new 2D weighted integral inequalitiesproposed in this paper, new delay-dependent exponential stability conditions are derived in terms oftractable matrix inequalities which can be solved by various computational tools to obtain maximumallowable bound of delays and exponential decay rate. Two numerical examples are given to illustrate theeffectiveness of the obtained results.

Modeling of a stereo vision system using a genetic algorithm based fuzzy linear regression

In this paper a fuzzy linear regression (FLR) model integrated with a genetic algorithm (GA) is proposed. The proposed GA-FLR model is applied to modeling of a stereo vision system. A set of empirical data from stereo vision object measurement is collected based on the full factorial design technique. Three regression models, namely ordinary least-squares regression (OLS), FLR, and GA-FLR, are developed, and with their performances compared. The results show that the proposed GA-FLR model performs better than OLS and FLR in modeling of a stereo vision system.

Constrained pole placement for linear systems using low-order output feedback controllers

The paper presents a simple approach to the problem of designing low-order output feedback controllers for linear continuous systems. The controller can place all of the closed-loop poles within a circle, C(- , 1/ β) , with centre at - and radius of 1/ β in the left half s-plane. The design method is based on transformation of the original system and then applying the bounded-real-lemma to the transformed system. It is shown that subjected to the solvability of an algebraic Riccati equation (ARE), output feedback controllers can then be systematically derived. Furthermore, the order of the controller is low and equals only the number of the open-loop poles lying outside the circle. A step-by-step design algorithm is given. Numerical examples are given to illustrate the design method.

Control loop for finding initial translator position of linear synchronous motor

This article presents a simple and reliable method for controlling the relative orientation between the two magnetic fields of a permanent magnet synchronous motor. Finding the initial (at motor powering- up time) value of this relative location is essential for the proper operation of the motor. After showing the system controllability, the utilized feedback control loop finds this initial relative orientation quickly and accurately. Further, using the proposed method allows considerable cost saving, as a transducer that is usually used for this purpose can be eliminated. The cost saving is most obvious in the case of linear motors and angle motors with large diameters. The way the problem is posed is an essential part of this work, and it is the reason behind the apparent simplicity of the solution. The method proposed relies on a single sensor, and it was tested when a relative encoder was used.

Design of a common observer for two linear systems with unknown inputs

This paper considers the design of a common linear functional observer for two linear time-invariant systems with unknown inputs. A structure for a common observer which only uses the available output information is proposed. Here, for the proposed structure, we show that the simultaneous functional observation problem of two plants is reduced to a problem of designing two observers: the first is a full-order unknown input observer of one of the two systems; the second observer is a common unknown input observer of a system comprises two-connected systems. In general, the existence conditions for the second observer are very difficult to satisfy. This paper thus concludes that it is indeed very difficult to find a common observer for two linear systems with unknown inputs.

Dynamic output feedback sliding-mode control using pole placement and linear functional observers

This paper presents a methodological approach to design dynamic output feedback sliding-mode control for a class of uncertain dynamical systems. The control action consists of the equivalent control and robust control components. The design of the equivalent control and the sliding function are based on the pole-placement technique. Linear functional observers are developed to implement the sliding function and the equivalent control. Stability of the resulting system under the proposed control scheme is guaranteed. A numerical example is given to demonstrate its efficacy.