This chapter introduces the subject of statistical pattern recognition (SPR). It starts by considering how features are defined and emphasizes that the nearest neighbor algorithm achieves error rates comparable with those of an ideal Bayes’ classifier. The concepts of an optimal number of features, representativeness of the training data, and the need to avoid overfitting to the training data are stressed. The chapter shows that methods such as the support vector machine and artificial neural networks are subject to these same training limitations, although each has its advantages. For neural networks, the multilayer perceptron architecture and back-propagation algorithm are described. The chapter distinguishes between supervised and unsupervised learning, demonstrating the advantages of the latter and showing how methods such as clustering and principal components analysis fit into the SPR framework. The chapter also defines the receiver operating characteristic, which allows an optimum balance between false positives and false negatives to be achieved.

Statistical Pattern Recognition

The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems. The finite time convergence of the observer is proved. Thus, the observer can be designed independently of the controller. A discrete version of the observer is considered and the corresponding accuracy is estimated.

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Second-order sliding-mode observer for mechanical systems

Dynamic analysis of flexible manipulators, a literature review

A review of atomic force microscopy imaging systems: application to molecular metrology and biological sciences

In this note, we present a new continuous control mechanism that compensates for uncertainty in a class of high-order, multiple-input-multiple-output nonlinear systems. The control strategy is based on limited assumptions on the structure of the system nonlinearities. A new Lyapunov-based stability argument is employed to prove semiglobal asymptotic tracking.

A continuous asymptotic tracking control strategy for uncertain nonlinear systems

This paper presents a novel asymptotic tracking controller for an underactuated quadrotor unmanned aerial vehicle using the robust integral of the signum of the error (RISE) method and an immersion and invariance (I&I)-based adaptive control methodology The control system is decoupled into two parts: the inner loop for attitude control and the outer loop for position control The RISE approach is applied in the inner loop for disturbance rejection, whereas the I&I approach is chosen for the outer loop to compensate for the parametric uncertainties The asymptotic tracking of the time-varying 3-D position and the yaw motion reference trajectories is proven via the Lyapunov-based stability analysis and LaSalle's invariance theorem Real-time experiment results, which are performed on a hardware-in-the-loop simulation testbed, are presented to illustrate the performance of the proposed control scheme

Nonlinear Robust Adaptive Tracking Control of a Quadrotor UAV Via Immersion and Invariance Methodology

A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems

This paper considers about the control problem for an underactuated quadrotor UAV system with model parameter uncertainty. Backstepping based techniques are utilized to design a nonlinear adaptive controller which can compensate for the mass uncertainty of the vehicle. Lyapunov based stability analysis shows that the proposed control design yields asymptotic tracking for the UAV's motion in x, y, z direction and the yaw rotation, while keep the stability of the closed loop dynamics of the quadrotor UAV. Numerical simulation results are provided to show the good tracking performance of proposed control laws.

Bin Xian

Papers

A continuous asymptotic tracking control strategy for uncertain nonlinear systems

Nonlinear Robust Adaptive Tracking Control of a Quadrotor UAV Via Immersion and Invariance Methodology

A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems

Adaptive tracking control of underactuated quadrotor unmanned aerial vehicles via backstepping

Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method