Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

In this paper, we present adaptive neural network tracking control of a robotic manipulator with input deadzone and output constraint A barrier Lyapunov function is employed to deal with the output constraints Adaptive neural networks are used to approximate the deadzone function and the unknown model of the robotic manipulator Both full state feedback control and output feedback control are considered in this paper For the output feedback control, the high gain observer is used to estimate unmeasurable states With the proposed control, the output constraints are not violated, and all the signals of the closed loop system are semi-globally uniformly bounded The performance of the proposed control is illustrated through simulations

Neural Network Control of a Robotic Manipulator With Input Deadzone and Output Constraint

The problem of asymptotic tracking control for a class of uncertain switched nonlinear systems under fuzzy approximation framework is solved in this paper. Superior to most existing results based on fuzzy adaptive control strategy that can only achieve bounded error tracking performance, our proposed control scheme can guarantee the local asymptotic tracking performance for the uncertain switched nonlinear systems under consideration. This is accomplished by constructing a nonsmooth Lyapunov function and introducing a novel discontinuous controller with dynamic feedback compensator in the design procedure. Meanwhile, some concepts, such as differential inclusion and set-valued map, are introduced to theoretically verify the local asymptotic tracking performance of the systems with our proposed controller. With the help of set-valued Lie derivative, the common virtual control functions, the desired controller, and the adaptive laws can be precisely constructed. Finally, simulation results are given to show the effectiveness of the proposed method.

Fuzzy Approximation Based Asymptotic Tracking Control for a Class of Uncertain Switched Nonlinear Systems

Evolving fuzzy and neuro-fuzzy approaches in clustering, regression, identification, and classification: A Survey

In this paper, an adaptive fuzzy output feedback control problem is investigated for a class of stochastic nonlinear systems in which the fuzzy logic systems are adopted to approximate the unknown nonlinear functions. A reduced-order observer and a general fault model are designed to observe the unavailable state variables and describe the actuator faults, respectively. An event-triggered control law is developed to reduce the communication burden from the controller to the actuator. Meanwhile, the barrier Lyapunov functions are constructed to guarantee that all the states of the stochastic nonlinear system are not to violate their constraints. Furthermore, an observer-based adaptive fuzzy event-triggered control strategy is proposed for the full-state-constrained nonlinear system with actuator faults based on backstepping technique, which can guarantee that all the signals in the closed-loop system are bounded and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.

Adaptive Fuzzy Event-Triggered Control for Stochastic Nonlinear Systems With Full State Constraints and Actuator Faults

Neural networks (NNs) have numerous applications to online processes, but the problem of stability is rarely discussed. This is an extremely important issue because, if the stability of a solution is not guaranteed, the equipment that is being used can be damaged, which can also cause serious accidents. It is true that in some research papers this problem has been considered, but this concerns continuous-time NN only. At the same time, there are many systems that are better described in the discrete time domain such as population of animals, the annual expenses in an industry, the interest earned by a bank, or the prediction of the distribution of loads stored every hour in a warehouse. Therefore, it is of paramount importance to consider the stability of the discrete-time NN. This paper makes several important contributions. 1) A theorem is stated and proven which guarantees uniform stability of a general discrete-time system. 2) It is proven that the backpropagation (BP) algorithm with a new time-varying rate is uniformly stable for online identification and the identification error converges to a small zone bounded by the uncertainty. 3) It is proven that the weights' error is bounded by the initial weights' error, i.e., overfitting is eliminated in the proposed algorithm. 4) The BP algorithm is applied to predict the distribution of loads that a transelevator receives from a trailer and places in the deposits in a warehouse every hour, so that the deposits in the warehouse are reserved in advance using the prediction results. 5) The BP algorithm is compared with the recursive least square (RLS) algorithm and with the Takagi-Sugeno type fuzzy inference system in the problem of predicting the distribution of loads in a warehouse, giving that the first and the second are stable and the third is unstable. 6) The BP algorithm is compared with the RLS algorithm and with the Kalman filter algorithm in a synthetic example.

/pdf/uniformly-stable-backpropagation-algorithm-to-train-a-3nqhmx1fwb.pdf

Uniformly Stable Backpropagation Algorithm to Train a Feedforward Neural Network

In previous investigations, the nonlinear hypothesis use the linear bounded maps. Nonlinear hypothesis are described as the combination of the first order terms, and after of the mentioned combination, one bounded map is applied to alter the result. This document proposes two nonlinear hypothesis which use different structures instead of using the linear bounded maps. They are termed as novel nonlinear hypothesis and second order nonlinear hypothesis and their goal is to improve the second order processes modeling. The proposed nonlinear hypothesis are described as the combination of the first order and second order terms. Since the delta parallel robot is a second order process, it is an excellent platform to prove the effectiveness of the two proposed hypothesis.

/pdf/novel-nonlinear-hypothesis-for-the-delta-parallel-robot-43w1jgouhn.pdf

Novel Nonlinear Hypothesis for the Delta Parallel Robot Modeling

Neural network updating via argument Kalman filter for modeling of Takagi-Sugeno fuzzy models

In this study, an observer for the states and disturbance estimation in two renewable energy systems is introduced. The restrictions of the gains in the proposed observer are found to guarantee its stability and the convergence of its error; furthermore, these results are utilized to obtain a good estimation. The introduced technique is applied for the states and disturbance estimation in a wind turbine and an electric vehicle. The wind turbine has a rotatory tower to catch the incoming air to be transformed in electricity and the electric vehicle has generators connected with its wheels to catch the vehicle movement to be transformed in electricity.

Uniform stable observer for the disturbance estimation in two renewable energy systems.

In this document, a control system is developed to allow a manipulator to learn and plan references from demonstrations given by an operator hand. Data entry is acquired by a sensor and is learned by the generalized learning model with least angle regression to create a desired reference in three dimensional space. A fifth reference profile is employed to smooth the desired reference. Direct and inverse kinematics are gotten to represent the transformation between the three dimensional space and each of the manipulator links. A dynamic model is gotten using Newton–Euler formulation. An evolving proportional derivative (PD) control is applied to get that the manipulator end effector follows the operator hand movements. The monitoring and control systems are implemented in an embedded platform for testing purposes.

Jaime Pacheco

Papers

Uniformly Stable Backpropagation Algorithm to Train a Feedforward Neural Network

Novel Nonlinear Hypothesis for the Delta Parallel Robot Modeling

Neural network updating via argument Kalman filter for modeling of Takagi-Sugeno fuzzy models

Uniform stable observer for the disturbance estimation in two renewable energy systems.

Learning of operator hand movements via least angle regression to be teached in a manipulator