Xiaotian Yu

Singularity-conquering ZG controllers of z2g1 type for tracking control of the IPC system

With wider investigations and applications of autonomous robotics and intelligent vehicles, the inverted pendulum on a cart (IPC) system has become more attractive for numerous researchers due to its concise and representative structure. In this article, the tracking-control problem of the IPC system is considered and investigated. Based on Zhang dynamics (ZD) and gradient dynamics (GD), a novel kind of ZG controllers are developed and investigated for achieving the tracking-control purpose, which contains controllers of z2g0 and z2g1 types according to the number of times of using the ZD and GD methods. Besides, theoretical analyses are presented to guarantee the global and exponential convergence performance of both z2g0 and z2g1 controllers. Computer simulations are further performed to substantiate the feasibility and effectiveness of ZG controllers. More importantly, comparative simulation results demonstrate that controllers of z2g1 type can conquer the singularity problem (i.e. the division-by-zero problem).

Cross-validation based weights and structure determination of Chebyshev-polynomial neural networks for pattern classification

Abstract This paper first proposes a new type of single-output Chebyshev-polynomial feed-forward neural network (SOCPNN) for pattern classification. A new type of multi-output Chebyshev-polynomial feed-forward neural network (MOCPNN) is then proposed based on such an SOCPNN. Compared with multi-layer perceptron, the proposed SOCPNN and MOCPNN have lower computational complexity and superior performance, substantiated by both theoretical analyses and numerical verifications. In addition, two weight-and-structure-determination (WASD) algorithms, one for the SOCPNN and another for the MOCPNN, are proposed for pattern classification. These WASD algorithms can determine the weights and structures of the proposed neural networks efficiently and automatically. Comparative experimental results based on different real-world classification datasets with and without added noise prove that the proposed SOCPNN and MOCPNN have high accuracy, and that the MOCPNN has strong robustness in pattern classification when equipped with WASD algorithms.

ZD and ZG controllers for explicit and implicit tracking of pendulum with singularity finally conquered

Zhang dynamics (ZD) and gradient dynamics (GD) are both powerful methods. Based on a pendulum system, this paper investigates both of the explicit and implicit tracking control using the ZD method. For solving the singularity-containing implicit tracking problems, this paper overcomes the singularities by using the ZD method in combination with the GD method (i.e., the ZG method). Analyses and simulations of an explicit tracking example and two implicit tracking examples show the superiority of the ZD and ZG methods.

Pruning-included weights and structure determination of 2-input neuronet using Chebyshev polynomials of Class 1

A new type of feed-forward 2-input neuronet using Chebyshev polynomials of Class 1 (2INCP1) is constructed and investigated in this paper. In addition, with the weights-direct-determination method exploited to obtain the optimal weights from hidden layer to output layer directly (i.e., just in one step), a new structure-automatic-determination method called weights-and-structure-determination (WASD) algorithm is proposed to determine the optimal number of hidden-layer neurons of the 2INCP1. Such a WASD algorithm includes a procedure of pruning the proposed neuronet (after the net grows up). Numerical results further substantiate the efficacy of the 2INCP1 equipped with the so-called WASD algorithm.

Weights and structure determination of multiple-input feed-forward neural network activated by Chebyshev polynomials of Class 2 via cross-validation

Differing from conventional improvements on backpropagation (BP) neural network, a novel neural network is proposed and investigated in this paper to overcome the BP neural-network weaknesses, which is called the multiple-input feed-forward neural network activated by Chebyshev polynomials of Class 2 (MINN-CP2). In addition, to obtain the optimal number of hidden-layer neurons and the optimal linking weights of the MINN-CP2, the paper develops an algorithm of weights and structure determination (WASD) via cross-validation. Numerical studies show the effectiveness and superior abilities (in terms of approximation and generalization) of the MINN-CP2 equipped with the algorithm of WASD via cross-validation. Moreover, an application to gray image denoising demonstrates the effective implementation and application prospect of the proposed MINN-CP2 equipped with the algorithm of WASD via cross-validation.

Pseudoinverse-based jerk-level solutions of D3Z0, D2Z1, D1Z2 and D0Z3 types to redundant manipulator's inverse kinematics

The pseudoinverse-based method, as a conventional method, is generally used in the motion planning and control of velocity and/or acceleration level(s) to solve the complicated inverse-kinematics (IK) problem. In this paper, we firstly propose a simple pseudoinverse-based solution at the jerk level to solve the IK problem by using direct derivative dynamics (DDD or D3 for short) thrice and without using Zhang dynamics (ZD), which is thus termed D3Z0 type. Note that, though the D3Z0 solution is simple, it has some inherent weaknesses, such as low control precision and lack of necessary feedbacks. Therefore, as an important branch of dynamics methods, ZD is adopted to solve the above weaknesses. According to the number of times of using ZD, three enhanced solutions termed D2Z1, D1Z2 and D0Z3 types are then proposed and investigated. Specifically, D2Z1 means that we use 3D twice and ZD once to construct the solution, and D1Z2 and D0Z3 can be obtained and defined similarly. Moreover, feedbacks of position, velocity and acceleration levels can be partially or fully incorporated into the D2Z1, D1Z2 and D0Z3 solutions. Meanwhile, based on D3Z0, D2Z1, D1Z2 and D0Z3 solutions, a relatively complete framework of DZ-type solutions is thus proposed for solving the IK problem at the jerk level. Finally, simulation results performed on a five-link redundant manipulator substantiate the effectiveness and superiority of the DZ-type solutions for manipulator motion planning and control, which further show both smooth and efficient tracking performance, especially for solving the jerk-level IK redundancy of manipulators.

ZG Controllers of z2g0 and z2g1 Types for Tracking Control of IPC Mathematical Model

Abstract Recently, the Zhang dynamics (ZD) and the gradient dynamics (GD) have been used for solving online problems, but they are usually investigated separately. In this paper, we firstly illustrate the ZD method and the GD method by employing them separately to solve the time-varying matrix inversion problem. Then, to solve the tracking-control problem of the mathematical model of the inverted pendulum on a cart (IPC) system, the ZD-based (i.e., z2g0) controller and the ZD-GD combined (i.e., z2g1) controller are designed. These two types of controllers with greatly simplified design procedure can achieve good performance in terms of tiny tracking error and quick response. The simulation results further substantiate the feasibility and superiority of the z2g0 controller and the smoother z2g1 controller for the output tracking of the mathematical model of the IPC system.

Controller design of nonlinear system for fully trackable and partially trackable paths by combining ZD and GD

Zhang dynamics (ZD), which is based on an indefinite error-monitoring function called Zhangian, is a powerful type of dynamics for online time-varying problems solving. Besides, gradient dynamics (GD), which was originally designed to solve constant problems, can be generalized for online time-varying problems solving. In this paper, the tracking-control problem of a general nonlinear system with fully trackable and partially trackable paths is presented and investigated. Then, by combining ZD and the generalized GD, an innovative method called ZD-GD method is proposed to solve this tracking-control problem. Simulation results on the nonlinear system further substantiate the feasibility and superiority of the combined ZD-GD method for both fully trackable and partially trackable paths.

Weights and structure determination (WASD) of multiple-input hermit orthogonal polynomials neural network (MIHOPNN)

Based on the theory of polynomial-interpolation and curve-fitting, a new multiple-input feed-forward neural network activated by Hermit orthogonal polynomials is proposed and investigated. Besides, the design makes the multiple-input Hermit orthogonal polynomials neural network (MIHOPNN) have no weakness of dimension explosion. To determine the optimal weights of the MIHOPNN, the weight direct determination (WDD) method is presented. To obtain the optimal structure of the MIHOPNN, the so-called weight and structure determination (WASD) method is finally proposed, which aims at achieving the best approximation accuracy while obtaining the minimal number of hidden-layer neurons. Numerical results further substantiate the efficacy of the MIHOPNN model and WASD method.

Zhang equivalence of different-level robotic schemes: An MVN case study based on PA10 robot manipulator

Inverse kinematics (or say, redundancy resolution) is a fundamental issue in operating redundant manipulators, which has been widely investigated in the past three decades. Many redundancy-resolution schemes have been proposed for such a problem solving, which mainly work at a single level (e.g., the joint-velocity level or the joint-acceleration level). In this paper, for robotic redundancy resolution, two general scheme-formulations at two different levels are presented and investigated, one of which corresponds to the velocity-level schemes and the other corresponds to the acceleration-level schemes. The equivalent relationship between such two robotic schemes at two different levels is established via Zhang et als neural-dynamics method, i.e., the so-called Zhang equivalence. Theoretical analysis on the case of minimum velocity norm (MVN) scheme, together with computer simulations based on the PA10 robot manipulator, substantiates well the reasonableness of Zhang equivalence. That is, the robotic redundancy-resolution schemes at different levels (e.g., at the joint-velocity level and at the joint-acceleration level) could be practically equivalent by using suitable performance indices and constraints.