Applications of Affine Systems of Walsh Type to Generate Smooth Basis

The question on affine Riesz basis of Walsh affine systems is considered. An affine Riesz basis is constructed, generated by a continuous periodic function that belongs to the space on the real line, which has a derivative almost everywhere; in connection with the construction of this example, we note that the functions of the classical Walsh system suffer a discontinuity and their derivatives almost vanish everywhere. A method of regularization (improvement of differential properties) of the generating function of Walsh affine system is proposed, and a criterion for an affine Riesz basis for a regularized generating function that can be represented as a sum of a series in the Rademacher system is obtained.

Homoclinic Orbits in Several Classes of Three-Dimensional Piecewise Affine Systems with Two Switching Planes

The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine systems with two switching planes regardless of the symmetry. An analytic proof is provided using the concrete expression forms of the analytic solution, stable manifold, and unstable manifold. Meanwhile, a sufficient condition for the existence of two homoclinic orbits is also obtained. Furthermore, two concrete piecewise affine asymmetric systems with two homoclinic orbits have been constructed successfully, demonstrating the method’s effectiveness.

On the state independency and log-linearity of error propagation for discrete group affine systems with application to attitude estimation

Purpose This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems. Design/methodology/approach The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems. Findings The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis. Practical implications An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results. Originality/value The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work.

Adaptive Coordinated Control Strategy of Multi Manipulator System based on Multi-Agent

With people's increasing awareness of life and the increasing complexity of exploration in unknown environment, a single robot can not meet the increasing demand, including the price, flexibility and efficiency of robots. As a common mechanical control system in industrial production instead of human production, multi manipulator system can be applied in complex environment, multi task and other conditions. In order to settle the coordinated control fault of multi manipulator system, we study adaptive coordinated control strategy with the help of multi-agent research method in this paper, which can simplify the complexity of the problem and design an efficient and feasible system control protocol. The complex items in the multi manipulator system are treated as non affine systems. Using the design idea of non affine algorithm, combined with implicit function theorem and median theorem, the non affine system is transformed into affine systems, the controller is separated, and a distributed adaptive control strategy is designed. The results indicate that manipulator systems can effectively track the active manipulator system in finite time and the significance of the algorithm is proven by MATLAB simulation analysis.