STABILITY OF LYAPUNOV EXPONENTS, WEAK INTEGRAL SEPARATION AND NONUNIFORM DICHOTOMY SPECTRUM

In this paper, a necessary and sufficient condition for the stability of Lyapunov exponents of linear differential system is proved in the sense that the equations satisfy the weaker form of integral separation instead of its classical one. Furthermore, the existence of full nonuniform exponential dichotomy spectrum under the condition of weak integral separateness is also presented.

Research on integral separation control of warp tension based on fuzzy parameter optimization

In textile machines, the stability of warp tension is one of the decisive factors for the reliability, stability and product quality of weaving process. In order to meet the improving requirement for weaving efficiency and fabric quality, it is proposed that a fuzzy optimization integral separation PID warp tension control scheme based on process sampling to improve the warp tension control level of loom. Aiming at the problems of time-varying, nonlinear and variable coupling in the warp tension control system of loom, the forming mechanism of warp tension is modeled and analyzed, and the sampling scheme of warp tension based on process is proposed. Based on the periodic change of warp tension at macro level and continuous fluctuation at micro level, the integral separation control and fuzzy optimization theory are introduced to optimize the control effect of the control system on the basis of classical PID control algorithm. Finally, the simulation and experiment show that the scheme can improve the tension controls performance and effectively reduce the tension error fluctuation.

Algebraic Criteria of the Integral Separation for Solving Certain Classes of Ordinary Differential Equations Systems

One of the important directions of the qualitative theory of ordinary differential equations is to study the properties of linear systems that satisfy the condition of integral separation. Anyway, integral separation becomes apparent in all studies concerning the asymptotic behavior of the solutions for the linear systems under the action of small perturbations.The papers of V.M. Millionschikov, B.F. Bylov, N.A. Izobov, I.N. Sergeev et al. proved that the available integral separation is the main reason for the rough stability of the characteristic Lyapunov exponents, the rough stability of the highest Lyapunov exponent, and the rough diagonalizability of systems by Lyapunov transformations, and other fundamental properties of linear differential systems.The paper presents the basic properties of the set of linear systems with constant, periodic, reducible coefficients and proves the algebraic criteria for their property of integral separation of solutions to be available.The results can be used in modeling dynamic processes.

Unmanned surface vessel heading control of model-free adaptive method with variable integral separated and proportion control

Based on model-free adaptive control theory, the heading control problem of unmanned surface vessels under uncertain influence is explored. Firstly, the problems of compact form dynamic linearization model-free adaptive control method applied to unmanned surface vessel heading control are analyzed. Secondly, by introducing proportional control and variable integral separation factor, an variable integral separation model-free adaptive control algorithm with proportional control is proposed. The introduction of proportional control and variable integral separation factor solves the problems of oscillation, instability, and integral saturation when rudder angle is controlled directly to control the heading of unmanned surface vessel with compact form dynamic linearization model-free adaptive control method. Finally, the effectiveness of the method is verified by the simulation and field experiments results of heading control with model perturbation and system time delay in unmanned surface vessel heading subsystem.