scholarly journals Variance and Entropy Assignment for Continuous-Time Stochastic Nonlinear Systems

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 25
Author(s):  
Xiafei Tang ◽  
Yuyang Zhou ◽  
Yiqun Zou ◽  
Qichun Zhang

This paper investigates the randomness assignment problem for a class of continuous-time stochastic nonlinear systems, where variance and entropy are employed to describe the investigated systems. In particular, the system model is formulated by a stochastic differential equation. Due to the nonlinearities of the systems, the probability density functions of the system state and system output cannot be characterised as Gaussian even if the system is subjected to Brownian motion. To deal with the non-Gaussian randomness, we present a novel backstepping-based design approach to convert the stochastic nonlinear system to a linear stochastic process, thus the variance and entropy of the system variables can be formulated analytically by the solving Fokker–Planck–Kolmogorov equation. In this way, the design parameter of the backstepping procedure can be then obtained to achieve the variance and entropy assignment. In addition, the stability of the proposed design scheme can be guaranteed and the multi-variate case is also discussed. In order to validate the design approach, the simulation results are provided to show the effectiveness of the proposed algorithm.

2015 ◽  
Vol 25 (4) ◽  
pp. 491-496 ◽  
Author(s):  
Tadeusz Kaczorek

AbstractThe conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.


Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Shijun Guan ◽  
Liandi Fang

This paper investigates the finite-time stability problem of p-norm stochastic nonlinear systems subject to output constraint. To cope with the constraint on system output, a tan-type barrier Lyapunov function (BLF) is constructed. By using the constructed BLF and the backstepping technique, a new control algorithm is proposed with a continuous state-feedback controller being designed, which guarantees not only that the requirement of output constraint is always achieved but also that the origin of the system is finite-time stable. This result is demonstrated by both the rigorous analysis and the simulation example.


2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Xiaohua Liu ◽  
Wuquan Li

This paper investigates the stability of a class of stochastic nonlinear systems with Markovian switching via output-feedback. Based on the backstepping design method and homogeneous domination technique, an output-feedback controller is constructed to guarantee that the closed-loop system has a unique solution and is almost surely asymptotically stable. The efficiency of the output-feedback controller is demonstrated by a simulation example.


Author(s):  
Shan-Liang Zhu ◽  
Ming-Xin Wang ◽  
Yu-Qun Han

In this paper, the problem of adaptive finite-time multi-dimensional Taylor network (MTN) control for a class of stochastic nonlinear systems is investigated. By combining the MTN-based approximate method and adaptive backstepping technique, a novel adaptive finite-time MTN control scheme is proposed. In this scheme, the MTNs are used to approximate the unknown nonlinear functions of the systems. The finite-time Lyapunov stability theory is utilized to prove the stability of the close-loop system. The proposed scheme can ensure that all signals in the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood of the origin in a finite time. Three simulation examples are presented to show the effectiveness of the control scheme. It should be pointed that the adaptive MTN controller proposed in this paper has the advantages of fast computational speed and good real-time performance thanks to the simple structure of the MTN.


Author(s):  
Tadeusz Kaczorek

AbstractThe positivity and stability of standard and fractional descriptor continuous-time linear and nonlinear systems are addressed. Necessary and sufficient conditions for the positivity of descriptor linear and sufficient conditions for nonlinear systems are established. Using an extension of Lyapunov method sufficient conditions for the stability of positive nonlinear systems are given. The considerations are extended to fractional nonlinear systems.


2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Valiollah Ghaffari ◽  
Hamid Reza Karimi ◽  
Navid Noroozi ◽  
S. Vahid Naghavi

This paper addresses two control schemes for stochastic nonlinear systems. Firstly, an adaptive controller is designed for a class of motion equations. Then, a robust finite-time control scheme is proposed to stabilize a class of nonlinear stochastic systems. The stability of the closed-loop systems is established based on stochastic Lyapunov stability theorems. Links between these two methods are given. The efficiency of the control schemes is evaluated using numerical simulations.


Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 202 ◽  
Author(s):  
Angelo Alessandri

Lyapunov functions enable analyzing the stability of dynamic systems described by ordinary differential equations without finding the solution of such equations. For nonlinear systems, devising a Lyapunov function is not an easy task to solve in general. In this paper, we present an approach to the construction of Lyapunov funtions to prove stability in estimation problems. To this end, we motivate the adoption of input-to-state stability (ISS) to deal with the estimation error involved by state observers in performing state estimation for nonlinear continuous-time systems. Such stability properties are ensured by means of ISS Lyapunov functions that satisfy Hamilton–Jacobi inequalities. Based on this general framework, we focus on observers for polynomial nonlinear systems and the sum-of-squares paradigm to find such Lyapunov functions.


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