Fractional-Order Control for a Novel Chaotic System Without Equilibrium

The control problem is discussed for a chaotic system without equilibrium in this paper.On the basis of the linear mathematical model of the two-wheeled self-balancing robot,a novel chaotic system which has no equilibrium is proposed.The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincar′e map.To further demonstrate the physical realizability of the presented novel chaotic system,a chaotic circuit is designed.By using fractional-order operators,a controller is designed based on the state-feedback method.According to the Gronwall inequality,Laplace transform and Mittag-Leffler function,a new control scheme is explored for the whole closed-loop system.Under the developed control scheme,the state variables of the closed-loop system are controlled to stabilize them to zero.Finally,the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.

Polynomial networks based adaptive attitude tracking control for NSVs with input constraints and stochastic noises

This paper proposes a backstepping technique and Multi-dimensional Taylor Polynomial Networks(MTPN)based adaptive attitude tracking control strategy for Near Space Vehicles(NSVs)subjected to input constraints and stochastic input noises.Firstly,considering the control input has stochastic noises,and the attitude motion dynamical model of the NSVs is actually modeled as the Multi-Input Multi-Output(MIMO)stochastic nonlinear system form.Furthermore,the MTPN is used to estimate the unknown system uncertainties,and an auxiliary system is designed to compensate the influence of the saturation control input.Then,by using backstepping method and the output of the auxiliary system,a MTPN-based robust adaptive attitude control approach is proposed for the NSVs with saturation input nonlinearity,stochastic input noises,and system uncertainties.Stochastic Lyapunov stability theory is utilized to analysis the stability in the sense of probability of the entire closed-loop system.Additionally,by selecting appropriate parameters,the tracking errors will converge to a small neighborhood with a tunable radius.Finally,the numerical simulation results of the NSVs attitude motion show the satisfactory flight control performance under the proposed tracking control strategy.