Research Into Multi-dimensional Taylor Network Control For Stochastic Nonlinear Systems

Nonlinearity is a common phenomenon in the field of engineering technology.Due to the wide application background,the stability analysis and controller design of nonlinear systems have always been the hotspots and the focus of research and theory,and many important results have been obtained.As an important part of nonlinear control theory,the investigation on stability analysis and control design of stochastic nonlinear systems has received more and more attention.Compared with the general deterministic nonlinear systems,the stochastic nonlinear systems have a better control precision and more widely application,and have successfully applied to aeronautic and aerospace engineering,chemical,economic and so on.However,the controller design and performance analysis for stochastic nonlinear systems are much more complicated and difficult due to taking into account of stochastic disturbances such as measurement error,modeling error and external environment.Despite that many developments have been achieved for the research of stochastic nonlinear systems,there are many issues worthy of study and resolve.Therefore,it is still a meaningful and challenging task to construct a simple but effective control algorithm for the stochastic nonlinear systems.In recent years,the multi-dimensional Taylor network(MTN)has been successfully used in nonlinear control systems,which provides a new simple approach for systematic design and stability analysis of nonlinear systems controllers.This dissertation is devoted to study the extension of the MTN control scheme to the stochastic nonlinear systems,address the problems of tracking control for several classes of stochastic nonlinear systems by using backstepping technique,adaptive control and dynamic surface control approach and so on.Moreover,the stability of the closed-loop systems is proved by employing Lyapunov theory.The main contributions of this thesis are summarized as follows:1.The problem of tracking control for single-input single-output stochastic nonlinear systems is studied,and a MTN control scheme that only dependent on system output is developed.The multi-dimensional Taylor network controller(MTNC)has the merits of simple structure,small calculation and convenient weights adjusting as well as practical engineering.By introducing a quartic Lyapunov function and using Lyapunov stability theory,it is proved theoretically that the designed multi-dimensional Taylor network controller can guarantee the stability of close-loop control system.Based on the quadratic cost function design learning algorithm,the tracking error is minimized to update the controller parameters,and the desired tracking performance is obtained.Finally,a numerical example is provided to illustrate the effectiveness of the proposed design approach.2.The problem of adaptive tracking control is investigated for single-input single-output uncertain stochastic nonlinear systems,by combining adaptive approach and backstepping technique,an adaptive MTN control scheme is proposed.It is shown that the proposed controller can guarantee that all signals of the closed-loop system remain bounded in probability,and the tracking error converges to an arbitrarily small neighbourhood around the origin.In the controller design,multi-dimensional Taylor networks are utilized to approximate the nonlinearities of the system,and an adaptive multi-dimensional Taylor network controller is constructively designed by the backstepping method.It should be noted that in order to reduce the number of multidimensional Taylor network,we lump all unknown functions into a suitable unknown function that is approximated by only an MTN in each step of the backstepping.In other words,for an-th order stochastic nonlinear system,only multidimensional Taylor networks are needed.By introducing a quartic Lyapunov function and using Lyapunov stability theory,it is proved theoretically that the designed multi-dimensional Taylor network controller can guarantee the stability of close-loop control system.Finally,numerical simulation examples results showed that the proposed method can get precise tracking results with low computational cost,and have a good real-time performance and convergence.3.Under the conditions of all the system states are available,the problem of adaptive tracking control is investigated for large-scale stochastic nonlinear systems,by combining adaptive approach and backstepping technique,a decentralized adaptive MTN control scheme is proposed.It is shown that the proposed controller can guarantee that all signals of the closed-loop system remain bounded in probability,and the tracking errors converge to an arbitrarily small neighbourhood around the origin.In the controller design,MTNs are utilized to approximate the nonlinearities of the system,and backstepping technique is used to construct decentralized adaptive MTN controller.The dynamic surface control(DSC)technique is used to avoid the problem of "explosion of complexity" in the backstepping design process.By introducing a quartic Lyapunov function and using Lyapunov stability theory,it is proved theoretically that the designed decentralized adaptive MTN controller can guarantee the stability of close-loop control system.Finally,numerical simulation examples results showed that the proposed method can get precise tracking results with low computational cost,and have a good real-time performance and convergence.4.Under the conditions of all the system states are not available except system outputs,the problem of adaptive tracking control is investigated for large-scale stochastic nonlinear systems.On the foundation of estimating the unmeasured states through the design of a nonlinear observer,by combining adaptive approach and backstepping technique,a decentralized adaptive MTN output-feedback control scheme is proposed.It is shown that the proposed controller can guarantee that all signals of the closed-loop system remain bounded in probability,and the tracking errors converge to an arbitrarily small neighbourhood around the origin.First,it is assumed that only the output of the system is measurable,so a state observer is designed to estimate the system states.Next,based on the designed observer,a decentralized adaptive MTN output-feedback controller based on backstepping technique is constructively design.Meanwhile,DSC technique is incorporated in adaptive backstepping control design in order to overcome the problem of the "explosion of complexity" in the backstepping design.Then,by introducing a quartic Lyapunov function and using Lyapunov stability theory,it is proved theoretically that the designed decentralized adaptive MTN output-feedback control can guarantee the stability of close-loop control system.Finally,numerical simulation examples results showed that the proposed method can get precise tracking results with low computational cost,and have a good real-time performance and convergence.