Adaptive Stabilization Researches For Two Classes Of Stochastic Nonlinear Systems

In the field of control science,stochastic nonlinear systems are generally regarded as an important and more general model of nonlinear systems,which has attracted extensive attention of scholars in recent decades and has received a lot of research.In this paper,we first discuss the stabilization problem on a class of stochastic high-order nonlinear systems with unknown control direction.In addition to the serious degree of nonlinearity,the most obvious feature of the system is that the control direction is unknown,that is,the signs of the control coefficients are unknown.By skillfully constructing Nussbaum function and adopting the method of adding power integrator method,an effective control design strategy is proposed for the system.The control strategy ensures that all states in the closed-loop system are almost bounded,and the states of the original system converge to the origin with probability one.In order to verify the correctness of the theory and results,simulation examples are used to illustrate.Secondly,we also consider the problem of adaptive stabilization for a class of stochastic nonlinear systems with unknown output gain.It is worth noting that only the sign of output gain is known,and its magnitude is unknown.In order to achieve the control objective,besides designing a full-order observer,a new unknown parameter is introduced to estimate and address the uncertainty of the system.Furthermore,by adding power integrator and homogeneous control method,an adaptive stability controller is constructed for the system,which can make the closed-loop system globally asymptotically stable.