Adaptive Dynamic Surface Control For Constrained Stochastic Nonstrict-feedback Nonlinear Systems

There are stochastic factors in the operating environment of any actual system.When modeling the actual system,it is also necessary to consider the influence of stochastic factors.Therefore,the research of stochastic systems in the control field is necessary,which makes the stochastic system always been research hotspots.This paper studies the tracking problems of several types of stochastic nonstrict-feedback systems with unmodeled dynamics,and proposes several adaptive control schemes.The main contents are as follows:(1)An adaptive neural control method is discussed for a class of stochastic nonstrict-feedback constrained nonlinear systems with input and state unmodeled dynamics.A dynamic signal produced by the first-order auxiliary system is employed to deal with the dynamical uncertain terms.Radial basis function neural networks(RBFNNs)are used to reconstruct unknown nonlinear continuous functions.With the help of themean value theorem and Young's inequality,only one learning parameter is adjusted online at recursive each step.Using the hyperbolic tangent function as nonlinear mapping,the output constrained stochastic nonstrict-feedback system in the presence of unmodeled dynamics is transformed into a novel unconstrained stochastic nonstrict-feedback system.Based on dynamic surface control(DSC)technology and the property of Gaussian function,adaptive neural control is developed for the transformed stochastic nonstrict-feedback system.By the Lyapunov method,all signals of the closed-loop control system are proved to be semi-global uniform ultimate bounded(SGUUB)in probability.The output abides by stochastic constraints in probability.(2)A stochastic adaptive DSC is discussed for stochastic nonstrict-feedback constrained nonlinear systems with input quantization and input unmodeled dynamics.Linearly parametrized neural networks(LPNNs)are used to estimate unknown continuous functions.With the help of MT-filters,the unmeasurable system states are observed.A auxiliary signal constructed by the property of unmodeled dynamics is utilized to deal with the dynamic uncertain terms.Input-quantized actuator is considered to possess quantization and unmodeled dynamics.Using the hyperbolic tangent function as invertible change,the output constrained stochastic nonstrict-feedback system is transformed into a novel stochastic nonstrict-feedback system without restrictions.Based on quantized DSC technology and the property of Gaussian function,adaptive neural control is developed for the transformed stochastic nonstrict-feedback system.By the Lyapunov synthesis approach,all signals in the whole system are proved to be SGUUB in probability.The output abides by stochastic time-varying constraints in probability.(3)A finite-time stochastic adaptive DSC is discussed for stochastic non-affine nonstrict-feedback constrained nonlinear systems with time-varying full state constraints.To cope with the asymmetric time-varying full state constraints,the hyperbolic tangent function are introduced to make all states maintain in the predefined area.A changing supply function is established to deal with stochastic inverse dynamics.Radial basis function neural networks are used to reconstruct unknown nonlinear continuous functions.Using the mean value theorem to convert non-affine structure to affine form.For the transformed system,the controller's structure designed by the improved dynamic surface control and the finite time method is simpler,and solves the"singularity" problem in the existing finite time control,and accelerates the convergence speed of the system.By the Lyapunov synthesis approach,all signals in the whole system are proved to be SGUUB in probability.The full state abides by stochastic constraints in probability.