Adaptive Learning Control For Uncertain Strict-feedback Dynamical Nonlinear Systems

Due to the coupling of dynamic behavior,the variation of working environment,and limitations imposed by sensor measurement,it is really difficult to obtain accurate mathematical models of uncertain systems.Taking uncertainties into consideration and analyzing their effects are of great significance.Intelligent learning algorithms effectively address this issue.The adaptive fuzzy control strategy based on the main working principles of fuzzy logic systems is effective.In order to further improve the intelligence and learning ability of the controller,reduce the impact of model uncertainty on the closedloop performance,and propose a universal control strategy for such uncertain nonlinear systems,this dissertation firstly considers the control problems for non-periodic nonlinear systems,and proposes two kinds of online adaptive learning control strategies to improve the system’s ability to cope with the issues caused by uncertain dynamic changes.Then,for periodic nonlinear systems with repetitive dynamic behavior,this dissertation studies the control problem of such systems perturbed by stochastic disturbances under non-strict repetition conditions and proposes an off-line adaptive learning control strategy.In addition,considering the structure similarity of periodic systems,this dissertation studies the iterative learning control problem of such systems under limited system bandwidth and restricted data transmission,and proposes a finite-iteration off-line adaptive learning control strategy.The main contents of this dissertation can be summarized as follows:1.This dissertation investigates the adaptive fuzzy control and uncertainty analysis problems for a class of lower-triangular nonlinear systems without repetitive dynamics.By designing a Lyapunov function and analyzing the performance of the closed-loop system,it is shown that the adaptive parameter estimation error of the fuzzy logic systems is uniformly ultimately bounded.That is,when the time is infinitely long,the approximation error can converge to a tunable neighborhood of the origin with suitable control parameters.Based on this,in order to improve the approximation speed of fuzzy logic systems and reduce the tracking errors caused by the complexity of adaptive parameter design and inaccurate selection of fuzzy basis functions,a cost function directly related to the approximation errors of fuzzy logic systems is defined.An online parameter update law containing direct feedback of the approximation error is established based on the first-order numerical optimization algorithm,gradient descent algorithm.Because of the fast convergence of the gradient descent scheme in solving optimal control problems,the proposed algorithm reduces the difficulties of fuzzy logic system design and improves its approximation accuracy to unknown nonlinear functions.2.This dissertation investigates the adaptive learning control problem for a class of general strict-feedback nonlinear systems without lower triangular structure and repetitive dynamics based on second-order numerical optimization algorithm,quasi-Newton method.As for the aforementioned gradient descent parameter update laws,the learning factor to be designed directly affects the approximation ability of the fuzzy logic systems.Based on this,a quasi-Newton adaptive learning control strategy with learning factor selfadjustment scheme is proposed.Compared with the gradient descent algorithm,which is based on the first-order Taylor expansion of the cost function,the quasi-Newton method replaces the original extremum point of the cost function with the extremum point of its second-order Taylor expansion.The fuzzy logic system designed based on this method shows faster convergence speed and higher approximation accuracy.The design of the filter error compensation based command filter control scheme effectively solves the “dimension explosion” problem during the backstepping control design process,reduces the difference between the output of the command filter and the virtual control signal,which thus simplifies the control design process.3.For a class of It(?) stochastic nonlinear systems which perform repetitive tasks,the effects of random disturbances and unknown nonlinear functions are considered.An offline adaptive iterative learning control scheme is designed based on the information from previous periods,and an off-line uncertainty compensation strategy is proposed.Since it is more easier to obtain off-line data from previous periods than obtaining online data from the current period,we mainly focus on the off-line iterative learning control problem for such periodic nonlinear systems.In addition,we design a novel error variable with both time domain property and iteration domain property based on the time-varying boundary layer technique,which solves the control design and iteration convergence analysis problems that arise because of the non-strict repeatability initial condition.The consideration of initial shifts makes the iterative learning control strategy for the aforementioned stochastic systems more applicable.4.For repetitive uncertain nonlinear systems,it is known from the analysis process of learning convergence that the iterative variable converges only when the number of period index tends to infinity.This implies that the control signal should be iteratively updated with the increase of period index,and the data transmission is done in every iteration period.However,under limited network bandwidth and communication resources,the above data transmission conditions are no longer met.Then,a novel event-triggered mechanism for iterative variable along with the iteration axis is proposed based on the time-domain event-triggering principle.A new idea of iterative learning control is thus proposed,which updates the iterative variable and control input only when the accumulated learning increment exceeds the dynamic threshold.The update of iterative variable and control signal are effectively reduced by the proposed event trigger-based finite iteration adaptive learning control strategy.The convergence of the iterative variable and the tracking error under the proposed scheme are proved by the energy function based method.