On Adaptive Output Feedback Dynamic Surface Control Of Several Classes Of Uncertain Nonlinear Systems

There exist a lot of uncertainties in practical nonlinear control systems, for examples, modeling errors, model simplification, measuring noises, external disturbances and input unmodeled dynamics, etc. They have great effect on the stability of control system and easily lead to the performance of the system to be bad or make the system unstable. The adaptive control of the nonlinear systems with unmodeled dynamics has been widely studied and has achieved fruitful results, which can effectively restrain the influence of the unmodeled dynamics on the control systems. For the nonlinear systems with input unmodeled dynamics, the discussions mainly focused on the stabilization problems of the control systems, and relatively, few results were provided in the existing literature. In the past decades, the robust adaptive control based on backstepping for nonlinear systems has obtained wide attention from researchers on control theory and control engineering, and it has also been one of hotspots of research in 1990’s. However, the controller based on backstepping has complex structure. Swaroop et al. proposed dynamic surface control (DSC) method by introducing one-order filters, which can overcome the drawback of backstepping. In recent years, some adaptive DSC schemes have been proposed by combining backstepping design with DSC technique, but few results that apply DSC method to design controllers for uncertain nonlinear systems and stochastic nonlinear systems are presented, and strict stability analysis under DSC still need further study.In this dissertation, combining the approximation of neural networks or fuzzy systems, K-filters design, backstepping, changing supply function, DSC with adaptive control, systematic design and analysis methods of adaptive DSC are proposed for several classes of uncertain nonlinear systems with state and input unmodeled dynamics. The detailed results are addressed as follows:(1) By introducing dynamic signal to deal with unmodeled dynamics, utilizing radial basis function neural network to approximate unknown nonlinear function, designing neural network K-filters to estimate unmeasurable state and utilizing Nussbaum function and special controller structure to handle unknown high-frequency gain sign, two adaptive output feedback control schemes are proposed based on DSC. Using bounded input bounded output property and the compact set defined in DSC, the stability analysis of the closed-loop system is presented, and the condition of assuming approximating error to be bounded, which is used in traditional backstepping method, is removed. Furthermore, a novel description of unmodeled dynamics is further proposed by expanding Lyapunov converse theorem on global exponential stability, and the problem of the stability proof of the closed-loop system with this description is resolved by a constructing method. With the DSC method, the assumptions of the unmodeled dynamics are relaxed, and the estimate of the unknown continuous function produced in theoretical analysis is canceled, thus the complexity of design is reduced.(2) An adaptive dynamic surface output feedback control scheme is proposed for a class of uncertain nonlinear systems with input unmodeled dynamics, input dead-zone and prescribed performance. The considered input unmodeled dynamics is of nonlinear form. Combining the character of reduced-order filters with K-filters, reduced-order neural K-filters are designed; input unmodeled dynamics is handled by introducing normalization signal; dead-zone nonlinear is dealt with by utilizing dead-zone linearization model. Through introducing the transformation of tracking error, the transient performance of the system is guaranteed. By combining DSC method with filters’ special structure, all the signals in the closed-loop system are proved to be bounded. Utilizing the feature of DSC technique, the assumption of input unmodeled dynamics is broadened.(3) A decentralized adaptive DSC scheme based on neural networks is proposed for a class of interconnected nonlinear large-scale systems in strict-feedback form with similar structure and unmodeled dynamics. Unmodeled dynamics is described by using the Lyapunov function method. Neural networks are used to approximate the unknown nonlinear continuous functions that are produced in theoretical analysis. The interconnected terms are effectively dealt with by using Young’s inequality and decomposition of the threefold summation term, and the decentralized control is realized by utilizing DSC technique. Compared with the existing results, the designed decentralized control laws do not contain the lower bound of control gain. By the theoretical analysis, the closed-loop control system is shown to be semi-globally uniformly ultimately bounded, with the tracking error converging to a small neighborhood of the origin. Simulation results for the inverted double pendulums on carts are presented to show the effectiveness of the proposed scheme.(4) Centralized and decentralized adaptive output feedback adaptive DSC schemes are proposed for a class of uncertain large-scale nonlinear systems with unmodeled dynamics and coupled outputs and states. Decentralized K-filters are constructed to estimate the unmeasured states of each subsystem. The coupling terms are handled by using separation theorem, Young’s inequality and the fact that the upper bound value of the norm of neural network(NN) radial basis function vector is independent of the NN inputs and the dimension of weight vector. Furthermore, an adaptive output feedback decentralized DSC strategy is further proposed for uncertain nonlinear interconnected systems with prescribed performance and direct input coupling. The considered control input and coupled input is of nonlinear input unmodeled dynamics. Extended decentralized K-filters are constructed to estimate unmeasured states. Normalization signals are designed to counteract the instable impact produced by nonlinear input unmodeled dynamics. With new variables being defined, the decentralized neural controllers can be obtained by solving the linear equations after the indirect control law of each subsystem is designed through DSC. By the theoretical analysis, all the signals in the closed-loop system are proved to be semi-globally uniformly ultimately bounded, and the transient tracking performance is guaranteed simultaneously.(5) An adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmodeled dynamics and unmeasured states. The neural networks weight vector used to approximate the black box function is adjusted online. The unknown nonlinear system functions are handled together with some functions resulting from theoretical deduction, and such method effectively reduces the number of adaptive tuning parameters. Using bounded input bounded output stability theorem and utilizing the filters’ special structure to construct linear equations, the stability of the closed-loop system is proved. Using DSC technique, Ito formula and Chebyshev’s inequality, the designed controller can guarantee that all the signals in the closed-loop system are bounded in probability.(6) An adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with input unmodeled dynamics and stochastic inverse dynamics. Stochastic inverse dynamics is dealt with by constructing a changing supply function. Combining DSC technique with stochastic input-to-state stability and small-gain condition, the designed robust adaptive controller can guarantee that all the signals in the closed-loop system are bounded in probability, and the error signals are semi-globally uniformly ultimately bounded in mean square or the sense of four-moment. Furthermore, utilizing Chebyshev’s inequality to build relationship between moment boundedness of nonnegative stochastic variable and probability boundedness of variable, a complete stability analysis for stochastic system is presented in strict mathematical form. The simulation results for single-link robotic manipulator system show the effectiveness of the proposed scheme.(7) By extending the results in (5), centralized and decentralized adaptive fuzzy output feedback control schemes are investigated for a class of stochastic nonlinear interconnected large-scale systems based on DSC and observer subsystem. Fuzzy systems are used to approximate the unknown nonlinear functions. Using the defined compact set in the stability analysis, the unknown smooth interconnections and black box functions are effectively dealt with. Using the feature of 2-norm of fuzzy basis vector, decentralized stochastic adaptive fuzzy output feedback control is carried out. The designed decentralized filters do not contain the fuzzy basis vectors and adjustable parameters. Therefore, the order of the filters is reduced. The theoretical analysis show that the designed robust adaptive controller can guarantee all the signals in the closed-loop system to be bounded in probability and the error signals semi-globally uniformly ultimately bounded in mean square or the sense of four-moment. Simulation results for the tripled inverted pendulums connected by springs demonstrate the effectiveness of the proposed approach.