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In this paper, an adaptive state-feedback control technique is proposed for a class of unknown pure-feedback systems. A remarkable feature is that not only the problem of full-state constraints and prescribed performance tracking is solved together, but also the design is an approximation-free control scheme for pure-feedback systems with completely unknown nonlinearities. These properties will lead to a difficult task for designing a stable controller. To this end, a novel prescribed performance-barrier Lyapunov function is developed to guarantee that all the state constraints are not violated and the tracking error is preserved within a specified prescribed performance bound at all times, simultaneously. Then, by utilizing the mean value theorem, Nussbaum gain technique, a low-pass filter and a novel bounded estimation approach at each step of back-stepping procedure, a novel adaptive dynamics surface control scheme is developed to remove the difficulties of pure-feedback characteristic, unknown nonlinearities, unknown control direction and “explosion of complexity”, which can guarantee that the proposed design is universal and low-complexity. Moreover, it is proved that all the signals in the closed-loop system are global uniformly bounded. Two simulation studies are worked out to illustrate the performance of the proposed approach.

In this study, an adaptive dynamic surface control scheme is developed for a class of nonlinear systems. The considered systems can be viewed as a class of unknown pure feedback non-affine systems with multiple constraints. One remarked advantage is that not only less adjustable parameters are used in the design but also the design structure is universal for different systems. The characteristics of the considered systems will lead to a difficult task for design a low-complexity and stable controller. To this end, the mean value theorem is employed to transform the pure feedback systems into a linear structure, but non-affine terms still exist. Then, a novel recursive design procedure is constructed to remove the difficulties of unknown model, pure feedback non-affine characteristic and multiple constraints by integrating two auxiliary elementary functions with a novel bounded estimation approach. Furthermore, based on Lyapunov stability theorem and decoupled back-stepping method, it is proved that all the signals in the close-loop system are global uniformly bounded and the tracking error satisfies prescribed transient and steady state performance indexes constraints. Finally, simulation studies clarify and verify the approach.

For a class of non-affine nonlinear systems with state constraints, input constraint, uncertain parameters and unknown external disturbance, a back-stepping control scheme is proposed based on mean value theorem, nonlinear mapping and prescribed performance bounds (PPB). The non-affine system is first transformed into a time-varying system with a linear structure by using the mean value theorem, and the intervals of the time-varying uncertain parameters are calculated. The bounded time-varying parameters and external disturbance are estimated by adaptive algorithms with projection; the estimation error is compensated by employing nonlinear damping technology. To handle the state and input constraints, the nonlinear mapping technique (NMT), hyperbolic tangent function and Nussbaum function are employed. The prescribed performance control method improves the performance of the system. It is proved that the proposed control scheme can guarantee that all signals of the closed-loop system are bounded through the Lyapunov analysis. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

To solve the control problem for a class of uncertain pure feedback nonlinear systems subjected to external disturbances and multiple constraints, an adaptive robust control methodology is proposed based on a disturbance observer. To handle unknown nonlinearity and external unknown disturbances, a nonlinear disturbance observer is constructed based on a radial basis function neural network, which uses a Butterworth low-pass filter to remove the algebraic loop problem. Then, to guarantee that the system can stably track the desired trajectory under the state constraints, input saturation, and prescribed tracking performance constraints, we developed a novel barrier Lyapunov function and a backstepping controller that combines an auxiliary bounded function, a Nussbaum function, and a first-order sliding-mode differentiator. Subsequently, the stability of the closed-loop system is rigorously proved by Lyapunov analysis. Finally, simulations are conducted to demonstrate the effectiveness of the proposed approach.

In this paper, the adaptive robust tracking control scheme is proposed for a class of multi-input and multi-output (MIMO) non-affine systems with uncertain structure and parameters, unknown control direction and unknown external disturbance based on backstepping technique. The MIMO non-affine system is first transformed into a time-varying system with strict feedback structure using the mean value theorem, and then the bounded time-varying parameters are estimated by adaptive algorithms with projection. To handle the possible "controller singularity" problem caused by unknown control direction, a Nussbaum function is employed, and the dynamic surface control (DSC) method is applied to solve the problem of "explosion of complexity" in backstepping control. It is proved that the proposed control scheme can guarantee that all signals of the closed-loop system are bounded through Lyapunov stability theorem and decoupled backstepping method. Simulation results are presented to illustrate the effectiveness of the proposed control scheme.

In this work, an adaptive control technique is proposed for a category of unknown pure feedback nonlinear systems by using back-stepping technique. To guarantee the low-complexity of controller, a novel back-stepping control scheme is developed to solve the problems of unknown nonlinearities and “explosion of complexity” by integrating the mean value theorem and supremum norm theory with first-order sliding-mode differentiator, which can guarantee that the number of adjustable parameters is only one and the design is an approximation-free control scheme. The developed adaptive controller guarantees that all signals in the closed-loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal. Finally, Simulation results further demonstrate the validity of the proposed control scheme.

In this paper, a tracking control problem for the unknown longitudinal model of hypersonic flight vehicle is investigated. One remarked advantage is that not only less adjustable parameters are used in the design but also the design is independent of the model. Based on the characteristics of the longitudinal dynamics, The hypersonic flight vehicle system is divided into two subsystems, including an attitude subsystem and a velocity subsystem. The prescribed performance control theory is adopted to construct nonlinear PID controller for velocity subsystem. Then, for attitude subsystems, a novel recursive design procedure is constructed to remove the difficulties of unknown model by integrating mean value theory with a novel bounded estimation approach. Finally, simulation results are provided to demonstrate the effectiveness of the proposed method.