This work removes the critical assumptions of continuity, differentiability, and state-independent boundedness, which are typical of compounded disturbances in disturbance observer-based adaptive designs. Crucial in removing such assumptions are a novel observer-based design with state-dependent gain in place of a constant one, and a novel set-invariance design. The designs use different a priori knowledge of the disturbance, but they can both handle state-dependent (e.g., possibly unbounded) disturbances, as well as non-smooth (e.g., non-differentiable and jump discontinuous) disturbances. The tracking error is proven to be as small as desired by appropriately choosing design parameters. For the second design, which uses the least a priori knowledge of the disturbance, stability is proven by enhancing Lyapunov theory with an invariant-set mechanism, so as to construct an appropriate compact set resulting an invariant set for the closed-loop trajectories.@en

This article proposes an output-feedback fixed-time trajectory tracking control methodology for hypersonic flight vehicles subject to asymmetric output constraints. In contrast to the state of the art, the most distinguishing feature of our control design lies in avoiding using conventional recursive design methods (e.g., backstepping technique, dynamic surface control, etc.) and in not relying on full-state availability. In the velocity control loop, an asymmetric integral barrier Lyapunov function is adopted to confine velocity variable within a well-defined compact set all the time. In the altitude control loop, after utilizing its cascaded property and proposing a novel scaling function, the original constrained system is transformed to an unconstrained one, which facilitates the control design and stability analysis. Moreover, the proposed control algorithm only involves one fuzzy logic approximator as well as one fixed-time differentiator in the transformed system and guarantees that the tracking errors of velocity and altitude converge into the user-defined residual sets within fixed time. Several comparative simulations have been conducted to highlight the superiorities of the developed method.@en

In dynamic surface control (DSC) methods, the control gain functions of systems are always assumed to be bounded, which is a restrictive assumption. This work proposes a novel DSC approach for an extended class of strict-feedback nonlinear systems whose control gain functions are continuous and possibly unbounded. Appropriate compact sets are constructed in such a way that the trajectories of the closed-loop system do not leave these sets, therefore, in these sets, maximums and minimums values of the continuous control gain functions are well defined even if the control gain functions are possibly unbounded. By using Lyapunov theory and invariant set theory, semi-globally uniformly ultimately boundedness is analytically proved: all the signals of closed-loop system will always stay in these compact sets, while the tracking error is shown to converge to a residual set that can be made as small as desired by adjusting design parameters appropriately. Finally, the effectiveness of the designed method is demonstrated via two examples.@en

This article solves the fixed-time trajectory tracking problem for hypersonic flight vehicles (HFVs) encountered with diverse actuator faults and asymmetric envelope constraints. In contrast to the state of the art, the crucial characteristics of our design lie in obviating the explosion of complexity of the conventional recursive design, and in realizing satisfactory preselected tracking qualities for flight states in the sense of guaranteeing asymmetric envelope constraints. More precisely, by exploiting the fixed-time command filters to produce certain command signals and their derivatives, a modified command-filtered control algorithm is formulated to circumvent heavy computation burden caused by repetitive derivative of intermediate control laws. A two-step control methodology is devised based on an auxiliary compensating dynamics, which is capable of compensating for the actuator faults completely without the need for prior knowledge about the lumped disturbances and the actuator faults. Time-varying asymmetric barrier Lyapunov functions are introduced to confine the flight state tracking errors within the corresponding time-varying compact sets all the time provided their initial values remain therein. The effectiveness of the proposed method is validated by comparative simulation results.@en

This work proposes a nonsingular adaptive fixed-time switching control method for a class of strict-feedback nonlinear dynamics subject to full state constraints. The peculiarity of this design lies in overcoming the singularity issue that typically appears in the existing backstepping-based fixed-time control methods caused by the iterative differentiation of fractional power terms as tracking errors approach to zero, while guaranteeing the nonviolation of full state constraints. Crucial in solving such singularity issue is to skillfully introduce a smooth switching between fractional power and integer power terms, which guarantees that fractional power term is confined within a positive interval all the time. An asymmetric time-varying barrier Lyapunov function is delicately incorporated into control design, rendering state variables to be within prescribed time-varying bounds. Besides, radial basis function neural network is employed to handle system unknown nonlinearities. It is rigorously proved that all the closed-loop signals eventually converge to small regions around origin within fixed-time. Comparative simulation results are finally given to validate the effectiveness and superiority of the proposed control strategy.@en

A novel scheme for disturbance observer is designed for an extended class of strict-feedback nonlinear systems with possibly unbounded, non-smooth, and state-independent compounded disturbance. To overcome these problems in disturbance observer design, the typical slide mode differentiators are improved by introducing hyperbolic tangent function to make the signals smooth, and then the improved slide mode differentiators are constructively used to estimate the errors of variables in the presence of disturbances. The unbounded, non-smooth or state-independent disturbances are therefore able to be eliminated by using the estimated variable errors. Thus, the bounded or differentiable conditions for disturbance observer design are removed. Furthermore, the convergence of the new disturbance observer is rigorously proved based on Lyapunov stability theorem, and the tracking error can be arbitrarily small. Finally, the simulation results are given to validate the feasibility and superiority of the proposed approach.@en

This work focuses on adaptive neural dynamic surface control (DSC) for an extended class of nonlinear MIMO strict-feedback systems whose control gain functions are continuous and possibly unbounded. The method is based on introducing a compact set which is eventually proved to be an invariant set: thanks to this set, the restrictive assumption that the upper and lower bounds of control gain functions must be bounded is removed. This method substantially enlarges the class of systems for which DSC can be applied. By utilizing Lyapunov theorem and invariant set theory, it is rigorously proved that all signals in the closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB) and the output tracking errors converge to an arbitrarily small residual set. A simulation example is provided to demonstrate the effectiveness of the proposed approach.@en

This work attempts to achieve precise tracking control for the longitudinal dynamics of hypersonic flight vehicles (HFVs) without adopting universal approximators (e.g., fuzzy logic systems, neural networks, etc.). To this purpose, the system nonlinearities are well constrained to be bounded within some compact sets and are tackled by means of adaptation technique. Apart from achieving precise tracking, some prescribed performances (e.g., convergence rate, maximum steady tracking error, etc.) of the tracking errors of velocity, altitude, flight path angle, angle of attack, and pitch rate are also preserved. The proposed method is complexity-reduced and structurally simple in the sense that the time derivatives of the virtual control laws are no longer required and that the number of adaptation parameters have been reduced to only five due to the absence of universal approximators. Barbalat lemma is combined with Lyapunov theory to prove the closed-loop stability, while guaranteeing that the tracking errors eventually converge to zero through choosing appropriate design parameters. The effectiveness of the proposed control scheme is demonstrated by comparative numerical simulations.@en

This work attempts to achieve precise tracking control for the longitudinal dynamics of hypersonic flight vehicles (HFVs) without adopting universal approximators (e.g., fuzzy logic systems, neural networks, etc.). To this purpose, the system nonlinearities are well constrained to be bounded within some compact sets and are tackled by means of adaptation technique. Apart from achieving precise tracking, some prescribed performances (e.g., convergence rate, maximum steady tracking error, etc.) of the tracking errors of velocity, altitude, flight path angle, angle of attack, and pitch rate are also preserved. The proposed method is complexity-reduced and structurally simple in the sense that the time derivatives of the virtual control laws are no longer required and that the number of adaptation parameters have been reduced to only five due to the absence of universal approximators. Barbalat lemma is combined with Lyapunov theory to prove the closed-loop stability, while guaranteeing that the tracking errors eventually converge to zero through choosing appropriate design parameters. The effectiveness of the proposed control scheme is demonstrated by comparative numerical simulations.@en

For the pure feedback systems with uncertain actuator nonlinearity and non-differentiable non-affine function, a novel adaptive neural control scheme is proposed. Firstly, the assumption that the non-affine function must be differentiable everywhere with respect to control input has been canceled; in addition, the proposed approach can not only be applicable to actuator input dead zone nonlinearity, but also to backlash nonlinearity without changing the controller. Secondly, the neural network (NN) is used to approximate unknown nonlinear functions of system generated in the process of control design and a nonlinear robust term is introduced to eliminate the actuator nonlinearity modeling error, the NN approximation error and the external disturbances. Semi-globally uniformly ultimately boundedness of all signals in the closed loop system is analytically proved by utilizing Lyapunov theory. Finally, the effectiveness of the designed method is demonstrated via two examples.@en

For the pure feedback systems with uncertain actuator nonlinearity and non-differentiable non-affine function, a novel adaptive neural control scheme is proposed. Firstly, the assumption that the non-affine function must be differentiable everywhere with respect to control input has been canceled; in addition, the proposed approach can not only be applicable to actuator input dead zone nonlinearity, but also to backlash nonlinearity without changing the controller. Secondly, the neural network (NN) is used to approximate unknown nonlinear functions of system generated in the process of control design and a nonlinear robust term is introduced to eliminate the actuator nonlinearity modeling error, the NN approximation error and the external disturbances. Semi-globally uniformly ultimately boundedness of all signals in the closed loop system is analytically proved by utilizing Lyapunov theory. Finally, the effectiveness of the designed method is demonstrated via two examples.@en

Adaptive tracking control problem for disturbed nonlinear systems with the time derivative of disturbance being unbounded is investigated in this paper. Different from the existing literatures, a new disturbance observer is constructively proposed with its parameters being functions rather than constants, which results in a new manner for our disturbance observer. The convergence of the new disturbance observer is then proved based on Lyapunov stability theorem. Moreover, it is proved that the tracking error of system can be regulated to arbitrary small by appropriately choosing the design functions and parameters. Finally, simulation results are given to demonstrate the effectiveness of designed method.@en

It is well known that backstepping method suffer from the problem of "explosion of terms", which is solved by dynamic surface control (DSC) method. This paper presents an improved dynamic surface control (IDSC) method, which constructs the state errors by directly using virtual control signals, rather than using the signals produced by first-order filters in DSC method. The signals produced by first-order filters will only be used to construct the virtual control laws and actual control law. This modification makes the state errors to be more free from the influence of first-order filters. The stability of systems controlled by the proposed IDSC method is proved based on Lyapunov theorem. Finally, the advantage of IDSC method has been shown by simulation results, and it can be seen in the simulation results that IDSC method has better tracking performance and is more stable than DSC method.@en