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.

This paper proposes a novel adaptive fuzzy dynamic surface control (DSC) method for an extended class of periodically disturbed strict-feedback nonlinear systems. The peculiarity of this extended class is that the control gain functions are not bounded a priori but simply taken to be continuous and with a known sign. In contrast with existing strategies, controllability must be guaranteed by constructing appropriate compact sets ensuring that all trajectories in the closed-loop system never leave these sets. We manage to do this by means of invariant set theory in combination with the Lyapunov theory. In other words, boundedness is achieved a posteriori as a result of stability analysis. The approximator composed of fuzzy logic systems and Fourier series expansion is constructed to deal with the unknown periodic disturbance terms.

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.

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.

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.