Abstract
The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by time-varying state delays are compensated for and unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method.
Highlights
During the past few decades, great achievements have been proposed for uncertain nonlinear systems based on adaptive control technique, especially for pure-feedback systems and strict-feedback systems with the lower-triangular structure
In order to tackle the problem of state constraints, some effective control techniques (e.g., model predictive control (MPC) [18, 19], reference governors (RGs) [20], one-to-one nonlinear mapping (NM) [21,22,23], and barrier Lyapunov functions (BLFs) [24,25,26,27,28]) have been presented
Due to the fact that MPC and RGs require strong online computing capability to guarantee constraints, this requirement restricts their applications in engineering design. erefore, one-to-one NM and the BLFs-based methods become the main methods to deal with the constrained nonlinear systems. ere exist many significant results which focus on lower-triangular structure nonlinear systems with different constraints
Summary
During the past few decades, great achievements have been proposed for uncertain nonlinear systems based on adaptive control technique, especially for pure-feedback systems (e.g., see [1,2,3,4,5]) and strict-feedback systems (e.g., see [6,7,8,9]) with the lower-triangular structure. E authors in [39] proposed an observed-based adaptive finite-time tracking control technique for a class of nonstrict-feedback nonlinear systems with input saturation. In [21,22,23,24,25,26,27,28], the effective controllers have been designed for the lower-triangular structure nonlinear systems with state constraints and unmodeled dynamics, but their considered systems did not include state delay and their control methods may be invalid to nonstrict-feedback systems on account of subsystem function which contains the whole state variables. To the best knowledge of the authors, finite-time tracking control for a class of uncertain nonstrict-feedback time-varying state-delayed nonlinear systems with full-state constraints and unmodeled dynamics has not been fully discussed in the literature, which is still open and remains unsolved. R denotes a set of real numbers, R+ denotes a set of nonnegative real numbers, Rm×n denotes a set of m × n real matrices, Rn denotes a set of n-dimensional real vectors, sup(·) denotes the least upper bound, ‖·‖ denotes 2-norm of a vector or matrix, |·| denotes an absolute value of a real number ·, exp(·) denotes an exponential function of ·, and log(·) denotes the natural logarithm of ·
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