Fixed‐time adaptive neural control for nonstrict‐feedback uncertain nonlinear systems with output constraints

Abstract

This paper addresses the fixed‐time output‐constrained control problem for a class of uncertain nonlinear systems in nonstrict‐feedback form. A novel fixed‐time adaptive neural control scheme is proposed by integrating the barrier Lyapunov function (BLF), neural networks, and fixed‐time control technique into the backstepping control design. Rigorous theoretical analysis for the semi‐global fixed‐time stability of the whole closed‐loop system is provided. The proposed controller can guarantee all the closed‐loop error signals converge to the small regions about zero in fixed time while ensuring the system output can always stay within the predefined output constraints. In addition, the proposed controller is structurally simple, which makes it affordable for practical applications. Finally, two simulation examples are performed to illustrate the effectiveness and benefits of the proposed control scheme.

Fixed‐time fuzzy adaptive robust H∞ control for nonstrict‐feedback nonlinear systems with input saturation and output constraints

“…Example 1. The first example is a practical electromechanical system studied in the articles 16,52 whose schematic is shown in Figure 2. The dynamic model of this system is considered as follows:…”

“…[4][5][6] Two categories of nonlinear systems which have been the most attention of researchers are strict-feedback 2,4,[7][8][9][10][11][12][13][14][15] and nonstrict-feedback systems. [16][17][18][19] For example, in Reference 8, the authors designed an adaptive fuzzy output feedback backstepping control method based on an observer for uncertain strict-feedback nonlinear systems with immeasurable states. The problem of event-triggered adaptive fuzzy asymptotic control for nonlinear strict-feedback systems with external disturbances is investigated in Reference 9.…”

“…After introducing fixed-time control in Reference 20, many researchers addressed the issue of fixed-time control and reported satisfactory results for a wide range of nonlinear systems. 7,16,18,[22][23][24][25][26] Also, the fixed-time approach has been used for many practical systems, among which the following can be mentioned: consensus control of multi-agent systems, [27][28][29][30] control for multiple unmanned aerial vehicles (UAVs) in Reference 31, control for an air-breathing hypersonic vehicle in Reference 32, attitude control for spacecraft, [33][34][35] and tracking control for permanent magnet synchronous motor. 36 For a wide range of practical systems, actuators may not be able to transfer the control signal obtained from the controller exactly to the input of the control system for various reasons.Input saturation is one of the well-known reasons mentioned above that inevitably reduces the tracking performance of designed control systems.…”

“…The well-known barrier Lyapunov function (BLF) is utilized as a useful tool to handle output constraint problems. 3,16,17,37,[40][41][42][43][44] The tan-type 3,43,45 and the log-type, 16,40,41 as two common types of BLFs, have been used in a wide range of nonlinear control systems with output constraints. For example, in Reference 43, based on tan-type BLF, a fixed-time controller is designed for nonstrict-feedback nonlinear systems to preserve the system output within the predefined constraints.…”

Fixed-Time Leader-Following Consensus Tracking Control for Nonliear Multi-Agent Systems under Jointly Connected Graph

“…In addition, work [ 23 ] proposed a backstepping distributed control model to design a fixed-time state observer, which could solve the formation problem of multiple UAVs. On the basis of the backstepping method, work [ 24 ] introduced a neural network and designed a novel fixed-time adaptive protocol to solve the fixed-time consensus problem of nonlinear multi-agent systems under switching graph. In addition, work [ 25 ] uses fuzzy logic control to make higher-order systems achieve practical consensus in a fixed time.…”