Finite‐time output‐feedback stabilization of high‐order nonholonomic systems

Abstract

Summary This paper investigates the problem of finite‐time output‐feedback stabilization of a class of high‐order nonholonomic systems under weaker conditions on system powers and nonlinearities. By constructing the appropriate Lyapunov function and observer, skillfully combining generalized adding a power integrator technique, sign function, and homogeneous domination method, and successfully introducing a new mathematical method, an output‐feedback controller is constructed to guarantee that all the states of the closed‐loop system converge to origin in a finite time.

Output feedback stabilization within prescribed finite time of asymmetric time‐varying constrained nonholonomic systems

“…That is, when there is no constraint requirements on the lower and/or upper bounds of p 1 , by letting k 11 → ∞ and/or k 12 → ∞, V k b 1 (p 1 ) in (10) will become the equivalent Lyapunov function widely employed for the unconstrained control designs. [19][20][21][22][23][36][37][38] Consequently, the present tan-type UBLF V b 1 (x 1 ) serves as a unified tool to handle the control problem simultaneously with asymmetric constraints (especially unilateral constraints), symmetric constraints, or without constraint requirements.…”

“…Subsequently, the works 20‐22 further extended the results in Reference 19 to the nonholonomic systems with uncertain parameters and/or perturbed terms. Based on the technique of homogeneous domination, an output feedback control strategy was proposed in Reference 23 to stabilize a family of high‐order nonholonomic systems in a finite time. However, a common weakness of the above‐mentioned studies is that the convergence time seriously relies on and increases with the initial conditions, which makes their inapplicable to achieve the desired performance in an exact predefined time.…”

“…Specifically, by introducing a novel universal barrier Lyapunov function (UBLF) to cope with asymmetric time‐varying output constraints, a fixed‐time control scheme is presented for the output feedback stabilization problem of a category of nonholonomic chained‐form systems. The significant contributions are highlighted as follows: Under the unified framework of the considered system with symmetric/asymmetric constraints or without constraint requirements, the fixed‐time output feedback stabilization problem is addressed for the first time. Different with the Lipschitz continuous condition for fixed‐time observer designs used in References 51 and 52, a Hölder continuous condition on characterizing the nonlinear functions of the system for its fixed‐time stabilization is given. The presence of the time‐varying constraints renders the existing finite/fixed‐time control techniques in References 19‐23,36,37, and 38 inapplicable (see Remark 1 below), to address such constraint requirements, a novel tan‐type UBLF fully taking advantage of structure feature of the system is introduced. By skillfully using the bi‐limit homogeneous technique to construct a novel switched observer, which estimates the unmeasurable states in fixed time, a systematic control design procedure of output feedback is presented to drive the states of closed‐loop system (CLS) to zero in a prescribed finite time while the asymmetric time‐varying output constraints are not violated. …”

Fixed‐time output feedback stabilization of a class of high‐order planar nonlinear systems

“…1,2 During the last few years, there have been many relevant researches concerned with the finite-time output feedback stabilization of high-order nonlinear systems. In the works, [3][4][5][6][7][8][9][10][11][12][13][14] several finite-time output feedback controllers were conducted for the stabilization of high-order nonlinear systems by combining the adding a power integrator technique with auxiliary filters. In the work, 15 a simple unified finite-time output feedback controller was developed for the stabilization of uncertain high-order planar systems by utilizing the homogeneous method together with an auxiliary filter.…”

Event‐triggered practical finite‐time output feedback stabilisation for switched non‐linear time‐delay systems

“…Over the past few decades, the finite‐time control has attracted much attention due to its advantage of rapid convergence rate. Some valuable results have been obtained for various systems, including linear systems [1], switched systems [2, 3], non‐holonomic systems [4], robotic systems [5], non‐linear systems [6–8] and Markovian jump systems [9]. Due to the inherent non‐linearity and complexity of control objects and devices in many practical systems, a lot of control systems are modelled by non‐linear system models instead of linear ones.…”