Smooth output feedback stabilization for a class of nonlinear systems with time‐varying powers

Summary In this paper, the robust stabilization problem is addressed for a class of high‐order stochastic nonlinear systems with output constraints and disturbances by using finite‐time control technique. One of the features of the considered stochastic systems is that the fractional powers are allowed to be any positive odd rational numbers, rather than grater than or equal to one. By constructing a novel tan‐type barrier Lyapunov function and using the adding a power integrator technique, the explicit steps on how to construct a backstepping‐like finite‐time controller have been developed to handle the robust stabilization and output constraint. Rigorous mathematical proof shows that the system states will finite‐time converge to a small region of the origin and the output constraint can be kept. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.

“…Besides, since v 2 ≥ 2, it is easy to obtain that there exist C 2 functions k 21 (x 2 ) ≥ 0, K 21 (x 2 ) ≥ 0 andk 21…”

Section: Finite-time Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Fang

Ding

et al. 2019

“…In recent years, nonlinear and adaptive output feedback control has made new and impressive progress. For example, by applying homogeneous domination approach, global output feedback control has been achieved for nonlinear systems with even stronger growth rate; in stochastic nonlinear control, output feedback stabilization has been achieved for stochastic nonholomomic nonlinear systems with unknown control coefficients using a new form of reduced‐order K‐filters, and for stochastic feedforward nonlinear systems with severe unknowns using a novel time‐varying low‐gain controller; with the development of finite‐time observer and controller design, finite‐time output feedback control is achieved for a broad class of lower‐triangular nonlinear systems; power‐integrator‐backstepping–based output feedback control is carried out for a class of nonlinear systems with time‐varying power, etc.…”

Section: Introductionmentioning

confidence: 99%

Universal output feedback adaptive control with uncertain nonlinearity and unknown high‐frequency gain sign: A new design

Huang

Zhang

Wang

2019

Summary In this paper, we propose a new universal output feedback adaptive controller to globally (or semiglobally) stabilize nonlinear output feedback systems, whose nonlinearities are bounded either by known functions with unknown parameters or by completely unknown functions. In addition, no a priori knowledge of the sign of high‐frequency gain is required. The new design focuses on properly arranging the control gains step by step in the filter backstepping design. Instead of Lyapunov‐based argument, an inductive contradiction argument is employed in the proof of stability, which is not common in literature.

“…where i is a positive function with respect to k i − 1 and̃i is a positive constant. Substituting (A19)-(A22) into (A16), it is easy to obtain (19).…”

mentioning

confidence: 99%

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

Xie

2019

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.