Adaptive state feedback stabilization of more general stochastic high‐order nonholonomic systems

Abstract

SummaryThis paper investigates adaptive state feedback stabilization for a class of more general stochastic high‐order nonholonomic systems. By constructing the appropriate Lyapunov function, skillfully combining parameter separation, sign function, and backstepping design methods, an adaptive state feedback controller is designed to eliminate the phenomenon of uncontrollability and guarantee global asymptotic stability in probability of the closed‐loop system. Two simulation examples are used to demonstrate the effectiveness of this method.

Output feedback stabilization for nonholonomic systems with unknown unmeasured states‐dependent growth

“…Remark In the case of , the uncertain nonholonomic system degenerates into a driftless chained‐form nonholonomic system proposed in the work of Murray and Sastry . In literature, the extensions such as nonlinear drifts, the time‐delayed case, stochastic noise, and consensus control, are discussed for such class of uncertain nonholonomic systems. Throughout this paper, we make the following assumption regarding system .…”

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

“…Remark We discuss the importance of Lemma . To overcome the obstacle caused by sign function, Sun et al first prove the case of p ≥ 1 being a positive odd constant, requiring that p ≥ 1 be a ratio of two odd constants. Lemma extends p to an arbitrary real number greater than or equal to 1, which plays an essential role in control design of system .…”

“…There are some remaining problems to be investigated. (i) In the newest papers, Li and Xie consider adaptive state‐feedback stabilization of stochastic high‐order nonholonomic systems, and study finite‐time stabilization of stochastic high‐order nonlinear systems with finite‐time stochastic input‐to‐state stability (FT‐SISS) inverse dynamics. However, high‐order p i of system in these two papers is a ratio of two odd integers, hence an interesting problem is how to design a finite‐time output‐feedback controller for stochastic high‐order nonholonomic systems with the time‐varying power q i ( t ) and arbitrary constant power p i .…”

“…Since 2 , 1 , and L are independent of each other, one can choose a sufficiently large L to guarantee 2 − 1 L −1 > 1 4 2 . Substituting (25)…”

Partial‐state feedback adaptive stabilization for a class of uncertain nonholonomic systems

“…This makes the stabilization control for such class of nonlinear systems become a challenging but interesting area within the nonlinear control field. 3 In past years, the stabilization problem was solved for several classes of nonholonomic systems with nonlinear drifts, [4][5][6][7][8][9][10][11] stochastic noises, [12][13][14][15][16][17][18] event-triggered control, [19][20][21] and distributed control, [22][23][24][25] and so forth.…”