Output feedback stabilization for stochastic nonholonomic systems with nonlinear drifts and Markovian switching

Abstract

This paper investigates the output feedback stabilization of stochastic nonholonomic systems which have both nonlinear drifts and Markovian switching. The state-scaling and backstepping techniques are exploited in the design of control laws. The output feedback stabilizing control laws and switching control strategy are proposed so that the closed-loop system can be stabilized in probability in the large. In the end, an example of nonholonomic mobile robots is provided to illustrate the effectiveness of control laws.

Output Feedback Stabilization for Stochastic Nonholonomic Systems under Arbitrary Switching

“…For any 0 ( 0 ) ̸ = 0, one has 0 ( ) ̸ = 0 in (6) at the time interval ∈ ( 0 , +∞) a.s. with a similar proof of Proposition 1 in [25].…”

“…There are two main differences between systems (1a) and (1b) and those in [24,25]. The first is the arbitrary switching mentioned in this paper.…”

“…The second will be illustrated in Remark 7. In addition, Assumptions 1 and 2 are similar to those in [24,25] …”

“…The first is state-feedback control: stabilization [13,14], adaptive stabilization [15][16][17][18], finite-time stabilization [19], stabilization with time-varying delays [20], and stabilization of mobile robots [21,22]. The second is the output feedback stabilization [23][24][25].…”

“…Zhang et al discussed the output feedback stabilizing controllers of SNSs whose virtual control contains gain parameter [25]. This will lead to a problem where the calculation of is very difficult, especially for ≥ 3, since the inequalities about were quintic.…”