Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems.

*(English)*Zbl 1115.93076Summary: The problem of decentralized adaptive output-feedback stabilization is investigated for large-scale stochastic nonlinear systems with three types of uncertainties, including parametric uncertainties, nonlinear uncertain interactions and stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystems are stochastic input-to-state stable, an adaptive output-feedback controller is constructively designed by the backstepping method. It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability. In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin. The contributions of the work are characterized by the following novel features: (1) even for centralized single-input single-output systems, this paper presents a first result in stochastic, nonlinear, adaptive, output-feedback asymptotic stabilization; (2) the methodology previously developed for deterministic large-scale systems is generalized to stochastic ones. At the same time, novel small-gain conditions for small signals are identified in the setting of stochastic systems design; (3) both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states; (4) parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields, which may appear nonlinearly; (5) the concept of stochastic input-to-state stability and the method of changing supply functions are adapted, for the first time, to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control.

##### MSC:

93D15 | Stabilization of systems by feedback |

93E03 | Stochastic systems in control theory (general) |

93C10 | Nonlinear systems in control theory |

93A15 | Large-scale systems |

##### Keywords:

decentralized control; stochastic nonlinear systems; stochastic input-to-state stable; inverse dynamics; output feedback; adaptive control
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\textit{S.-J. Liu} et al., Automatica 43, No. 2, 238--251 (2007; Zbl 1115.93076)

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