Global adaptive output feedback control for a class of stochastic nonlinear systems with unknown homogeneous growth rates

Abstract

This article focuses on the adaptive output feedback stabilization for a class of stochastic nonlinear systems whose drift and diffusion terms satisfy homogeneous growth conditions. Since the homogeneous growth rates are unknown, two dynamic gains are coupled into the full‐order homogeneous observer. By virtue of adding a power integrator technique and the homogeneity theory, two adaptive laws and a homogeneous output feedback controller are designed. Based on the celebrated nonnegative semimartingale convergence theorem and the general stochastic Barbˇlat's lemma, it is indicated that all the signals of the closed‐loop system are bounded almost surely, and all the system states of the closed‐loop system converge to origin almost surely. Finally, the effectiveness of the proposed control scheme is verified by means of both numerical and practical examples.

Global stabilization for a class of upper‐triangular stochastic nonlinear systems with input delay via sampled‐data output feedback

“…where i = 2, 3, … , n − 1; 𝛾 18 (Θ) > 0, 𝛾 19 (𝜃, b * ) > 0 and ρi (b i ) > 0, i = 2, 3, … , n − 2, denote the constants. From the inequality (38), the second term in the right-hand side of (37) can be handled as…”

“…Further, the previous existing literature 5‐32 only focus on the sampled‐data studies for the deterministic systems, and we should also note that an engineering system is inevitable to be affected by the external stochastic disturbances, under this case, the engineering system can only be described as a stochastic nonlinear system 33‐40 . Fault‐tolerant controllers were constructed in References 33 and 34 for two stochastic nonlinear systems with full‐state constraints and input quantization; the switched stochastic nonlinear systems with time delay and output‐constrained were respectively analyzed in References 35‐37 to address the adaptive control problems; global adaptive control was realized in Reference 38 for a stochastic nonlinear system with unknown homogeneous growth rates; and observer‐based event‐triggered fuzzy control was discussed in References 39 and 40 for the stochastic nonlinear systems.…”