State‐feedback stabilization for high‐order stochastic nonlinear systems with stochastic inverse dynamics

Abstract

For a class of high‐order stochastic nonlinear systems with stochastic inverse dynamics which are neither necessarily feedback linearizable nor affine in the control input, this paper investigates the problem of state‐feedback stabilization for the first time. Under some weaker assumptions, a smooth state‐feedback controller is designed, which ensures that the closed‐loop system has an almost surely unique solution on [0, ∞), the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability, and the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme. Copyright © 2007 John Wiley & Sons, Ltd.

Output feedback stabilization based on dynamic surface control for a class of uncertain stochastic nonlinear systems

“…Theorem 1 Under Assumptions 1-3, based on the Lemmas 1-3, consider the closed-loop system (38) consisting of plants (3), (4), (5), with the observers (12), (13), the virtual control variables (22), (25), and the actual controller (28), filters (23) and (26); choose ρ 1 (·) given by Lemma 2 chooseλk ez (s) ≥ ρ 1 (λ 1 (s))α 02 (s),λ 2 (s) = α z2 (α −1 01 (4α 03 (·))) ∈ K ∞ , withλ 1 (s) = α z2 (α −1 01 (4α 02 (·))), then the system (16) …”

“…However, these results in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][28][29][30][31] still inherit the open problem of "explosion of complexity" caused by the repeated differentiations of virtual controllers. This drawback makes it difficult to carry out the designed back-stepping schemes.…”

“…Since then, a series of extensions have been made under different assumptions or for different stochastic systems. Many interesting control schemes [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] have been proposed by using the backstepping technique to solve the stochastic nonlinear disturbance, such as several SISO systems including time-delay systems [9,12,13], tracking control [10,12,15], and MIMO systems with decentralized control [5,6,9,11], high-order systems [28][29][30][31] are studied.…”

Adaptive control of stochastic nonlinear systems with uncontrollable linearization

“…no feedback linearization design works. Xie and Tian [26] presented a state-feedback stabilization controller for high-order stochastic nonlinear systems with stochastic inverse dynamics under the assumption (t) = I .…”

Adaptive State-Feedback Stabilization for High-Order Stochastic Nonlinear Systems with Time-Varying Control Coefficients

“…Recently, for several classes of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions, by using the long-term average tracking risk-sensitive cost criteria in [10], and the dynamic signal and changing supply function in [9,14], different adaptive output-feedback control schemes were studied. For the case where p i 1 and d i (t) = 1, Xie and Tian considered state-feedback stabilization in [15], which maybe the first investigation on such type of control problems. It must be noticed, however, that all the results are obtained under the assumption of d i (t) = 1.…”