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

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.

[1]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[2]  A. Isidori.  Nonlinear Control Systems , 1985 .

[3]  B. Øksendal.  Stochastic Differential Equations , 1985 .

[4]  Riccardo Marino,et al.  Nonlinear control design , 1995 .

[5]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[6]  M. Krstić,et al.  Stochastic nonlinear stabilization—II: inverse optimality , 1997 .

[7]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[8]  T. Başar,et al.  Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems , 1998, IEEE Trans. Autom. Control..

[9]  T. Başar,et al.  Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-Sensitive Cost Criterion , 1999 .

[10]  Miroslav Krstic,et al.  Output-feedback stochastic nonlinear stabilization , 1999, IEEE Trans. Autom. Control..

[11]  Wei Lin,et al.  Recursive design of discontinuous controllers for uncertain driftless systems in power chained form , 2000, IEEE Trans. Autom. Control..

[12]  Wei Lin,et al.  Adaptive regulation of high-order lower-triangular systems : an adding a power integrator technique , 2000 .

[13]  Wei Lin,et al.  Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems , 2000 .

[14]  Ruth J. Williams,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[15]  Murat Arcak,et al.  Constructive nonlinear control: a historical perspective , 2001, Autom..

[16]  Kevin M. Passino,et al.  Stable Adaptive Control and Estimation for Nonlinear Systems , 2001 .

[17]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[18]  Wei Lin,et al.  Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization , 2001 .

[19]  Miroslav Krstic,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 2001, IEEE Trans. Autom. Control..

[20]  Arthur J. Krener,et al.  Backstepping design with local optimality matching , 2001, IEEE Trans. Autom. Control..

[21]  Wei Lin,et al.  Global stabilization of cascade systems by C0 partial-state feedback , 2002, IEEE Trans. Autom. Control..

[22]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: the smooth feedback case , 2002, IEEE Trans. Autom. Control..

[23]  Wei Lin,et al.  Practical output tracking of nonlinear systems with uncontrollable unstable linearization , 2002, IEEE Trans. Autom. Control..

[24]  Wei Lin,et al.  Nonsmooth adaptive stabilization of cascade systems with nonlinear parameterization via partial-state feedback , 2003, IEEE Trans. Autom. Control..

[25]  Wei Lin,et al.  Nonsmooth output feedback stabilization of a class of genuinely nonlinear systems in the plane , 2003, IEEE Trans. Autom. Control..

[26]  Liu Yungang,et al.  Design of satisfaction output feedback controls for stochastic nonlinear systems under quadratic tracking risk-sensitive index , 2003 .

[27]  Yungang Liu,et al.  Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost , 2003, IEEE Trans. Autom. Control..

[28]  Wei Lin,et al.  Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback , 2004, IEEE Trans. Autom. Control..

[29]  Ji-Feng Zhang,et al.  Reduced-order observer-based control design for nonlinear stochastic systems , 2004, Syst. Control. Lett..

[30]  Ji-Feng Zhang,et al.  Minimal-order observer and output-feedback stabilization control design of stochastic nonlinear systems , 2004 .

[31]  Wei Lin,et al.  Robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization , 2005, IEEE Transactions on Automatic Control.

[32]  Xue-Jun Xie,et al.  Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function , 2006 .

[33]  Ji-Feng Zhang,et al.  Practical Output-Feedback Risk-Sensitive Control for Stochastic Nonlinear Systems with Stable Zero-Dynamics , 2006, SIAM J. Control. Optim..

[34]  Yungang Liu,et al.  Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics , 2007, Science in China Series : Information Sciences.