Time-varying state-feedback stabilisation of stochastic feedforward nonlinear systems with unknown growth rate

ABSTRACT We consider the time-varying state-feedback stabilisation problem for a class of stochastic feedforward nonlinear systems with unknown growth rate in this paper. A new LaSalle-type theorem for stochastic time-varying systems is firstly established by using the generalized weakly positive definite function. As an application, to deal with serious uncertainties in the unknown growth rate, a time-varying approach, rather than an adaptive one, is adopted to design the scheme of a state-feedback controller for stochastic feedforward systems. Based on the established LaSalle-type theorem, it is shown that all signals of the resulting closed-loop system converge to zero almost surely. Illustrative examples are given to verify the theoretical findings.

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

[2]  Luc Baron,et al.  Design of Stabilizing Controllers With a Dynamic Gain for Feedforward Nonlinear Time-Delay Systems , 2011, IEEE Transactions on Automatic Control.

[3]  Guo-Ping Liu,et al.  On Input-to-State Stability of Switched Stochastic Nonlinear Systems Under Extended Asynchronous Switching , 2016, IEEE Transactions on Cybernetics.

[4]  Yigang He,et al.  Global sampled-data output feedback stabilisation of a class of upper-triangular systems with input delay , 2013 .

[5]  Hossin Hosseinian,et al.  Power Electronics , 2020, 2020 27th International Conference on Mixed Design of Integrated Circuits and System (MIXDES).

[6]  Ian R. Petersen,et al.  Absolute Stabilization and Minimax Optimal Control of Uncertain Systems with Stochastic Uncertainty , 1997 .

[7]  Guo-Ping Liu,et al.  Stability Analysis of A Class of Hybrid Stochastic Retarded Systems Under Asynchronous Switching , 2014, IEEE Transactions on Automatic Control.

[8]  Jong-Tae Lim,et al.  Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain , 2014, Syst. Control. Lett..

[9]  Xin Yu,et al.  Output Feedback Regulation of Stochastic Nonlinear Systems With Stochastic iISS Inverse Dynamics , 2010, IEEE Transactions on Automatic Control.

[10]  Wei Xing Zheng,et al.  Delay-Dependent Stochastic Stability and $H_{\infty} $-Control of Uncertain Neutral Stochastic Systems With Time Delay , 2009, IEEE Transactions on Automatic Control.

[11]  A. Teel.  Using Saturation to Stabilize a Class of Single-Input Partially Linear Composite Systems , 1992 .

[12]  M. P. Tzamtzi,et al.  An explicit formula of bounded feedback stabilizers for feedforward systems , 2001, Syst. Control. Lett..

[13]  Yungang Liu,et al.  Adaptive stabilization for a class of feedforward systems with zero-dynamics , 2015, J. Syst. Sci. Complex..

[14]  Frédéric Mazenc,et al.  Tracking trajectories of the cart-pendulum system , 2003, Autom..

[15]  L. Praly,et al.  Adding an integration and global asymptotic stabilization of feedforward systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[16]  Hamid Reza Karimi,et al.  Stability of Stochastic Nonlinear Systems With State-Dependent Switching , 2013, IEEE Transactions on Automatic Control.

[17]  Chunjiang Qian,et al.  Global Output Feedback Stabilization of a Class of Nonlinear Systems via Linear Sampled-Data Control , 2012, IEEE Transactions on Automatic Control.

[18]  H. J. Kushner,et al.  Stochastic Stability , 2005 .

[19]  Shihua Li,et al.  Global stabilization of a class of uncertain upper‐triangular systems under sampled‐data control , 2013 .

[20]  Heinz Unbehauen,et al.  Global adaptive stabilization for a class of feedforward nonlinear systems , 2004, IEEE Transactions on Automatic Control.

[21]  Feiqi Deng,et al.  A New Type of Stability Theorem for Stochastic Systems With Application to Stochastic Stabilization , 2016, IEEE Transactions on Automatic Control.

[22]  Liang Liu,et al.  State feedback stabilization for stochastic feedforward nonlinear systems with time-varying delay , 2013, Autom..

[23]  Luc Baron,et al.  Feedback stabilization for high order feedforward nonlinear time-delay systems , 2011, Autom..

[24]  Cong-Ran Zhao,et al.  Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay , 2014, Autom..

[25]  X. Mao.  LaSalle-Type Theorems for Stochastic Differential Delay Equations , 1999 .

[26]  Wei Xing Zheng,et al.  Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems , 2013, IEEE Transactions on Automatic Control.

[27]  Shengyuan Xu,et al.  Decentralized global stabilization for stochastic high-order feedforward nonlinear systems with time-varying delays , 2014, J. Frankl. Inst..

[28]  Frédéric Mazenc,et al.  Asymptotic tracking of a reference state for systems with a feedforward structure , 2000, Autom..

[29]  Xuerong Mao,et al.  The Improved LaSalle-Type Theorems for Stochastic Differential Delay Equations , 2012 .

[30]  Xin Yu,et al.  Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics , 2010, Autom..

[31]  Chunjiang Qian,et al.  Output Feedback Stabilization of Nonlinear Feedforward Systems using Low Gain Homogeneous Domination , 2007, 2007 IEEE International Conference on Control and Automation.

[32]  Wei Xing Zheng,et al.  Stability analysis and control for switched stochastic delayed systems , 2016 .