Robust finite-time stabilization of uncertain nonlinear systems based on partial stability

This paper presents a new approach to design a robust finite-time partial stabilization for uncertain nonlinear systems. The main contribution of this paper is to divide system state into two subsystems based on their required stability properties, and to stabilize just one of them in finite-time. First, integral sliding mode control is applied and the system is converted to a chain of integrators. Then, a finite-time state feedback controller with dynamical gains is utilized. Since guidance issue is an appropriate example in which stabilization of all of the state variables is not desirable, the proposed approach is employed to design a robust finite-time convergent guidance law. Simulation results justify that the proposed method is reliable in terms of robustness and effectiveness.

[1]  Arie Levant,et al.  Homogeneity approach to high-order sliding mode design , 2005, Autom..

[2]  V. Haimo.  Finite time controllers , 1986 .

[3]  V. I. Vorotnikov.  Partial stability and control: The state-of-the-art and development prospects , 2005 .

[4]  Wassim M. Haddad,et al.  A unification between partial stability and stability theory for time-varying systems , 2002 .

[5]  Wei Lin,et al.  Global finite-time stabilization of a class of uncertain nonlinear systems , 2005, Autom..

[6]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[7]  K. Teo,et al.  Guidance Laws with Finite Time Convergence , 2009 .

[8]  Chieh-Chuan Feng.  Integral Sliding-Based Robust Control , 2011 .

[9]  Changyin Sun,et al.  Finite time integral sliding mode control of hypersonic vehicles , 2013 .

[10]  Jie Huang,et al.  On an output feedback finite-time stabilization problem , 2001, IEEE Trans. Autom. Control..

[11]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[12]  V. V. Rumiantsev.  On asymptotic stability and instability of motion with respect to a part of the variables: PMM vol. 35, n≗1, 1971, pp. 138–143 , 1971 .

[13]  Mohammad Javad Yazdanpanah,et al.  Partial stabilization of uncertain nonlinear systems. , 2012, ISA transactions.

[14]  Franck Plestan,et al.  Higher order sliding mode control based on integral sliding mode , 2007, Autom..

[15]  Yen-Sheng Chen,et al.  Synchronization of mutual coupled chaotic systems via partial stability theory , 2007 .

[16]  Qun Zong,et al.  Brief paper: Higher order sliding mode control with self-tuning law based on integral sliding mode , 2010 .

[17]  Gang Feng,et al.  Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems , 2012, Autom..

[18]  Sheng Sun,et al.  A guidance law with finite time convergence accounting for autopilot lag , 2013 .

[19]  Zhong-Ping Jiang,et al.  Finite-Time Stabilization of Nonlinear Systems With Parametric and Dynamic Uncertainties , 2006, IEEE Transactions on Automatic Control.

[20]  Arie Levant,et al.  Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence , 2001, IEEE Trans. Autom. Control..

[21]  Di Zhou,et al.  Adaptive Sliding-Mode Guidance of a Homing Missile , 1999 .

[22]  Michael Defoort,et al.  A novel higher order sliding mode control scheme , 2009, Syst. Control. Lett..

[23]  Iman Mohammadzaman,et al.  Finite-time convergent guidance law based on integral backstepping control , 2014 .

[24]  V. I. Vorotnikov.  Partial stability and control , 1998 .

[25]  Jiang Wang,et al.  An approach of partial control design for system control and synchronization , 2009 .

[26]  Mohammad Javad Yazdanpanah,et al.  Robust partial control design for non-linear control systems: a guidance application , 2012, J. Syst. Control. Eng..

[27]  Chaker Jammazi.  Finite-time partial stabilizability of chained systems , 2008 .

[28]  A. Levant.  Universal SISO sliding-mode controllers with finite-time convergence , 2001 .

[29]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[30]  Arie Levant,et al.  Integral High-Order Sliding Modes , 2007, IEEE Transactions on Automatic Control.