Observation and Identification via HOSM Observers

Control systems normally perform under uncertainties/disturbances and with measurement signals corrupted by noise. For systems with reliable models and noisy measurements, a filtration approach (Kalman filters, for example) is efficient. However, as shown in Chap. 3, sliding mode observers based on first-order sliding modes are effective in the presence of uncertainties/disturbances. Nevertheless, as discussed in that chapter, they are only applicable when the relative degree of the outputs with respect to the uncertainties/disturbances is one, and differentiation of noisy outputs signals is not needed.

[1]  Yuri B. Shtessel,et al.  HOSM Observer for a Class of Non-Minimum Phase Causal Nonlinear MIMO Systems , 2010, IEEE Transactions on Automatic Control.

[2]  Leonid M. Fridman,et al.  High order sliding mode observer for linear systems with unbounded unknown inputs , 2010, Int. J. Control.

[3]  Elio Usai,et al.  An algebraic observability approach to chaos synchronization by sliding differentiators , 2002 .

[4]  Leonid M. Fridman,et al.  Second-order sliding-mode observer for mechanical systems , 2005, IEEE Transactions on Automatic Control.

[5]  W. Greub.  Linear Algebra , 1981 .

[6]  Ben M. Chen.  Robust and H[∞] control , 2000 .

[7]  Leonid Fridman,et al.  STATE OBSERVATION FOR NONLINEAR SWITCHED SYSTEMS USING NONHOMOGENEOUS HIGH-ORDER SLIDING MODE OBSERVERS , 2012 .

[8]  Leonid Fridman,et al.  Unmatched uncertainties compensation based on high‐order sliding mode observation , 2013 .

[9]  Alexander S. Poznyak,et al.  Observation of linear systems with unknown inputs via high-order sliding-modes , 2007, Int. J. Syst. Sci..

[10]  Arie Levant,et al.  High-order sliding-mode observation for linear systems with unknown inputs , 2011 .

[11]  Elio Usai,et al.  A chaotic modulation scheme based on algebraic observability and sliding mode differentiators , 2005 .

[12]  M. I. Castellanos,et al.  Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs , 2007, Int. J. Syst. Sci..

[13]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[14]  L. Fridman,et al.  Exact state estimation for linear systems with unknown inputs based on hierarchical super‐twisting algorithm , 2007 .

[15]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[16]  T. Floquet,et al.  On Sliding Mode Observers for Systems with Unknown Inputs , 2006, International Workshop on Variable Structure Systems, 2006. VSS'06..

[17]  Leonid M. Fridman,et al.  Robust Control With Exact Uncertainties Compensation: With or Without Chattering? , 2011, IEEE Transactions on Control Systems Technology.

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

[19]  Leonid M. Fridman,et al.  Finite-time state observation for non-linear uncertain systems via higher-order sliding modes , 2009, Int. J. Control.

[20]  L. Fridman,et al.  Higher‐order sliding‐mode observer for state estimation and input reconstruction in nonlinear systems , 2008 .

[21]  Hocine Imine.  Sliding Mode Based Analysis and Identification of Vehicle Dynamics , 2011 .

[22]  M. Hautus.  Strong detectability and observers , 1983 .