An Interpolation Technique for Input Constrained Robust Stabilization

This paper presents an interpolation technique of two given robust stabilizing gains for input constrained uncertain systems. The proposed interpolated feedback gain is computed at every sampling instance by solving an optimization problem with a single decision variable. Use of the interpolated feedback gain can bring about not only large invariant set but also good control performance. Moreover, it is shown that the feasible and invariant set yielded by the proposed control is the convex hull of the two invariant sets by the known controls. The simulation results show that the proposed interpolation based feedback gain indeed results in both large invariant set and good control performance.

[1]  P. Grieder,et al.  Using interpolation to simplify explicit model predictive control , 2004, Proceedings of the 2004 American Control Conference.

[2]  C. Ong,et al.  Robust explicit model predictive control for linear systems via interpolation techniques , 2010 .

[3]  Matthew C. Turner,et al.  Antiwindup for stable linear systems with input saturation: an LMI-based synthesis , 2003, IEEE Trans. Autom. Control..

[4]  Sophie Tarbouriech,et al.  Local stabilization of discrete-time linear systems with saturating controls: an LMI-based approach , 2001, IEEE Trans. Autom. Control..

[5]  B. De Moor,et al.  Interpolation based MPC for LPV systems using polyhedral invariant sets , 2005, Proceedings of the 2005, American Control Conference, 2005..

[6]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[7]  Yuanqing Xia,et al.  Overall convergence rate of delta operator systems subject to actuator saturation , 2017 .

[8]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[9]  Hong Jang,et al.  Move blocking strategy applied to re-entrant manufacturing line scheduling , 2015 .

[10]  Per-Olof Gutman,et al.  Explicit constraint control based on interpolation techniques for time-varying and uncertain linear discrete-time systems , 2011 .

[11]  Marko Bacic,et al.  Interpolation based computationally efficient predictive control , 2004 .

[12]  Jongeun Choi,et al.  Optimal LPV control with hard constraints , 2016 .

[13]  Morten Hovd,et al.  Constrained Control of Uncertain, Time-varying Linear Discrete-Time Systems Subject to Bounded Disturbances , 2015, IEEE Transactions on Automatic Control.

[14]  P. Grieder,et al.  Two level model predictive control for the maximum control invariant set , 2004, Proceedings of the 2004 American Control Conference.

[15]  Guang-Ren Duan,et al.  Unified Parametric Approaches for Observer Design in Matrix Second-order Linear Systems , 2005 .

[16]  Jung-Su Kim,et al.  Robust tracking model predictive control for input-constrained uncertain linear time invariant systems , 2014, Int. J. Control.

[17]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[18]  Faryar Jabbari,et al.  Controllers for linear systems with bounded actuators: Slab scheduling and anti-windup , 2013, Autom..

[19]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[20]  Mayuresh V. Kothare,et al.  An e!cient o"-line formulation of robust model predictive control using linear matrix inequalities (cid:1) , 2003 .

[21]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[22]  Basil Kouvaritakis,et al.  Constrained robust model predictive control based on periodic invariance , 2006, Autom..

[23]  Hoai-Nam Nguyen,et al.  More efficient interpolating control , 2014, 2014 European Control Conference (ECC).

[24]  Muhammad Tufail,et al.  Stabilisation of locally Lipschitz non-linear systems under input saturation and quantisation , 2017 .

[25]  Young Il Lee,et al.  Input Constrained Receding Horizon Control with Nonzero Set Points and Model Uncertainties , 2000 .

[26]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[27]  George Bitsoris,et al.  Design techniques for the control of discrete-time systems subject to state and control constraints , 1999, IEEE Trans. Autom. Control..

[28]  Ali Saberi,et al.  A Semi-Global Low-and-High Gain Design Technique for Linear Systems with Input Saturation - Stabiliz , 1993 .