Further results and properties of indirect adaptive model predictive control for linear systems with polytopic uncertainty

We extend a recently developed design for indirect adaptive model predictive control (IAMPC) and presents additional results on its stability properties. The IAMPC guarantees constraints satisfaction including during the learning transient, is input-to-state stable (ISS) with respect to the parameter estimation error, and has computational burden comparable to that of non-adaptive MPC. In this paper we extend the IAMPC to the case of uncertain input-to-state matrix, we provide a new method to design robust constraints, and we show additional stability results, in particular that asymptotic stability does not require the parameter estimation error to be zero, which also allow us to derive a tighter ISS Lyapunov function.

[1]  Stefano Di Cairano,et al.  The development of Model Predictive Control in automotive industry: A survey , 2012, 2012 IEEE International Conference on Control Applications.

[2]  Jamal Daafouz,et al.  Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties , 2001, Syst. Control. Lett..

[3]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[4]  Martin Guay,et al.  Adaptive Model Predictive Control for Constrained Nonlinear Systems , 2008 .

[5]  Stefano Di Cairano,et al.  Model adjustable predictive control with stability guarantees , 2015, 2015 American Control Conference (ACC).

[6]  Manfred Morari,et al.  An improved approach for constrained robust model predictive control , 2002, Autom..

[7]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[8]  Lorenzo Fagiano,et al.  Adaptive receding horizon control for constrained MIMO systems , 2014, Autom..

[9]  Stefano Di Cairano,et al.  Model Predictive Control for simultaneous station keeping and momentum management of low-thrust satellites , 2015, 2015 American Control Conference (ACC).

[10]  Stefano Di Cairano,et al.  Indirect adaptive model predictive control for linear systems with polytopic uncertainty , 2015, 2016 American Control Conference (ACC).

[11]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .

[12]  S. Shankar Sastry,et al.  Provably safe and robust learning-based model predictive control , 2011, Autom..

[13]  Stefano Di Cairano,et al.  An Industry Perspective on MPC in Large Volumes Applications: Potential Benefits and Open Challenges , 2012 .

[14]  David Q. Mayne,et al.  Robust model predictive control using tubes , 2004, Autom..

[15]  Stefano Di Cairano,et al.  Projection-free parallel quadratic programming for linear model predictive control , 2013, Int. J. Control.