Optimal input signal design for data-centric estimation methods

Data-centric estimation methods such as Model-on-Demand and Direct Weight Optimization form attractive techniques for estimating unknown functions from noisy data. These methods rely on generating a local function approximation from a database of regressors at the current operating point with the process repeated at each new operating point. This paper examines the design of optimal input signals formulated to produce informative data to be used by local modeling procedures. The proposed method specifically addresses the distribution of the regressor vectors. The design is examined for a linear time-invariant system under amplitude constraints on the input. The resulting optimization problem is solved using semidefinite relaxation methods. Numerical examples show the benefits in comparison to a classical PRBS input design.

[1]  Jacob Roll,et al.  Nonlinear system identification via direct weight optimization , 2005, Autom..

[2]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[3]  David P. Williamson,et al.  Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.

[4]  Panos M. Pardalos,et al.  Quadratic programming with one negative eigenvalue is NP-hard , 1991, J. Glob. Optim..

[5]  Aharon Ben-Tal,et al.  Lectures on modern convex optimization , 1987 .

[6]  Lennart Ljung,et al.  Perspectives on system identification , 2010, Annu. Rev. Control..

[7]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[8]  George Cybenko,et al.  Just-in-Time Learning and Estimation , 1996 .

[9]  Daniel E. Rivera,et al.  Model-on-Demand predictive control for nonlinear hybrid systems with application to adaptive behavioral interventions , 2010, 49th IEEE Conference on Decision and Control (CDC).

[10]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[11]  Y. Nesterov.  Semidefinite relaxation and nonconvex quadratic optimization , 1998 .

[12]  Daniel E. Rivera,et al.  A 'Model-on-Demand' identification methodology for non-linear process systems , 2001 .

[13]  M. Laurent.  Sums of Squares, Moment Matrices and Optimization Over Polynomials , 2009 .

[14]  Ian R. Manchester,et al.  Input design for system identification via convex relaxation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[15]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[16]  Raghunathan Rengaswamy,et al.  Plant Friendly Input Design: Convex Relaxation and Quality , 2011, IEEE Transactions on Automatic Control.

[17]  Daniel E. Rivera,et al.  Towards Patient-Friendly Input Signal Design for Optimized Pain Treatment Interventions , 2012 .

[18]  Anders Stenman,et al.  Model on Demand: Algorithms, Analysis and Applications , 1999 .

[19]  Wei Yu,et al.  High purity distillation column: Simulation and optimization , 2013 .

[20]  H. Müller,et al.  Local Polynomial Modeling and Its Applications , 1998 .

[21]  Hyunjin Lee,et al.  Constrained multisine input signals for plant-friendly identification of chemical process systems , 2009 .

[22]  Daniel E. Rivera,et al.  A control engineering approach for designing an optimized treatment plan for fibromyalgia , 2011, Proceedings of the 2011 American Control Conference.

[23]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[24]  Lennart Ljung,et al.  Nonlinear black-box modeling in system identification: a unified overview , 1995, Autom..

[25]  Yinyu Ye,et al.  Approximating quadratic programming with bound and quadratic constraints , 1999, Math. Program..