Piecewise affine direct virtual sensors with Reduced Complexity

In this paper, a piecewise-affine direct virtual sensor is proposed for the estimation of unmeasured outputs of nonlinear systems whose dynamical model is unknown. In order to overcome the lack of a model, the virtual sensor is designed directly from measured inputs and outputs. The proposed approach generalizes a previous contribution, allowing one to design lower-complexity estimators. Indeed, the reduced-complexity approach strongly reduces the effect of the so-called “curse of dimensionality”, and can be applied to relatively high-order systems, while enjoying all the convergence and optimality properties of the original approach.

[1]  L. Ljung.  Convergence analysis of parametric identification methods , 1978 .

[2]  Carlo Novara,et al.  Direct Identification of Optimal SM-LPV Filters and Application to Vehicle Yaw Rate Estimation , 2011, IEEE Transactions on Control Systems Technology.

[3]  Lorenzo Fagiano,et al.  Vehicle side-slip angle estimation using a direct MH estimator , 2010, 2010 IEEE International Conference on Control Applications.

[4]  Marco Storace,et al.  Piecewise-Linear Identification of Nonlinear Dynamical Systems in View of Their Circuit Implementations , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Roberto Guerrieri,et al.  A Geometric Approach to Maximum-Speed n-Dimensional Continuous Linear Interpolation in Rectangular Grids , 1998, IEEE Trans. Computers.

[6]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[7]  Marco Storace,et al.  Digital architectures realizing piecewise‐linear multivariate functions: Two FPGA implementations , 2011, Int. J. Circuit Theory Appl..

[8]  Marco Storace,et al.  A method for the approximate synthesis of cellular non‐linear networks—Part 1: Circuit definition , 2003, Int. J. Circuit Theory Appl..

[9]  Harold W. Kuhn,et al.  Some Combinatorial Lemmas in Topology , 1960, IBM J. Res. Dev..

[10]  Alberto Bemporad,et al.  High-Speed Piecewise Affine Virtual Sensors , 2012, IEEE Transactions on Industrial Electronics.

[11]  K. Poolla,et al.  Filter design from data: direct vs. two-step approaches , 2006, 2006 American Control Conference.

[12]  Carlo Novara,et al.  The filter design from data (FD2) problem: Nonlinear Set Membership approach , 2009, Autom..

[13]  Alfredo C. Desages,et al.  Orthonormal high-level canonical PWL functions with applications to model reduction , 2000 .

[14]  Marco Storace,et al.  A method for the approximate synthesis of cellular non‐linear networks—Part 2: Circuit reduction , 2003, Int. J. Circuit Theory Appl..

[15]  Lorenzo Fagiano,et al.  A study on the use of virtual sensors in vehicle control , 2008, 2008 47th IEEE Conference on Decision and Control.