Computation and approximation of piecewise affine control laws via binary search trees

We present an algorithm for generating a binary search tree that allows efficient computation of piecewise affine (PWA) functions defined on a polyhedral partition. This is useful for PWA control approaches, such as explicit model predictive control (MPC), as it allows the controller to be implemented on-line with small computational effort. The computation time is logarithmic in the number of regions in the PWA partition. A method for generating an approximate PWA function based on a binary search tree is also presented, giving further simplification of PWA control.

[1]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[2]  P. R. Bélanger,et al.  Piecewise-linear LQ control for systems with input constraints , 1994, Autom..

[3]  A. Vicino,et al.  Sequential approximation of feasible parameter sets for identification with set membership uncertainty , 1996, IEEE Trans. Autom. Control..

[4]  Stephen P. Boyd,et al.  Quadratic stabilization and control of piecewise-linear systems , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[5]  Quadratic Stabilization of Discrete-Time Uncertain Nonlinear Multi-Model Systems using Piecewise A ne State-Feedback , 1998 .

[6]  B. Foss,et al.  Constrained quadratic stabilization of discrete-time uncertain non-linear multi-model systems using piecewise affine state-feedback , 1999 .

[7]  Sophie Tarbouriech,et al.  Piecewise-Linear Robust Control of Systems with Input Constraints , 1999, Eur. J. Control.

[8]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[9]  M. Morari,et al.  Optimal controllers for hybrid systems: stability and piecewise linear explicit form , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[10]  G. Goodwin,et al.  Global analytical model predictive control with input constraints , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[11]  A. Bemporad,et al.  Suboptimal explicit MPC via approximate multiparametric quadratic programming , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[12]  M. Morari,et al.  Piecewise linear robust model predictive control , 2001 .

[13]  Alberto Bemporad,et al.  A Hybrid Approach to Traction Control , 2001, HSCC.

[14]  T. Johansen,et al.  An algorithm for multi-parametric quadratic programming and explicit MPC solutions , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[15]  Alberto Bemporad,et al.  Convexity recognition of the union of polyhedra , 2001, Comput. Geom..

[16]  A. Grancharova,et al.  APPROXIMATE EXPLICIT MODEL PREDICTIVE CONTROL IMPLEMENTED VIA ORTHOGONAL SEARCH TREE PARTITIONING , 2002 .

[17]  T. Johansen,et al.  COMPLEXITY REDUCTION IN EXPLICIT LINEAR MODEL PREDICTIVE CONTROL , 2002 .

[18]  Alberto Bemporad,et al.  Model predictive control based on linear programming - the explicit solution , 2002, IEEE Transactions on Automatic Control.

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

[20]  Tor Arne Johansen,et al.  Explicit sub-optimal linear quadratic regulation with state and input constraints , 2002, Autom..

[21]  A. Bemporad,et al.  Suboptimal Explicit Receding Horizon Control via Approximate Multiparametric Quadratic Programming , 2003 .

[22]  Alberto Bemporad,et al.  An algorithm for multi-parametric quadratic programming and explicit MPC solutions , 2003, Autom..