Analytical expression of explicit MPC solution via lattice piecewise-affine function

An analytical expression of the explicit solution to linear model predictive control (MPC) is proposed by the introduction of a lattice piecewise-affine (PWA) function. A systematic procedure is developed for building a lattice PWA representation from a continuous explicit MPC solution obtained by a multi-parametric program. A simple method is presented to remove the redundant parameters in the lattice expression of MPC control laws. The effectiveness of this approach is supported by the study of three benchmark MPC problems. The proposed analytical expression provides a very efficient and practically viable method for implementing the explicit MPC solutions regarding its online calculation and memory space requirements.

[1]  Hao Zhang,et al.  A novel compact piecewise-linear representation: Research Articles , 2005 .

[2]  L. Chua,et al.  The complete canonical piecewise-linear representation. I. The geometry of the domain space , 1992 .

[3]  Alberto Bemporad,et al.  Evaluation of piecewise affine control via binary search tree , 2003, Autom..

[4]  Shuning Wang,et al.  Identification of dynamic systems using Piecewise-Affine basis function models , 2007, Autom..

[5]  Tor Arne Johansen,et al.  Continuous Selection and Unique Polyhedral Representation of Solutions to Convex Parametric Quadratic Programs , 2007 .

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

[7]  Yugeng Xi,et al.  Improving off-line approach to robust MPC based-on nominal performance cost , 2007, Autom..

[8]  T. O'Mahony,et al.  An Orthogonal Partitioning Approach to Simplify Robust Model Predictive Control , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[9]  A. Bemporad,et al.  Efficient on-line computation of constrained optimal control , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[10]  Alberto Bemporad,et al.  Piecewise linear optimal controllers for hybrid systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[11]  J. M. Tarela,et al.  A representation method for PWL functions oriented to parallel processing , 1990 .

[12]  Alberto Bemporad,et al.  The explicit solution of model predictive control via multiparametric quadratic programming , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[13]  J. M. Tarela,et al.  Region configurations for realizability of lattice Piecewise-Linear models , 1999 .

[14]  Shuning Wang,et al.  A novel compact piecewise-linear representation , 2005, Int. J. Circuit Theory Appl..

[15]  Bo Lincoln,et al.  Relaxing dynamic programming , 2006, IEEE Transactions on Automatic Control.

[16]  M. Morari,et al.  Efficient evaluation of piecewise control laws defined over a large number of polyhedra , 2007, 2007 European Control Conference (ECC).

[17]  Tor Arne Johansen,et al.  Hardware Synthesis of Explicit Model Predictive Controllers , 2007, IEEE Transactions on Control Systems Technology.

[18]  T.A. Johansen,et al.  Utilizing Reachability Analysis in Point Location Problems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[20]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

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

[22]  M. Morari,et al.  On-line optimization via off-line parametric optimization tools , 2000 .

[23]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[24]  Xiaoyan Ma,et al.  A max-piecewise-linear neural network for function approximation , 2008, Neurocomputing.

[25]  Francis J. Doyle,et al.  Analysis of linear programming in model predictive control , 2004, Comput. Chem. Eng..

[26]  A. Rantzer,et al.  Suboptimal dynamic programming with error bounds , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[27]  Tor Arne Johansen,et al.  Approximate explicit constrained linear model predictive control via orthogonal search tree , 2003, IEEE Trans. Autom. Control..

[28]  Richard H. Middleton,et al.  Networked control design for linear systems , 2003, Autom..

[29]  L. Chua,et al.  A generalized canonical piecewise-linear representation , 1990 .

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

[31]  Colin Neil Jones,et al.  A logarithmic-time solution to the point location problem for parametric linear programming , 2006, Autom..

[32]  Shuning Wang,et al.  A compact f-f model of high-dimensional piecewise-linear function over a degenerate intersection , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.