Nonlinear model predictive control using adaptive hinging hyperplanes model

This paper deals with the problem of nonlinear model predictive control using a piecewise linear predictive model: the adaptive hinging hyperplanes (AHH). The AHH model is adaptive and efficient, thus depicts the relationship of the nonlinear system very well. Thanks to the piecewise linear property of the predictive model, a series of convex quadratic programming are constructed in the controller design step. The existence of a global optimum is guaranteed and a descent search algorithm is performed to get a reasonable control sequence within the sampling interval. Simulation results are also presented to illustrate the potential of the proposed methodologies.

[1]  M. Houkari,et al.  A neural adaptive controller , 1993, Proceedings of IEEE Systems Man and Cybernetics Conference - SMC.

[2]  Bryon R. Maner,et al.  Polymerization reactor control using autoregressive‐plus Volterra‐based MPC , 1997 .

[3]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..

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

[5]  Xu Cheng,et al.  Robust stability constrained model predictive control , 2004, Proceedings of the 2004 American Control Conference.

[6]  Michael A. Henson,et al.  Nonlinear model predictive control: current status and future directions , 1998 .

[7]  Peter Craven,et al.  Smoothing noisy data with spline functions , 1978 .

[8]  James B. Rawlings,et al.  Model predictive control with linear models , 1993 .

[9]  J. Maciejowski,et al.  Robust feasibility in model predictive control: necessary and sufficient conditions , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[10]  G. Wahba.  Smoothing noisy data with spline functions , 1975 .

[11]  Haralambos Sarimveis,et al.  A Simulated Annealing Algorithm for Prioritized Multiobjective Optimization—Implementation in an Adaptive Model Predictive Control Configuration , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  Jay H. Lee,et al.  Dynamically scheduled MPC of nonlinear processes using hinging hyperplane models , 1998 .

[13]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[14]  Junghui Chen,et al.  Neural network-based predictive control for multivariable processes , 2002 .

[15]  Shuning Wang,et al.  Generalization of hinging hyperplanes , 2005, IEEE Transactions on Information Theory.

[16]  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).

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

[18]  J. Maciejowski,et al.  Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[19]  T. Alamo,et al.  Stability analysis of systems with bounded additive uncertainties based on invariant sets: Stability and feasibility of MPC , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[20]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[21]  T. J. McAvoy,et al.  Dynamics of pH in Controlled Stirred Tank Reactor , 1972 .

[22]  Leon O. Chua,et al.  Canonical piecewise-linear representation , 1988 .

[23]  Xiaolin Huang,et al.  Adaptive Hinging Hyperplanes , 2008 .

[24]  Leo Breiman,et al.  Hinging hyperplanes for regression, classification, and function approximation , 1993, IEEE Trans. Inf. Theory.

[25]  M. Baotic,et al.  An efficient algorithm for computing the state feedback optimal control law for discrete time hybrid systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[26]  Shuning Wang,et al.  Adaptive hinging hyperplanes and its applications in dynamic system identification , 2009, Autom..