MPC and Optimization, Tor Arne Johansen, NTNU

Fast Model Predictive Control

Traditionally Model Predictive Control (MPC) is implemented via real-time optimization. Our objective is to find explicit state feedback laws that are equivalent to MPC and thereby allow MPC to be implemented simply via the evaluation of a piecewise linear function. Our results show that this is possible for applications of moderate size. The benefits of this are

• MPC can be implemented at high sampling rates (milliseconds or less) on inexpensive computers using fixed-point arithmetic
• MPC software reliability can be easily verified and applied in safety-critical applications

Multi-parametric programming:

• J. Spjøtvold, E. C. Kerrigan, C. N. Jones, P. Tøndel, T. A. Johansen, On the Facet-to-Facet Property of Solutions to Convex Parametric Quadratic Programs, Automatica, Vol. 42, pp. 2209-2204, 2006
• J. Spjøtvold, P. Tøndel, T. A. Johansen, A continuous selection and unique polyhedral representation of solutions to convex multiparametric quadratic programs, J. Optimization Theory and Applications, 2006
• A. Grancharova, T. A. Johansen, and P. Tøndel, Computational aspects of approximate explicit model predictive control, International workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, Freudenstadt-Lauterbad, Germany, 2005
• T. A. Johansen, Approximate Explicit Receding Horizon Control of Constrained Nonlinear Systems, Automatica, Vol. 40, pp. 293-300, 2004
• P. Tøndel, T. A. Johansen and A. Bemporad, Further results on Multi-parametric quadratic programming, IEEE Conf. Decision and Control, Maui, Hawaii, 2003
• P. Tøndel, T. A. Johansen and A. Bemporad, An algorithm for multi-parametric quadratic programming and explicit MPC solutions, Automatica, Vol. 39, pp. 489-497, 2003
• T. A. Johansen and A. Grancharova, Approximate explicit constrained linear model predictive control via orthogonal search tree, IEEE Trans. Automatic Control, Vol. 48, pp. 810-815, 2003
• T. A. Johansen, Reduced Explicit Constrained Linear Quadratic Regulators, IEEE Trans. Automatic Control, Vol. 48, pp. 823-828, 2003
• T. A. Johansen, On Multi-parametric Nonlinear Programming and Explicit Nonlinear Model Predictive Control, IEEE Conf. Decision and Control, Las Vegas, NV, 2002
• T. A. Johansen, I. Petersen and O. Slupphaug, Explicit Subopitmal Linear Quadratic Regulation with Input and State Constraints, Automatica, accepted, 2002
• P. Tøndel, T. A. Johansen, Complexity reduiction in explicit model predictive control, IFAC World Congress, Barcelona, 2002

Online computations in explicit MPC

• F. Bayat, T. A. Johansen, A. A. Jalali, Flexible Piecewise Function Evaluation Methods Based on Truncated Binary Search Trees and Lattice Representation in Explicit MPC, IEEE Trans. Control Systems Technology, accepted, 2011
• F. Bayat, T. A. Johansen, A. A. Jalali, Using hash tables to manage time-storage complexity in point location problem: Application to Explicit MPC, Automatica, accepted, 2011
• T. A. Johansen, W. Jackson, R. Schreiber, P. Tøndel, Hardware Synthesis of Explicit Model Predictive Controllers, IEEE Transactions Control Systems Technology, vol. 15, pp. 191-197, 2007
• P. Tøndel, T. A. Johansen and A. Bemporad, Evaluation of Piecewise Affine Control via Binary Search Tree, Automatica, Vol. 39, pp. 743-749, May, 2003

Applications of explicit MPC

• L. Feng, C. R. Gutvik, T. A. Johansen, D. Sui, A. O. Brubakk, Approximate Explicit Nonlinear Receding Horizon Control for Decompression of Divers, IEEE Trans. Control Systems Technology, accepted, 2011
• C. R. Gutvik, T. A. Johansen, A. O. Brubakk, Optimal Decompression of Divers - Procedures for constraining predicted bubble growth, IEEE Control Systems Magazine, Vol. 31, No. 1, pp. 19-28, 2011; DOI:10.1109/MCS.2010.939141
• L. Feng, C. R. Gutvik, T. A. Johansen, Optimal Decompression Through Multi-parametric Nonlinear Programming, IFAC NOLCOS, Bologna, Italy, 2010
• A.Grancharova, T. A. Johansen, Design and Comparison of Explicit Model Predictive Controllers for an Electropneumatic Clutch Actuator Using On/Off Valves, IEEE/ASME Trans. Mechatronics, accepted, 2011
• Grancharova, T. A. Johansen and J. Kocijan, Explicit model predictive control of gas-liquid separation plant, Computers and Chemical Engineering, Vol. 28, 2004

Other MPC formulation

• A. Grancharova, T. A. Johansen, Distributed Quasi-Nonlinear Model Predictive Control by Dual Decomposition, IFAC World Congress, Milano, 2011
• A. Grancharova and T. A. Johansen, A computational approach to explicit feedback stochastic nonlinear model predictive control, IEEE Conf. Decision and Control, Atlanta, 2010
• J. Spjøtvold, E. C. Kerrigan, T. A. Johansen, D. Q. Mayne, Inf-Sup Control of Discontinuous Piecewise Affine Systems, International Journal of Robust and Nonlinear Control, Vol. 19, pp. 1471-1492, 2009
• A. Grancharova, T. A. Johansen, Computation, approximation and stability of explicit feedback min-max nonlinear model predictive control, Automatica, Vol. 45, pp. 1134-1143, 2009
• A. Grancharova, J. Kocijan, T. A. Johansen, Explicit stochastic predictive control of combustion plants based on Gaussian process models, Automatica, Vol. 44, pp. 1621-1631, 2008
• A. Grancharova, T. A. Johansen, Explicit Approximate Model Predictive Control of Constrained Nonlinear Systems with Quantized Inputs, International Workshop on Assessment and Future Directions of NMPC, Pavia, Italy, 2008 (revised ).

Optimizing constrained control allocation

Control allocation deals with the task of coordinating a redundant set of actuators to produce a totalt effort, taking into account actuator and operational constraints and objective functions.

Key publications

• J. Tjønnås, T. A. Johansen, Stabilization of Automotive Vehicles using Active Steering and Adaptive Brake Control Allocation, IEEE Trans. Control Systems Technology, accepted, 2010; DOI:10.1109/TCST.2009.2023981
• J. Spjøtvold, T. A. Johansen, Fault Tolerant Control Allocation for a Thruster-Controlled Floating Platform using Parametric Programming, IEEE Conf. Decision and Control, Shanghai, 2009
• J. Tjønnås, T. A. Johansen, Adaptive Control Allocation, Automatica, Vol. 44, pp. 2754-2766, 2008
• T. A. Johansen, T. P. Fuglseth, P. Tøndel, T. I. Fossen, Optimal constrained control allocation in marine surface vessels with rudders, Control Engineering Practise, Vol. 16,  pp. 457-464, 2008
• T. I. Fossen and T. A. Johansen, A Survey of Control Allocation Methods for Ships and Underwater Vehicles, 14th Mediterranean Conference on Control and Automation, Ancona, 2006
• J. Spjøtvold, P. Tøndel, T. A. Johansen, Decomposing Linear Control Allocation Problems, 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan, 2006
• T. A. Johansen, T. I. Fossen, P. Tøndel, Efficient Optimal Constrained Control Allocation via Multi-Parametric Programming, AIAA J. Guidance, Control and Dynamics, Vol. 28, pp. 506-515, 2005
• T. A. Johansen, T. I. Fossen, Svein P. Berge, Constrained Nonlinear Control Allocation with Singularity Avoidance using Sequential Quadratic Programming, IEEE Trans. Control Systems Technology, Vol. 12, pp. 211-216, 2004
• P. Tøndel, and T. A. Johansen, Control allocation for Yaw Stabilization in Automotive Vehicles using Multiparametric Nonlinear Programming, submitted ACC, 2004
• T. A. Johansen, Optimizing nonlinear control allocation, IEEE Conf. Decision and Control, Bahamas, 2004
• T. A. Johansen, D. Sbarbaro, Optimizing control of over-actuated linear systems with nonlinear output maps via control Lyapunov functions, European Control Conference, Cambridge, 2003.