Solutions to constrained linear model predictive control problems can be pre-computed off-line in an explicit form as a piecewise linear state feedback on a polyhedral partition of the state space, avoiding real-time optimization. We suggest an algorithm that will determine an approximate explicit piecewise linear state feedback by imposing an orthogonal search tree structure on the partition. This leads to a real-time computational complexity that is logarithmic in the number of regions in the partition, and the algorithm yields guarantees on the sub-optimality, asymptotic stability and constraint fulfillment.

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It has recently been shown that the feedback solution to linear and quadratic constrained Model Predictive Control (MPC) problems has an explicit representation as a piecewise linear (PWL) state feedback. For nonlinear MPC the prospects of explicit solutions are even higher than for linear MPC, since the bene…ts of computational e¢ ciency and veri…ability are even more important. Preliminary studies on approximate explicit PWL solutions of convex nonlinear MPC problems, based on multi-parametric Nonlinear Programming (mp-NLP) ideas show that sub-optimal PWL controllers of practical complexity can indeed be computed o¤-line. However, for non-convex problems there is a need to investigate practical computational methods that not necessarily lead to guaranteed properties, but when combined with veri…cation and analysis methods will give a practical tool for development and implementation of explicit NMPC. The present paper focuses on the development of such methods. As a case study, the application of the developed approaches to compressor surge control is considered.

Energy production is one of the largest sources of air pollution. A feasible method to reduce the harmful flue gas emissions and to increase the efficiency is to improve the control strategies of the existing thermoelectric power plants.This makes the Nonlinear Model Predictive Control (NMPC) method very suitable for achieving an efficient combustion control. Recently, an explicit approximate approach for stochastic NMPC based on a Gaussian process model was proposed. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation, which is an essential issue in safety-critical applications. This paper considers the application of an explicit approximate approach for stochastic NMPC to the design of an explicit reference tracking NMPC controller for a combustion plant based on its Gaussian process model. The controller brings the air factor (respectively the concentration of oxygen in the flue gas) on its optimal value with every change of the load factor and thus an optimal operation of the combustion plant is achieved.