Implementation of Mixed-integer Programming on Embedded System

Abstract

One of the most widespread modern control strategies is the discrete-time Model Predictive Control (MPC) method which requires the solution of the quadratic programming problem. For systems with binary input variables the quadratic problem is replaced by more challenging Mixed-Integer Quadratic Programming (MIQP) problem. The objective of this work is the implementation of MIQP problem solver in a low power embedded computing platform with limited computational power and limited memory. The MIQP problem is solved using branch-and-bound method and the solution of the relaxed original quadratic problems with equality and inequality constraints solved in the nodes of a binary tree is found with interior-point algorithm. A simulation study of the reserve constrained economic dispatch problem for power generators with prohibited zones is presented. Simulation results show the applicability of the proposed solver for small size MIQP problems.

Mixed-integer MPC for the temperature control of the batch reactor

“…are valid because only kM = 1 is allowed for cold water kC=1 as given in the value set (7). Increasing the horizons may increase the performance of the controller, but it increases the complexity of the mixed-integer programming procedure.…”

“…The main methods are tailored optimization methods for particular embedded platform. Several application of embedded MIQP solvers have been proposed in [6], [7]. Many methods have been developed for solution of the MIQP problem, however branch-and-bound method have proved superior to other methods such as decomposition method or logic-based method [8].…”

Hybrid Model Predictive Control for Fully Electric Vehicle Thermal Management System Optimal Mode Selection

“…Moreover, it could be feasible to run the optimization in real-time (implicit or online MPC), which is not covered in this work. Successful MCU implementation of the B&B algorithm was reported in [13], thus real-time decision algorithm could also be the possible direction in this field.…”

Compensation Of Valve Deadzone Using Mixed Integer Predictive Control

“…The problem is constrained by limits for input variables, binary variables  and relations defining the evolution of the predicted states. The problem is solved using the branch-and-bound strategy and interior point method is used for solution of the relaxed problems (Novak and Chalupa, 2015). Using the successive linearization strategy the parameters of augmented model are obtained at each sampling period using the current state ( ) x k and linearization of (12).…”