Abstract
Quadratic programming problems (QPs) frequently appear in control engineering. For use on embedded platforms, a QP solver implementation is required in the programming language C. A new solver for quadratic optimization problems, EmbQP, is described, which was implemented in well readable C code. The algorithm is based on the dual method of Goldfarb and Idnani and solves strictly convex QPs with a positive definite objective function matrix and linear equality and inequality constraints. The algorithm is outlined and some details for an efficient implementation in C are shown, with regard to the requirements of embedded systems. The newly implemented QP solver is demonstrated in the context of control allocation of an over-actuated vehicle as application example. Its performance is assessed in a simulation experiment.
Highlights
Quadratic programming problems occur in various areas, for example in portfolio optimization where the risk-adjusted return shall be maximized [1], in signal processing operations, in audio applications [2], and in machine learning [3]
The EmbQP solver is assessed against the Fortran QL solver [9] by means of comparative simulations of a path-following scenario with the ROMO
The Fortran QL solver only needed to be replaced by EmbQP, which is easy to accomplish, since both solvers can be interfaced into the Modelica environment using so-called external C functions
Summary
Quadratic programming problems occur in various areas, for example in portfolio optimization where the risk-adjusted return shall be maximized [1], in signal processing operations, in audio applications [2], and in machine learning [3]. Simple control structures provide benefits for the use on embedded platforms since, e.g., loops with a fixed number of iterations and the avoidance of jump statements make it easier to analyze the overall execution of the code and to determine the real-time capability of the code. A handwritten well-readable and embedded system suitable C code implementation of the QL solver was developed As an application example for the use of QPs, the control allocation problem from [11] is considered. In the work presented here, the new EmbQP solver is used in this application example, and the simulation results of the two solvers are shown and compared.
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