Fast and robust QP solver for embedded optimization
ODYS QP Solver is a fast and robust solver for Quadratic Programming (QP) problems. It is optimized for problems arising in real-time embedded optimization and embedded MPC. It supports general inequality constraints, equality constraints, and bound constraints on the optimization variables.
Get in touch with us to request a trial version of the software or a quote for the full version. We will be happy to discuss with you the needs of your application. If you use ODYS QP Solver in a scientific paper, please add a citation.
ODYS QP Solver is designed to solve very efficiently small and medium scale convex quadratic programming problems of the form:
We have successfully applied the solver in many real-time optimization problems that require computing the solution in the millisecond range and on limited computational resources. It is fast and has low memory footprint. It provides accurate and robust results even when used in single-precision arithmetic.
The tables on the right show the results obtained by running the solver on an Intel Core i7 2.2GHz, for QP problems of different sizes and with an average of 40% constraints active at the optimal solution. Tests are carried out in double-precision hardware, where single-precision is emulated.
Results obtained with ODYS QP Solver v4.1, released in April 2021
Solving QP problems efficiently is the key enabler for deploying real-time linear and nonlinear model predictive control in industrial production.
Although the basic version of ODYS QP Solver software can already solve problems arising from MPC, we have developed a dedicated MPC version to further improve both the speed of execution and the memory occupancy of the optimization algorithm.
By exploiting the special structure of the cost function and constraints of a predictive control problem formulation, the MPC version of ODYS QP Solver is twice as fast and takes half the memory as the basic version, on typical embedded control problems.
This specialized version is integrated into ODYS Embedded MPC, our proprietary toolchain for real-time implementation of MPC controllers in industrial applications.
Quantifying with accuracy the worst-case execution time of the optimizer is typically necessary for industrial embedded systems, to meet real-time requirements and avoid oversizing the processor.
Most QP algorithms simply impose a maximum number of iterations to make sure that the problem is solved within the prescribed amount of time, without any guarantee on the quality of the computed solution. On the other hand, ODYS QP Solver comes with a complexity analyzer that computes exactly the maximum number of iterations needed to reach the optimal solution, for a given set of problems that depend linearly on parameters, with no over-estimation!
This is helpful to select the appropriate computing hardware in the control design phase, validate an existing design, and identify possible situations where the problem is infeasible.
ODYS QP Solver is distributed as a shared library and supports all the main operating systems, in 32-bit and 64-bit architectures.
The software includes built-in interfaces and demos for MATLAB®, Simulink®, Python, and C. Customers can readily integrate it in any framework that allows importing shared libraries.
The solver is coded in plain C, is compliant with MISRA-C 2012 requirements, and does not require any OS-dependent function or library. As such, the solver can be compiled on virtually any platform supporting floating-point operations.
Please contact us if you are interested in obtaining the code for compiling the solver in your target platform.
Graphics by www.giuliaferrandi.com