Introducing the quadratically-constrained quadratic programming framework in HPIPM

This paper introduces the quadraticallyconstrained quadratic programming (QCQP) framework recently added in HPIPM alongside the original quadraticprogramming (QP) framework. The aim of the new framework is unchanged, namely providing the building blocks to efficiently and reliably solve (more general classes of) optimal control problems (OCP). The newly introduced QCQP framework provides full features parity with the original QP framework: three types of QCQPs (dense, optimal control and tree-structured optimal control QCQPs) and interior point method (IPM) solvers as well as (partial) condensing and other pre-processing routines. Leveraging the modular structure of HPIPM, the new QCQP framework builds on the QP building blocks and similarly provides fast and reliable IPM solvers.

[1]  M. Diehl,et al.  acados—a modular open-source framework for fast embedded optimal control , 2019, Mathematical Programming Computation.

[2]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[3]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[4]  Real-Time Solution to Quadratically Constrained Quadratic Programs for Predictive Converter Control , 2020 .

[5]  Moritz Diehl,et al.  An efficient implementation of partial condensing for Nonlinear Model Predictive Control , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[6]  Stephen P. Boyd,et al.  OSQP: an operator splitting solver for quadratic programs , 2017, 2018 UKACC 12th International Conference on Control (CONTROL).

[7]  Moritz Diehl,et al.  Continuous Control Set Nonlinear Model Predictive Control of Reluctance Synchronous Machines , 2019, ArXiv.

[8]  N. Maratos,et al.  Exact penalty function algorithms for finite dimensional and control optimization problems , 1978 .

[9]  M. Diehl,et al.  Survey of sequential convex programming and generalized Gauss-Newton methods , 2021, ESAIM: Proceedings and Surveys.

[10]  Masao Fukushima,et al.  A Sequential Quadratically Constrained Quadratic Programming Method for Differentiable Convex Minimization , 2002, SIAM J. Optim..

[11]  Moritz Diehl,et al.  Local Convergence of Sequential Convex Programming for Nonconvex Optimization , 2010 .

[12]  Giampaolo Torrisi,et al.  Predictive Converter Control: Hidden Convexity and Real-Time Quadratically Constrained Optimization , 2021, IEEE Transactions on Control Systems Technology.

[13]  Moritz Diehl,et al.  Determining the Exact Local Convergence Rate of Sequential Convex Programming , 2020, 2020 European Control Conference (ECC).

[14]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[15]  David Q. Mayne,et al.  Robust model predictive control of constrained linear systems with bounded disturbances , 2005, Autom..

[16]  M. Diehl,et al.  HPIPM: a high-performance quadratic programming framework for model predictive control , 2020, IFAC-PapersOnLine.

[17]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[18]  Daniel Axehill,et al.  Controlling the level of sparsity in MPC , 2014, Syst. Control. Lett..

[19]  Stephen P. Boyd,et al.  ECOS: An SOCP solver for embedded systems , 2013, 2013 European Control Conference (ECC).

[20]  Masao Fukushima,et al.  A successive quadratic programming algorithm with global and superlinear convergence properties , 1986, Math. Program..

[21]  Moritz Diehl,et al.  A high-performance Riccati based solver for tree-structured quadratic programs , 2017 .

[22]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[23]  A. F. Izmailov,et al.  Newton-Type Methods for Optimization and Variational Problems , 2014 .

[24]  Field Oriented Economic Model Predictive Control for Permanent Magnet Synchronous Motors , 2020 .

[25]  Manfred Morari,et al.  Efficient interior point methods for multistage problems arising in receding horizon control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[26]  Stephen J. Wright Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

[27]  Gianluca Frison,et al.  Algorithms and Methods for High-Performance Model Predictive Control , 2016 .

[28]  Jorge Nocedal,et al.  Adaptive Barrier Update Strategies for Nonlinear Interior Methods , 2008, SIAM J. Optim..