Exact Complexity Certification of Active-Set Methods for Quadratic Programming

Cimini, Gionata; Bemporad, Alberto

doi:10.1109/tac.2017.2696742

Cited by 81 publications

(72 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…3 shows the block scheme of the proposed MPC, where q −1 represents the one-step delay operator. Problem (12) can be cast into the parametric unconstrained QP problem min .…”

Section: Model Predictive Controlmentioning

confidence: 99%

Model predictive control for pre‐compensated voltage mode controlled DC–DC converters

Cavanini

Cimini

Ippoliti

et al. 2017

IET Control Theory & Applications

Self Cite

View full text Add to dashboard Cite

This study introduces the use of model predictive control (MPC) to improve the performance of pre-compensated power supplies, and in particular of DC-DC converters, by dynamically modifying their output voltage reference. The importance of developing controllers for pre-compensated converters is twofold. First, the hierarchical structure is particularly useful when the primal controller is already coded, or hardware based, and cannot be changed. Second, the double-loop and, possible, multi-rate structure represents a computationally cheaper alternative to a direct MPC that would replace the primal controller and would require a much higher sampling frequency. In this study a MPC controller has been applied for the regulation of a pre-compensated synchronous DC-DC buck converter. The aim is to improve the performance of standard voltage mode control (VMC), without replacing the linear controller and without drastically affecting the computational burden. The algorithm has been tested both in simulation and experimentally, on commercially available hardware. The results show the performance improvement with respect to the standard VMC, as well as the feasibility of the proposed approach in an embedded platform. Tests with different primal controller tunings, and unknown varying loads, confirm the advantages of the method.

show abstract

“…3 shows the block scheme of the proposed MPC, where q −1 represents the one-step delay operator. Problem (12) can be cast into the parametric unconstrained QP problem min .…”

Section: Model Predictive Controlmentioning

confidence: 99%

Model predictive control for pre‐compensated voltage mode controlled DC–DC converters

Cavanini

Cimini

Ippoliti

et al. 2017

IET Control Theory & Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…This paper extends the result in [18], which handles the strictly convex case, to also handle positive semi-definite mpQPs, leading to additional theoretical as well as numerical results. In addition to being able to certify the complexity of primal active-set methods applied to positive semi-definite mpQPs, it is shown that this extension allows for dual activeset QP methods and active-set methods for linear programs to be certified with the presented method, enabling the results in [18], [19] and [12] to be viewed in a unified framework.…”

Section: Introductionmentioning

confidence: 99%

“…A challenging aspect of the analysis of the primal activeset QP algorithm considered in this work is that it turns out that all iterates are not necessarily affine in the parameter, in contrast to the methods studied in [19], [20] and [12]. Nonaffine iterates are shown to lead to a partition of the parameter space consisting of both linear and quadratic inequalities, in contrast to only linear inequalities which is the case in [19], [20] and [12].…”

Section: Introductionmentioning

confidence: 99%

Exact Complexity Certification of a Standard Primal Active-Set Method for Quadratic Programming

Arnström

Axehill

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

In model predictive control (MPC) an optimization problem has to be solved at each time step, which in realtime applications makes it important to solve these optimization problems efficiently and to have good upper bounds on worst-case solution time. Often for linear MPC problems, the optimization problem in question is a quadratic program (QP) that depends on parameters such as system states and reference signals. A popular class of methods for solving such QPs is active-set methods, where a sequence of linear systems of equations are solved. We propose an algorithm for computing which sequence of subproblems an active-set algorithm will solve, for every parameter of interest. By knowing these sequences, a worst-case bound on how many iterations, and ultimately the maximum time, the active-set algorithm needs to converge can be determined. The usefulness of the proposed method is illustrated on a set of QPs, originating from MPC problems, by computing the exact worst-case number of iterations primal and dual active-set algorithms require to reach optimality.

show abstract

“…Implementation of a typical MPC approach requires to online solve an optimization problem based on system model at each sampling time. A constrained finite-horizon optimal control problem must be solved at each time step, making the online implementation of MPC in embedded boards a challenge [2]. One way to avoid the online solution is to represent the solution explicitly via reformulation of the MPC problem into an equivalent multi-parametric quadratic programming (mp-QP) problem.…”

Section: Introductionmentioning

confidence: 99%

Complexity Reduction of Explicit Model Predictive Control via Combining Separator Function and Binary Search Trees

Arezoo¹,

Salahshoor²

2018

AJCST

View full text Add to dashboard Cite

The explicit Model Predictive Control (MPC) has emerged as a powerful technique to solve the optimization problem offline for embedded applications where computations is performed online. Despite practical obstacles in implementation of explicit model predictive control (MPC), the main drawbacks of MPC, namely the need to solve a mathematical program on line to compute the control action are removed. This paper addresses complexity of explicit model predictive control (MPC) in terms of online evaluation and memory requirement. Complexity reduction approaches for explicit MPC has recently been emerged as techniques to enhance applicability of MPC. Individual deployment of the approaches has not had enough effect on complexity reduction. In this paper, merging the approaches based on complexity reduction is addressed. The binary search tree and complexity reduction via separation are efficient methods which can be confined to small problems, but merging them can result in significant effect and expansion of its applicability. The simulation tests show proposed approach significantly outperforms previous methods.

show abstract

Exact Complexity Certification of Active-Set Methods for Quadratic Programming

Cited by 81 publications

References 40 publications

Model predictive control for pre‐compensated voltage mode controlled DC–DC converters

Model predictive control for pre‐compensated voltage mode controlled DC–DC converters

Exact Complexity Certification of a Standard Primal Active-Set Method for Quadratic Programming

Complexity Reduction of Explicit Model Predictive Control via Combining Separator Function and Binary Search Trees

Contact Info

Product

Resources

About