/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Model predictive control (MPC) has established itself as a promising control methodology in power electronics. This survey paper highlights the most relevant MPC techniques for power electronic systems. These can be classified into two major groups, namely, MPC without modulator, referred to as direct MPC, and MPC with a subsequent modulation stage, known as indirect MPC. Design choices, and parameters that affect the system performance, closed-loop stability, and controller robustness are discussed. Moreover, solvers, and control platforms that can be employed for the real-time implementation of MPC algorithms are presented. Finally, the MPC schemes in question are assessed, among others, in terms of design, and computational complexity, along with their performance, and applicability depending on the power electronic system at hand.

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Model Predictive Control of Power Electronic Systems: Methods, Results, and Challenges

The alternating direction method of multipliers is a powerful operator splitting technique for solving structured optimization problems. For convex optimization problems, it is well known that the algorithm generates iterates that converge to a solution, provided that it exists. If a solution does not exist, then the iterates diverge. Nevertheless, we show that they yield conclusive information regarding problem infeasibility for optimization problems with linear or quadratic objective functions and conic constraints, which includes quadratic, second-order cone, and semidefinite programs. In particular, we show that in the limit the iterates either satisfy a set of first-order optimality conditions or produce a certificate of either primal or dual infeasibility. Based on these results, we propose termination criteria for detecting primal and dual infeasibility.

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Infeasibility Detection in the Alternating Direction Method of Multipliers for Convex Optimization

We introduce a code generation software package that accepts a parametric description of a quadratic program (QP) as input and generates tailored C code that compiles into a fast and reliable optimization solver for the QP that can run on embedded platforms. The generated code is based on OSQP, a novel open-source operator splitting solver for quadratic programming. Our software supports matrix factorization caching and warm starting, and allows updates of the problem parameters during runtime. The generated C code is library-free and has a very small compiled footprint. Examples arising in real-world applications show that the generated code outperforms state-of-the-art embedded and desktop QP solvers.

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Embedded code generation using the OSQP solver

In hybrid model predictive control (MPC), a mixed-integer quadratic program (MIQP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC, we expect consecutive problem instances to be nearly identical. This article addresses the question of how computations performed at one time step can be reused to accelerate ( warm start ) the solution of subsequent MIQPs. Reoptimization is not a rare practice in integer programming: for small variations of certain problem data, the branch-and-bound algorithm allows an efficient reuse of its search tree and the dual bounds of its leaf nodes. In this article, we extend these ideas to the receding-horizon settings of MPC. The warm-start algorithm we propose copes naturally with arbitrary model errors, has a negligible computational cost, and frequently enables an a priori pruning of most of the search space. Theoretical considerations and experimental evidence show that the proposed method tends to reduce the combinatorial complexity of the hybrid MPC problem to that of a one-step look-ahead optimization, greatly easing the online computation burden.

Warm Start of Mixed-Integer Programs for Model Predictive Control of Hybrid Systems

We present a novel branch-and-bound solver for mixed-integer quadratic programs (MIQPs) that efficiently exploits the first-order OSQP solver for the quadratic program (QP) sub-problems. Our algorithm is very robust, requires no dynamic memory allocation and is division-free once an initial factorization is computed. Thus, it suitable for embedded applications with low computing power. Moreover, it does not require any assumption on the problem data such as strict convexity of the objective function. We exploit factorization caching and warm-starting to reduce the computational cost of QP relaxations during branch-and-bound and over repeated solutions of parametric MIQPs such as those arising in embedded control, portfolio optimization, and machine learning. Numerical examples show that our method, using a simple high-level Python implementation interfaced with the OSQP solver, is competitive with established commercial solvers.

Embedded Mixed-Integer Quadratic optimization Using the OSQP Solver

Embedded Mixed-Integer Quadratic Optimization using Accelerated Dual Gradient Projection

A Numerically Robust Mixed-Integer Quadratic Programming Solver for Embedded Hybrid Model Predictive Control

This paper presents a novel two-stage regularized moving-horizon algorithm for PieceWise Affine (PWA) regression. At the first stage, the training samples are processed iteratively, and a Mixed-Integer Quadratic-Programming (MIQP) problem is solved to find the sequence of active modes and the model parameters which best match the training data, within a relatively short time window in the past. According to a moving-horizon strategy, only the last element of the optimal sequence of active modes is kept, and the next sample is processed by shifting forward the estimation horizon. A regularization term on the model parameters is included in the cost of the formulated MIQP problem, to partly take into account also the past training data outside the considered time horizon. At the second stage, linear multi-category discrimination techniques are used to compute a polyhedral partition of the regressor space based on the estimated sequence of active modes.

Regularized moving-horizon piecewise affine regression using mixed-integer quadratic programming

Correspondence Manas Mejari, IDSIA, Dalle Molle Institute for Artificial Intelligence SUPSI-USI, 6928 Manno, Switzerland. Email: manas.mejari@idsia.ch Summary This article presents a two-stage algorithm for piecewise affine (PWA) regression. In the first stage, a moving horizon strategy is employed to simultaneously estimate the model parameters and to classify the training data by solving a small-size mixed-integer quadratic programming problem. In the second stage, linear multicategory separation methods are used to partition the regressor space. The framework of PWA regression is adapted to the identification of PWA AutoRegressive with eXogenous input (PWARX) models as well as linear parameter-varying (LPV) models. The performance of the proposed algorithm is demonstrated on an academic example and on two benchmark experimental case studies. The first experimental example concerns modeling the placement process in a pick-and-place machine, while the second one consists in the identification of an LPV model describing the input-output relationship of an electronic bandpass filter with time-varying resonant frequency.

Vihangkumar V. Naik

Papers

Embedded Mixed-Integer Quadratic optimization Using the OSQP Solver

Embedded Mixed-Integer Quadratic Optimization using Accelerated Dual Gradient Projection

A Numerically Robust Mixed-Integer Quadratic Programming Solver for Embedded Hybrid Model Predictive Control

Regularized moving-horizon piecewise affine regression using mixed-integer quadratic programming

Identification of hybrid and linear parameter‐varying models via piecewise affine regression using mixed integer programming