Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems

in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration. In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver. I

High-Performance Small-Scale Solvers for Moving Horizon Estimation

In this paper we present a moving horizon estimation (MHE) formulation suitable to easily describe the quadratic programs (QPs) arising in constrained and nonlinear MHE. We propose algorithms for factorization and solution of the underlying Karush-Kuhn-Tucker (KKT) system, as well as the efficient implementation techniques focusing on small-scale problems. The proposed MHE solver is implemented using custom linear algebra routines and is compared against implementations using BLAS libraries. Additionally, the MHE solver is interfaced to a code generation tool for nonlinear model predictive control (NMPC) and nonlinear MHE (NMHE). On an example problem with 33 states, 6 inputs and 15 estimation intervals execution times below 500 microseconds are reported for the QP underlying the NMHE. 1

Approche modulaire de l'optimisation des flux de puissance multi-sources et multi-clients, à visée temps réel

The energy systems describe a class of systems whose from structural and functional characteristics raise the problem of the energy distribution to satisfy the services in real time. The solution of this multi-objectives problem, namely energetic, is the energy management strategy, whose design is still an open problem. The solutions studied in this thesis are incorporated in the framework of an industrial partnership and particularly in those systemic design approaches. The first contribution is a methodology of modular and generic design of the energy management strategy, for the multi- clients and multi-sources systems. It defines two types of functional elements: the clients and the sources, interacting through a node, which is the carrier of thestrategy. The second contribution deals with thegeneric formulation of the strategy and itssimplification by means of decomposition in accordance with two problems: the hybridization of sources and the competition of clients, which a real ready known in the literature. The third contribution is partial to the selection of innovative or existing algorithms, which are compatible with a real-time target to execute the strategy. Finally, the energy strategy of a refrigerated truck with a hybrid energy architecture is designed by the proposed modular approach, and the algorithm feasibility is validated by the simulation.Les systèmes énergétiques désignent une classe de systèmes dont les spécificités structurelles et fonctionnelles posent la question de la distribution de l’énergie, en temps réel, pour satisfaire des services. Cette problématique multi-objectifs, nommée énergétique, a pour solution une stratégie de gestion,dont la conception représente un problème ouvert. Les verrous étudiés dans cette thèse s’inscrivent dans le cadre d’un partenariat industriel et en particulier celui des démarches de conception systémique. Trois contributions sont apportées. La première est une méthodologie de conception modulaire et générique de la stratégie énergétique, pour les systèmes multi-clients et multi-sources. Elle définit deux types d’éléments fonctionnels : les clients et les sources, interagissant par le biais d’un nœud, porteur de la stratégie. La seconde traite la simplification de la stratégie par une décomposition selon deux problématiques déjà connues de la littérature : l’hybridation de sources et la concurrence de clients. La troisième porte sur la sélection d’algorithmes novateurs ou existants, compatibles avec une cible temps réel, pour exécuter la stratégie. Enfin, la stratégie énergétique d’un camion frigorifique disposant d’une architecture énergétique hybride série est conçue par notre approche modulaire, et la faisabilité algorithmique est validée en simulation