Optimisation quadratique successive

L'optimisation quadratique successive est un algorithme de résolution d'un problème d'optimisation non linéaire. Un tel problème consiste à déterminer des paramètres qui minimisent une fonction, tout en respectant des contraintes d'égalité et d'inégalité sur ces paramètres. On parle aussi de l'algorithme OQS pour Optimisation Quadratique Successive ou de l'algorithme SQP pour Sequential Quadratic Programming, en anglais. C'est un algorithme newtonien appliqué aux conditions d'optimalité du premier ordre du problème. Plus précisément, on peut le voir comme un algorithme de Josephy-Newton appliqué à ces conditions d'optimalité, écrites comme un problème d'inclusion fonctionnelle ou comme un problème de complémentarité. De ce fait, l'algorithme bénéficie d'une convergence locale rapide, mais chaque itération pourra demander beaucoup de temps de calcul (c'est surtout vrai dans les premières itérations). Par ailleurs, l'algorithme ne fait pas de distinction entre minima et maxima (comme l'

Decentralized in-order execution of a sequential task-based code for shared-memory architectures

Charly Nicolas Lucien Castes

The hardware complexity of modern machines makes the design of adequate programming models crucial for jointly ensuring performance, portability, and productivity in high-performance computing (HPC). Sequential task-based programming models paired with advanced runtime systems allow the programmer to write a sequential algorithm independently of the hardware architecture in a productive and portable manner, and let a third party software layer -the runtime system- deal with the burden of scheduling a correct, parallel execution of that algorithm to ensure performance. Many HPC algorithms have successfully been implemented following this paradigm, as a testimony of its effectiveness. Developing algorithms that specifically require fine-grained tasks along this model is still considered prohibitive, however, due to per-task management overhead [1], forcing the programmer to resort to a less abstract, and hence more complex "task+X" model. We thus investigate the possibility to offer a tailored execution model, trading dynamic mapping for efficiency by using a decentralized, conservative in-order execution of the task flow, while preserving the benefits of relying on the sequential taskbased programming model. We propose a formal specification of the execution model as well as a prototype implementation, which we assess on a shared-memory multicore architecture with several synthetic workloads. The results show that under the condition of a proper task mapping supplied by the programmer, the pressure on the runtime system is significantly reduced and the execution of fine-grained task flows is much more efficient.

IEEE COMPUTER SOC2022

Real-Time Nonlinear Model Predictive Control for Fast Mechatronic Systems

Petr Listov

This thesis presents an efficient and extensible numerical software framework for real-time model-based control. We are motivated by complex and challenging mechatronic applications spanning from flight control of fixed-wing aircraft and thrust vector control drones to autonomous driving.In the first part, we present PolyMPC, a novel C++ software framework for real-time embedded nonlinear optimal control and optimisation. A key feature of the package is a highly optimised implementation of the pseudospectral collocation method that exploits instruction set parallelism available on many modern computer architectures. Polynomial representation of the state and control trajectories allows the tool to be used as a standalone controller and as an efficient solver for low-level tracking controllers in hierarchical schemes. Algorithmically, the choice is made towards computational speed. For nonlinear problems, we combine a sequential quadratic programming (SQP) strategy with the alternating direction method of multipliers (ADMM) for quadratic programs (QP), which is especially favourable for embedded applications thanks to the low computational cost per iteration.In the second part, the developed numerical methods and software are used to experimentally study optimisation-based control of airborne wind energy (AWE) systems. For this purpose, we designed and built a small-scale prototype of a single-line rigid-wing AWE kite which comprises an aircraft fitted with necessary sensors and computers and a fully autonomous ground station for tether control. The prototype serves as a research platform for studying flight navigation and control systems thanks to very flexible custom mission management and control software. We further develop a dynamic optimisation based methodology for parameter identification and provide a validated flight simulator that matches well the real behaviour of the system. Finally, a model-predictive path following flight controller is designed and tested in real-world experiments.The third part of the thesis is concerned with the application of real-time nonlinear model predictive control (NMPC) to autonomous driving at the limits of handling, which requires high sampling rates and robustness of the motion control system. We propose a dynamic optimization-based hierarchical framework for the local refinement of the racing lines that takes into account the nonlinear vehicle and actuator dynamics, adaptive tyre constraints, and the safety corridor around the initial path. The top layer receives a discrete obstacle-free local path computed by a coarse planner and transforms it into auto-differentiable look-up tables (LUT) for efficient continuous sampling.Separately, we investigated the problem of safe trajectory planning under parametric model uncertainties motivated by automotive applications. We use generalised polynomial chaos expansions for efficient nonlinear uncertainty propagation and distributionally robust inequalities for chance constraint approximation. Inspired by tube-based model predictive control, an ancillary feedback controller is used to control the deviations of stochastic modes from the nominal solution, and therefore, decrease the variance. Our approach reduces conservatism related to nonlinear uncertainty propagation while guaranteeing constraint satisfaction with a high probability.

EPFL2022

Performance Comparison of Alternating Direction Optimization Methods for Linear-OPF based Real-time Predictive Control

Rahul Kumar Gupta, Mario Paolone, Fabrizio Sossan, Vladimir Sovljanski

The paper contributes to improving the computational performance of controls of distributed energy resources (DERs) in distribution grids for efficient real-time control and short-term scheduling. The considered setting is a distribution grid with heterogeneous DERs controlled with model predictive control (MPC) to track a dispatch plan at its grid connection point (GCP) subject to DERs’ and grid’s constraints. The MPC control is first expressed as a quadratic programming (using linearized grid models) and, then, solved with several state-of-the-art alternating direction optimization methods: AMA, ADMM, AADMM (ADMM with adaptive penalty parameter) and their accelerated variants: FAMA, FAADMM, and FAADMM with restart rule. Performance is tested in terms of computational performance, constraints satisfaction, and optimality against the centralized MPC. The case studies are the CIGRE and IEEE benchmark grid for low- and medium voltage systems hosting different numbers of controllable DERs.

IEEE2021

Real-Time Nonlinear Model Predictive Control for Fast Mechatronic Systems

Petr Listov

EPFL2022