Invited Session Tue.1.H 0112

Tuesday, 10:30 - 12:00 h, Room: H 0112

Cluster 16: Nonlinear programming [...]

Real-time optimization I


Chair: Victor M. Zavala and Sebastian Sager



Tuesday, 10:30 - 10:55 h, Room: H 0112, Talk 1

Hans Joachim Ferreau
The ACADO code generation tool for high-speed model predictive control and moving horizon estimation

Coauthors: Moritz Diehl, Rien Quirynen, Milan Vukov


Model predictive control (MPC) is an advanced feedback control strategy that predicts and optimises the future behaviour of a dynamic system in real-time. This requires full knowledge of the current system state, which typically needs to be estimated from noisy measurements, e.g., by means of moving horizon estimation (MHE). Both MPC and MHE require to solve a constrained, nonlinear optimisation problem in real-time, possibly on slow embedded hardware. The recently proposed ACADO Code Generation tool allows the user to automatically export nonlinear real-time iteration algorithms that are customised based on a symbolic MPC/MHE problem formulation. This talk presents major algorithmic extensions of this tool: First, it now also handles dynamic systems described by differential algebraic equations. Second, not only explicit but also implicit Runge-Kutta integrators can be exported now. Third, auto-generated sparse quadratic programming solvers have been added for speeding-up solution in case of long prediction horizons. We illustrate the efficiency of the exported MPC/MHE algorithms by controlling small-scale but challenging nonlinear systems at sampling times of a few milliseconds.



Tuesday, 11:00 - 11:25 h, Room: H 0112, Talk 2

Janick Frasch
Fast mixed-level iteration schemes for nonlinear model predictive control on multicore architectures

Coauthors: Hans-Georg Bock, Sebastian Sager, Leonard Wirsching


Nonlinear model predictive control (MPC) algorithms generally require the (approximate) solution of a nonlinear program (NLP) at each sampling time for feedback generation. Providing sufficiently high feedback rates therefore poses a major computational challenge for systems with fast dynamics. Recent approaches to overcome this challenge extend the multiple shooting-based real-time iteration scheme to multi-level iteration schemes. These algorithms generate feedback by repeatedly solving a quadratic program (QP), updating its data parts - constraint residuals, gradients, and Hessians and constraint Jacobians of the NLP - on three levels of increasing computational complexity.
In this contribution we consider mixed-level updates of the QP data, which intervalwise apply different update levels. In particular we apply higher-level updates more frequently on the first intervals of the control horizon, given their importance in the MPC context. Targeting at modern computers with multi-core processing units, we describe an efficient parallel implementation of the mixed-level iteration approach and apply it to a benchmark problem from automotive engineering.



Tuesday, 11:30 - 11:55 h, Room: H 0112, Talk 3

Moritz Diehl
Real-time optimization of large distributed systems

Coauthors: Hans Joachim Ferreau, Attila Kozma


When large interconnected systems shall be optimally operated using model-based optimization,
it is desirable to have parallelism in the used algorithms as well as decentralized decision making.
As decentralized decision making with only vector exchanges leads to
extremely slow linear or even sublinear convergence rates to the centrally optimal solution, we focus on parallelism
with decentralized data storage, but coordinated decision making.
In particular, we discuss the distributed multiple shooting (DMS) method that allows one to decompose
large-scale optimal control problems in both space and time and
to completely parallelize the expensive function and derivative generation in shooting methods.
Due to their superior warm starting capabilities in the real-time context,
we focus on SQP type methods. Here, the QP solution is the only part of the algorithm that is not trivial to distribute, and we
discuss several strategies for distributed QP solution and compare their convergence properties and
warm starting capabilities.


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