arXiv subjects

Morten Wahlgreen Kaysfeld

Publications and source records attributed to Morten Wahlgreen Kaysfeld.

3 recordsLinked to original sources

arXiv2024

Numerical Discretization Methods for the Extended Linear Quadratic Control Problem

In this study, we introduce numerical methods for discretizing continuous-time linear-quadratic optimal control problems (LQ-OCPs). The discretization of continuous-time LQ-OCPs is formulated into differential equation systems, and we can obtain the discrete equivalent by solving these systems. We present the ordinary differential equation (ODE), matrix exponential, and a novel step-doubling method for the discretization of LQ-OCPs. Utilizing Euler-Maruyama discretization with a fine step, we reformulate the costs of continuous-time stochastic LQ-OCPs into a quadratic form, and show that the stochastic cost follows the $χ^2$ distribution. In the numerical experiment, we test and compare the proposed numerical methods. The results ensure that the discrete-time LQ-OCP derived using the proposed numerical methods is equivalent to the original problem.

eess.SY↗

arXiv2023

Performance Quantification of a Nonlinear Model Predictive Controller by Parallel Monte Carlo Simulations of a Closed-loop System

This paper presents a parallel Monte Carlo simulation based performance quantification method for nonlinear model predictive control (NMPC) in closed-loop. The method provides distributions for the controller performance in stochastic systems enabling performance quantification. We perform high-performance Monte Carlo simulations in C enabled by a new thread-safe NMPC implementation in combination with an existing high-performance Monte Carlo simulation toolbox in C. We express the NMPC regulator as an optimal control problem (OCP), which we solve with the new thread-safe sequential quadratic programming software NLPSQP. Our results show almost linear scale-up for the NMPC closed-loop on a 32 core CPU. In particular, we get approximately 27 times speed-up on 32 cores. We demonstrate the performance quantification method on a simple continuous stirred tank reactor (CSTR), where we perform 30,000 closed-loop simulations with both an NMPC and a reference proportional-integral (PI) controller. Performance quantification of the stochastic closed-loop system shows that the NMPC outperforms the PI controller in both mean and variance.

eess.SY↗

arXiv2023

Dynamic Optimization for Monoclonal Antibody Production

This paper presents a dynamic optimization numerical case study for Monoclonal Antibody (mAb) production. The fermentation is conducted in a continuous perfusion reactor. We represent the existing model in terms of a general modeling methodology well-suited for simulation and optimization. The model consists of six ordinary differential equations (ODEs) for the non-constant volume and the five components in the reactor. We extend the model with a glucose inhibition term to make the model feasible for optimization case studies. We formulate an optimization problem in terms of an optimal control problem (OCP) and consider four different setups for optimization. Compared to the base case, the optimal operation of the perfusion reactor increases the mAb yield with 44% when samples are taken from the reactor and with 52% without sampling. Additionally, our results show that multiple optimal feeding trajectories exist and that full glucose utilization can be forced without loss of mAb formation.

math.OC↗