Systems governed by Differential Equations Optimization

Time-Domain Decomposition for Mixed-Integer Optimal Control Problems

  • Falk M. Hante
  • Richard Krug
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , ,

    We consider mixed-integer optimal control problems, whose optimality conditions involve global combinatorial optimization aspects for the corresponding Hamiltonian pointwise in time. We propose a time-domain decomposition, which makes this problem class accessible for mixed-integer programming using parallel-in-time direct discretizations. The approach is based on a decomposition of the optimality system and the interpretation of the … Read more

    Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems with Mixed Two-Point Boundary Conditions

  • Richard Krug
  • Günter Leugering
  • Martin Schmidt
  • Dieter Weninger
  • Alexander Martin
    • Categories Systems governed by Differential Equations Optimization Tags , , , ,

    In this article, we continue our work (Krug et al., 2021) on time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations in that we now consider mixed two-point boundary value problems and provide an in-depth well-posedness analysis. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems … Read more

    Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems

  • Richard Krug
  • Günter Leugering
  • Martin Schmidt
  • Dieter Weninger
  • Alexander Martin
    • Categories Systems governed by Differential Equations Optimization Tags , , , ,

    In this article, we extend the time-domain decomposition method described by Lagnese and Leugering (2003) to semilinear optimal control problems for hyperbolic balance laws with spatio-temporal varying coefficients. We provide the design of the iterative method applied to the global first-order optimality system, prove its convergence, and derive an a posteriori error estimate. The analysis … Read more

    Learning Dynamical Systems with Side Information

  • Amir Ali Ahmadi
  • Bachir El Khadir
    • Categories Convex Optimization, Semi-definite Programming, Systems governed by Differential Equations Optimization Tags , , ,

    We present a mathematical and computational framework for the problem of learning a dynamical system from noisy observations of a few trajectories and subject to side information. Side information is any knowledge we might have about the dynamical system we would like to learn besides trajectory data. It is typically inferred from domain-specific knowledge or … Read more

    KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

  • Drew P. Kouri
  • Denis Ridzal
  • Ray Tuminaro
    • Categories Control Applications, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the … Read more

    Mixed-Integer Optimal Control for Multimodal Chromatography

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Potschka
  • Dominik H. Cebulla
    • Categories (Mixed) Integer Nonlinear Programming, Chemical Engineering, Systems governed by Differential Equations Optimization Tags , , ,

    Multimodal chromatography is a powerful tool in the downstream processing of biopharmaceuticals. To fully benefit from this technology, an efficient process strategy must be determined beforehand. To facilitate this task, we employ a recent mechanistic model for multimodal chromatography, which takes salt concentration and pH into account, and we present a mathematical framework for the … Read more

    A Personalized Switched Systems Approach for the Optimal Control of Ventricular Assist Devices based on Atrioventricular Plane Displacement

  • Rüdiger C. Braun-Dullaeus
  • Sebastian Sager
  • Jeremi Kaj Mizerski
  • Thomas Rauwolf
  • Alexander Schmeisser
  • Clemens Zeile
    • Categories Biomedical Applications, Control Applications, Systems governed by Differential Equations Optimization Tags , , ,

    Objective: A promising treatment for congestive heart failure is the implementation of a left ventricular assist device (LVAD) that works as a mechanical pump. Modern LVADs work with adjustable constant rotor speed and provide therefore continuous blood flow; however, recently undertaken efforts try to mimic pulsatile blood flow by oscillating the pump speed. This work … Read more

    A numerical study of transformed mixed-integer optimal control problems

  • Sebastian Sager
  • Manuel Tetschke
  • Clemens Zeile
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Systems governed by Differential Equations Optimization Tags , , , ,

    Time transformation is a ubiquitous tool in theoretical sciences, especially in physics. It can also be used to transform switched optimal con trol problems into control problems with a fixed switching order and purely continuous decisions. This approach is known either as enhanced time transformation, time-scaling, or switching time optimization (STO) for mixed-integer optimal control. … Read more

    Binary Optimal Control by Trust-Region Steepest Descent

  • Mirko Hahn
  • Sven Leyffer
  • Sebastian Sager
    • Categories Distributed Control, Integer Programming, Systems governed by Differential Equations Optimization Tags , ,

    We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control function as an indicator function of a measurable set and makes set-valued adjustments derived from the sublevel sets of a topological gradient function. By combining this type of update with a trust-region framework, … Read more

    Inversion of Convection-Diffusion Equation with Discrete Sources

  • Mirko Hahn
  • Sven Leyffer
  • Bart van Bloemen Waanders
  • Lars Ruthotto
  • Meenarli Sharma
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization

    We present a convection-diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formulated as a large-scale mixed-integer nonlinear optimization problem. We show empirically that current state-of-the-art mixed-integer solvers cannot solve this problem … Read more