optimal control

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

    Matching Algorithms and Complexity Results for Constrained Mixed-Integer Optimal Control with Switching Costs

  • Felix Bestehorn
  • Christian Kirches
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms Tags , , , ,

    We extend recent work on the performance of the combinatorial integral approximation decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs) in the presence of combinatorial constraints or switching costs on an equidistant grid. For the time discretized problem, we reformulate the emerging rounding problem in the decomposition approach as a matching problem on a bipartite … Read more

    Global Dynamic Optimization with Hammerstein-Wiener Models Embedded

  • D. Bongartz
  • Alexander Mitsos
  • Jaromił Najman
  • C. D. Kappatou
  • S. Sass
    • Categories Global Optimization Theory Tags , , , ,

    Hammerstein-Wiener models constitute a significant class of block-structured dynamic models, as they approximate process nonlinearities on the basis of input-output data without requiring identification of a full nonlinear process model. Optimization problems with Hammerstein-Wiener models embedded are nonconvex, and thus local optimization methods may obtain suboptimal solutions. In this work, we develop a deterministic global … 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

    Enhancements to the DIDO© Optimal Control Toolbox

  • Isaac Ross
    • Categories Applications - Science and Engineering, Optimization Software and Modeling Systems, Optimization Software Design Principles Tags , , , ,

    In 2020, DIDO© turned 20! The software package emerged in 2001 as a basic, user-friendly MATLAB teaching tool to illustrate the various nuances of Pontryagin’s Principle but quickly rose to prominence in 2007 after NASA announced it had executed a globally optimal maneuver using DIDO. Since then, the toolbox has grown in applications well beyond … Read more

    Mixed-Integer Optimal Control Problems with switching costs: A shortest path approach

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms Tags , , , ,

    We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the … Read more

    Risk-Averse Optimal Control

  • Alois Pichler
  • Ruben Schlottter
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    In the context of multistage stochastic optimization, it is natural to consider nested risk measures, which originate by repeatedly composing risk measures, conditioned on realized observations. Starting from this discrete time setting, we extend the notion of nested risk measures to continuous time by adapting the risk levels in a time dependent manner. This time … Read more

    Generalized Gradients in Problems of Dynamic Optimization, Optimal Control, and Machine Learning

  • Vladimir I. Norkin
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , , , , , , ,

    In this work, nonconvex nonsmooth problems of dynamic optimization, optimal control in discrete time (including feedback control), and machine learning are considered from a common point of view. An analogy is observed between tasks of controlling discrete dynamic systems and training multilayer neural networks with nonsmooth target function and connections. Methods for calculating generalized gradients … Read more

    Mixed-Integer Optimal Control under Minimum Dwell Time Constraints

  • Nicolò Robuschi
  • Sebastian Sager
  • Clemens Zeile
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , , , ,

    Tailored mixed-integer optimal control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems by solving one continuous nonlinear program and one mixed-integer linear program. … Read more