Systems governed by Differential Equations Optimization

Experimental operation of a solar-driven climate system with thermal energy storages using mixed-integer nonlinear MPC

  • Adrian Bürger
  • Daniel Bull
  • Parantapa Sawant
  • Markus Bohlayer
  • Angelika Altmann-Dieses
  • Marco Braun
  • Moritz Diehl
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Systems governed by Differential Equations Optimization Tags , , , ,

    This work presents the results of experimental operation of a solar-driven climate system using mixed-integer nonlinear Model Predictive Control (MPC). The system is installed in a university building and consists of two solar thermal collector fields, an adsorption cooling machine with different operation modes, a stratified hot water storage with multiple inlets and outlets as … Read more

    Proximal Method for $\ell_0- based Sparse Enhanced Control Problems in Large-scale Interconnected Systems

  • Wah June Leong
  • Hong Seng Sim
  • Kok Lay Teo
  • Changzhi Wu
    • Categories Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization

    This paper considers linear quadratic optimal control problem of large-scale interconnected systems. An algorithmic framework is constructed to design controllers that provide a desired tradeoff between the system performance and the sparsity of the static feedback matrix. This is accomplished by introducing a minimization problem involving $\ell_0-$norm of the feedback matrix subject to a maximum … Read more

    Nonlinear Optimization of District Heating Networks

  • Richard Krug
  • Volker Mehrmann
  • Martin Schmidt
    • Categories Applications - Science and Engineering, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , , ,

    We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic 1d partial differential equations. In addition, a pooling-type mixing model is required at the nodes of the network to treat the mixing … Read more

    Dynamic Optimization with Complementarity Constraints: Smoothing for Direct Shooting

  • Lorenz T. Biegler
  • Adrian Caspari
  • Alexander Mitsos
  • Pascal Schäfer
  • Lukas Lüken
  • Adel Mhamdi
  • Yannic Vaupel
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    We consider optimization of differential-algebraic equations (DAEs) with complementarity constraints (CCs) of algebraic state pairs. Formulating the CCs as smoothed nonlinear complementarity problem (NCP) functions leads to a smooth DAE, allowing for the solution in direct shooting. We provide sufficient conditions for well-posedness. Thus, we can prove that with the smoothing parameter going to zero, … 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

    Multiphase Mixed-Integer Nonlinear Optimal Control of Hybrid Electric Vehicles

  • Francesco Braghin
  • Nicolò Robuschi
  • Sebastian Sager
  • Federico Cheli
  • Clemens Zeile
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Systems governed by Differential Equations Optimization

    This paper considers the problem of computing the non-causal minimum-fuel energy management strategy of a hybrid electric vehicle on a given driving cycle. Specifically, we address the multiphase mixed-integer nonlinear optimal control problem arising when optimal gear choice, torque split and engine on/off controls are sought in off-line evaluations. We propose an efficient model by … Read more

    RaBVItG:An Algorithm for Solving a Class of Multi-Players Feedback Nash Differential Games

  • Jorge Herrera de la Cruz
  • Benjamin Ivorra
  • Ángel M. Ramos
    • Categories Systems governed by Differential Equations Optimization Tags , ,

    In this work, we introduce a novel numerical algorithm, called RaBVItG (Radial Basis Value Iteration Game) to approximate feedback-Nash equilibria for deterministic differential games. More precisely, RaBVItG is an algorithm based on value iteration schemes in a meshfree context. It is used to approximate optimal feedback Nash policies for multi-players, trying to tackle the dimensionality … Read more

    Planning for Dynamics under Uncertainty

  • Dicong Qiu
  • Karsh Tharyani
    • Categories Dynamic Programming, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , ,

    Planning under uncertainty is a frequently encountered problem. Noisy observation is a typical situation that introduces uncertainty. Such a problem can be formulated as a Partially Observable Markov Decision Process (POMDP). However, solving a POMDP is nontrivial and can be computationally expensive in continuous state, action, observation and latent state space. Through this work, we … Read more

    A switching cost aware rounding method for relaxations of mixed-integer optimal control problems

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags ,

    This article investigates a class of Mixed-Integer Optimal Control Problems (MIOCPs) with switching costs. We introduce the problem class of Minimal-Switching-Cost Optimal Control Problems (MSCP) with an objective function that consists of two summands, a continuous term depending on the state vector and an encoding of the discrete switching costs. State vectors of Mixed-Integer Optimal … Read more

    Convergence of Finite-Dimensional Approximations for Mixed-Integer Optimization with Differential Equations

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

    We consider a direct approach to solve mixed-integer nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach … Read more