optimal control

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

    Improved Penalty Algorithm for Mixed Integer PDE Constrained Optimization (MIPDECO) Problems

  • Dominik Garmatter
  • Margherita Porcelli
  • Francesco Rinaldi
  • Martin Stoll
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Optimization of Systems modeled by PDEs Tags , , ,

    Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the Branch-and-Bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially … Read more

    Optimal Control of Differential Inclusions

  • Boris S. Mordukhovich
    • Categories Other Topics Tags , , , , ,

    This paper is devoted to optimal control of dynamical systems governed by differential inclusions in both frameworks of Lipschitz continuous and discontinuous velocity mappings. The latter framework mostly concerns a new class of optimal control problems described by various versions of the so-called sweeping/Moreau processes that are very challenging mathematically and highly important in applications … Read more

    Design, Implementation and Simulation of an MPC algorithm for Switched Nonlinear Systems under Combinatorial Constraints

  • Angelika Altmann-Dieses
  • Moritz Diehl
  • Sebastian Sager
  • Adrian Bürger
  • Clemens Zeile
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , , ,

    Within this work, we present a warm-started algorithm for Model Predictive Control (MPC) of switched nonlinear systems under combinatorial constraints based on Combinatorial Integral Approximation (CIA). To facilitate high-speed solutions, we introduce a preprocessing step for complexity reduction of CIA problems, and include this approach within a new toolbox for solution of CIA problems with … Read more

    Optimal switching sequence for switched linear systems

  • Qie He
  • Zeyang Wu
    • Categories Combinatorial Optimization, Control Applications, Dynamic Programming Tags , , , , ,

    We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n matrices and an n-dimensional vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the … Read more

    Variational Analysis and Optimization of Sweeping Processes with Controlled Moving Sets

  • Boris S. Mordukhovich
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    This paper briefly overviews some recent and very fresh results on a rather new class of dynamic optimization problems governed by the so-called sweeping (Moreau) processes with controlled moving sets. Uncontrolled sweeping processes have been known in dynamical systems and applications starting from 1970s while control problems for them have drawn attention of mathematicians, applied … Read more

    Moments and convex optimization for analysis and control of nonlinear partial differential equations

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Milan Korda
    • Categories Distributed Control, Optimization of Systems modeled by PDEs, Semi-definite Programming Tags , , , ,

    This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a \emph{linear} equation in the space of Borel measures. This equation is then used as a constraint of an infinite-dimensional linear programming problem (LP). This LP is … Read more

    Combinatorial Integral Approximation Decompositions for Mixed-Integer Optimal Control

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

    Solving mixed-integer nonlinear programs (MINLPs) is hard in theory and practice. Decomposing the nonlinear and the integer part seems promising from a computational point of view. In general, however, no bounds on the objective value gap can be guaranteed and iterative procedures with potentially many subproblems are necessary. The situation is different for mixed-integer optimal … Read more

    Combining Multi-Level Real-time Iterations of Nonlinear Model Predictive Control to Realize Squatting Motions on Leo

  • Christian Kirches
  • Ivan Koryakovskiy
  • Manuel Kudruss
  • Katja Mombaur
  • Heike Vallery
    • Categories Constrained Nonlinear Optimization, Control Applications, Nonlinear Systems and Least-Squares Tags , , , , ,

    Today’s humanoid robots are complex mechanical systems with many degrees of freedom that are built to achieve locomotion skills comparable to humans. In order to synthesize whole-body motions, real-tme capable direct methods of optimal control are a subject of contemporary research. To this end, Nonlinear Model Predictive Control is the method of choice to realize … Read more

    High-Level Interfaces for the Multiple Shooting Code for Optimal Control MUSCOD

  • Christian Kirches
  • Manuel Kudruss
  • Felix Lenders
    • Categories Modeling Languages and Systems, Optimization Software Design Principles, Problem Solving Environments Tags , , , ,

    The demand for model-based simulation and optimization solutions requires the availability of software frameworks that not only provide computational capabilities, but also help to ease the formulation and implementation of the respective optimal control problems. In this article, we present and discuss recent development efforts and applicable work flows using the example of MUSCOD, the … Read more