Control Applications

Approximate Maximum Principle for Discrete Approximations of Optimal Control Systems with Nonsmooth Objectives and Endpoint Constraints

  • Boris S. Mordukhovich
  • Ilya Shvartsman
    • Categories Control Applications, Convex and Nonsmooth Optimization Tags , , ,

    The paper studies discrete/finite-difference approximations of optimal control problems governed by continuous-time dynamical systems with endpoint constraints. Finite-difference systems, considered as parametric control problems with the decreasing step of discretization, occupy an intermediate position between continuous-time and discrete-time (with fixed steps) control processes and play a significant role in both qualitative and numerical aspects of … Read more

    Sensitivity analysis for the outages of nuclear power plants

  • Kengy Barty
  • Joseph Frédéric Bonnans
  • Laurent Pfeiffer
    • Categories Control Applications Tags , , ,

    Nuclear power plants must be regularly shut down in order to perform refueling and maintenance operations. The scheduling of the outages is the first problem to be solved in electricity production management. It is a hard combinatorial problem for which an exact solving is impossible. Our approach consists in modelling the problem by a two-level … Read more

    Bundle method for non-convex minimization with inexact subgradients and function values

  • Dominikus Noll
    • Categories Control Applications, Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

    We discuss a bundle method to minimize non-smooth and non-convex locally Lipschitz functions. We analyze situations where only inexact subgradients or function values are available. For suitable classes of non-smooth functions we prove convergence of our algorithm to approximate critical points. CitationTo appear in: Computational and Analytical Mathematics. Springer Proceedings in MathematicsArticleDownload View PDF

    Constraint Reduction with Exact Penalization for Model-Predictive Rotorcraft Control

  • Aaron L. Greenfield
  • Meiyun Y. He
  • Vineet Sahasrabudhe
  • André L. Tits
    • Categories Applications - Science and Engineering, Control Applications, Quadratic Programming Tags , , , , , , , , ,

    Model Predictive Control (also known as Receding Horizon Control (RHC)) has been highly successful in process control applications. Its use for aerospace applications has been hindered by its high computational requirements. In the present paper, we propose using enhanced primal-dual interior-point optimization techniques in the convex-quadratic-program-based RHC control of a rotorcraft. Our enhancements include a … Read more

    Algebraic Relaxations and Hardness Results in Polynomial Optimization and Lyapunov Analysis

  • Amir Ali Ahmadi
    • Categories Control Applications, Convex Optimization, Semi-definite Programming Tags , , , , ,

    The contributions of the first half of this thesis are on the computational and algebraic aspects of convexity in polynomial optimization. We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves … Read more

    Optimizing the Spectral Radius

  • Yurii Nesterov
  • Vladimir Protasov
    • Categories Control Applications Tags , , ,

    We suggest an approach for finding the maximal and the minimal spectral radius of linear operators from a given compact family of operators, which share a common invariant cone (e.g. for a family of nonnegative matrices). In case of families with so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and … Read more

    On the Difficulty of Deciding Asymptotic Stability of Cubic Homogeneous Vector Fields

  • Amir Ali Ahmadi
    • Categories Control Applications, Semi-definite Programming, Systems governed by Differential Equations Optimization Tags , ,

    It is well-known that asymptotic stability (AS) of homogeneous polynomial vector fields of degree one (i.e., linear systems) can be decided in polynomial time e.g. by searching for a quadratic Lyapunov function. Since homogeneous vector fields of even degree can never be AS, the next interesting degree to consider is equal to three. In this … Read more

    Joint Spectral Radius and Path-Complete Graph Lyapunov Functions

  • Amir Ali Ahmadi
  • Raphaël Jungers
  • Pablo A. Parrilo
  • Mardavij Roozbehani
    • Categories Approximation Algorithms, Control Applications, Semi-definite Programming Tags , , , , ,

    We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of … Read more

    Joint Spectral Radius and Path-Complete Graph Lyapunov Functions

  • Amir Ali Ahmadi
    • Categories Approximation Algorithms, Control Applications, Semi-definite Programming Tags , , , , ,

    We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of … Read more