Control Applications

Convergent Network Approximation for the Continuous Euclidean Length Constrained Minimum Cost Path Problem

  • Natashia Boland
  • Ranga Muhandiramge
  • Song Wang
    • Categories Control Applications, Network Optimization, Semi-infinite Programming

    In many path planning situations we would like to find a path of constrained Euclidean length in 2D that minimises a line integral. We call this the Continuous Length-Constrained Minimum Cost Path Problem (C-LCMCPP). Generally, this will be a non-convex optimization problem, for which continuous approaches only ensure locally optimal solutions. However, network discretisations yield … Read more

    Processor Speed Control with Thermal Constraints

  • David Atienza
  • Stephen Boyd
  • Giovanni De Micheli
  • Rajesh Gupta
  • Srinivasan Murali
  • Almir Mutapcic
    • Categories Control Applications, Optimization of Systems modeled by PDEs Tags , , , , ,

    We consider the problem of adjusting speeds of multiple computer processors sharing the same thermal environment, such as a chip or multi-chip package. We assume that the speed of processor (and associated variables, such as power supply voltage) can be controlled, and we model the dissipated power of a processor as a positive and strictly … Read more

    Local convergence for alternating and averaged nonconvex projections

  • Adrian Lewis
  • Jérôme Malick
  • Russell Luke
    • Categories Constrained Nonlinear Optimization, Control Applications, Nonsmooth Optimization Tags , , , , , , , ,

    The idea of a finite collection of closed sets having “strongly regular intersection” at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically, we consider the case of two sets, one of which we assume to be suitably “regular” (special cases being convex … Read more

    Constrained linear system with disturbance: stability under disturbance feedback

  • Chong-Jin Ong
  • Melvyn Sim
  • Chen Wang
    • Categories Control Applications, Robust Optimization Tags

    This paper proposes a control parametrization under Model Predictive Controller (MPC) framework for constrained linear discrete time systems with bounded additive disturbances. The proposed approach has the same feasible domain as that obtained from parametrization over the family of time-varying state feedback policies. In addition, the closed-loop system is stable in the sense that the … Read more

    An Adaptive Primal-Dual Warm-Start Technique for Quadratic Multiobjective Optimization

  • Jörg Fliege
    • Categories Control Applications, Multi-Criteria Optimization, Quadratic Programming Tags , , ,

    We present a new primal-dual algorithm for convex quadratic multicriteria optimization. The algorithm is able to adaptively refine the approximation to the set of efficient points by way of a warm-start interior-point scalarization approach. Results of this algorithm when applied on a three-criteria real-world power plant optimization problem are reported, thereby illustrating the feasibility of … Read more

    Selected Topics in Robust Convex Optimization

  • Aharon Ben-Tal
  • Arkadi Nemirovski
    • Categories Control Applications, Robust Optimization, Stochastic Programming Tags , , ,

    Robust Optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic “uncertain-but-bounded” data perturbations. In this paper, we overview several selected topics in this popular area, specifically, (1) recent extensions of the basic concept of {\sl robust counterpart} of an optimization problem with uncertain data, (2) tractability of robust counterparts, (3) links … Read more

    On Self-Regulated Swarms, Societal Memory, Speed and Dynamics

  • Carlos Fernandes
  • Vitorino Ramos
  • Agostinho C. Rosa
    • Categories Control Applications, Nonlinear Optimization, Stochastic Approaches Tags , , , ,

    Wasps, bees, ants and termites all make effective use of their environment and resources by displaying collective “swarm” intelligence. Termite colonies – for instance – build nests with a complexity far beyond the comprehension of the individual termite, while ant colonies dynamically allocate labor to various vital tasks such as foraging or defense without any … Read more

    On Time-Invariant Purified-Output-Based Discrete Time Control

  • Aharon Ben-Tal
  • Stephen Boyd
  • Arkadi Nemirovski
    • Categories Control Applications, Convex Optimization, Semi-definite Programming Tags , ,

    In http://www.optimizationonline.org/DB_HTML/2005/05/1136.html 05/25/05, we have demonstrated that the family of all affine non-anticipative output-based control laws in a discrete time linear dynamical system affected by uncertain disturbances is equivalent, as far as state-control trajectories are concerned, to the family of all affine non-anticipative “purified-output-based” control laws. The advantage of the latter representation of affine controls … Read more

    Efficient Robust Optimization for Robust Control with Constraints

  • Paul J. Goulart
  • Daniel Ralph
  • EC Kerrigan
    • Categories Control Applications, Robust Optimization Tags , , , , ,

    This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed polytopic constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques … Read more

    Nonlinear optimal control: Numerical approximations via moments and LMI-relaxations

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Christophe Prieur
    • Categories Control Applications, Systems governed by Differential Equations Optimization

    We consider the class of nonlinear optimal control problems with all data (differential equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of LMI-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Preliminary results show that good approximations are obtained with few moments. Citation LAAS … Read more