4 Presentations

• 
  10:30 AM - 10:55 AM

  A New Approach to Analysis of the Cucker-Smale Continuous Time Model

  • Sadegh Bolouki, presenter, GERAD, Polytechnique Montréal
  • Roland Malhamé, GERAD - Polytechnique Montréal

  The Cucker-Smale continuous time model describing dynamics of a multi agent system is presented. It is shown that, under certain conditions, agents converge to a consensus, i.e., agents' velocities converge to the same limit. The comparison between the sufficient condition derived here for consensus and the one derived by Cucker and Smale is done.

• 
  10:55 AM - 11:20 AM

  Hybrid Optimal Control On Riemannian Manifolds and Geometric Optimization Algorithms

  • Farzin Taringoo, presenter, McGill University
  • Peter Caines, GERAD - McGill University

  This paper provides Newton Geodesic algorithm for the optimization of autonomous hybrid systems based on the geometrical properties of switching manifolds. The first and second sections of the paper introduce optimal hybrid control systems and the third section deals with the analysis of the Hybrid Maximum Principle (HMP) algorithm introduced in [1].
  The HMP algorithm in [1] is then extended to a geometrical algorithm by employing the notion of Hessian geodesic curves on switching manifolds. The convergence analysis for the proposed algorithm is based on Lasalle Theory.

  [1] M.S. Shaikh and P.E. Caines ''On the Hybrid Optimal Control Problems: Theory and Algorithms'', IEEE Trans Automatic Control, Vol. 52, No. 9, pp. 1587-1603, Sep 2007. Corrigendum: Vol. 54. No. 6, June, 2009, p 1428

• 
  11:20 AM - 11:45 AM

  The Approximative Solution for Singular Integro-Differential Equations

  • Iurie Caraus, presenter, Moldova State University

  We have elaborated the numerical schemes of collocation method and mechanical quadrature method for approximate solution of singular integro- differential equations with kernels of Cauchy type. The equations are defined on the arbitrary smooth closed contour of complex plane. The researched methods are based on discretization by Fejer points. Theoretical background of collocation method and mechanical quadrature method has been obtained in classical Holder spaces.

• 
  11:45 AM - 12:10 PM

  Optimisation of Hybrid Thermodynamic Control Systems with Phase Transitions

  • Dmitry Gromov, presenter, McGill University
  • Peter Caines, GERAD - McGill University

  In this contribution, a systematic approach to the modelling of thermodynamic systems with phase transitions is presented. It is shown that the dynamics of these systems can be adequately represented within the regional hybrid systems framework. This means that the discrete state changes autonomously at fixed submanifold boundaries. Furthermore, we assume that in each single phase the system's dynamics can be described in terms of equilibrium thermodynamics. This allows for the application of well developed methods from contact geometry. The minimisation of entropy plays a central role in all processes involving energy transformation and storage. So for this class of systems, there is a natural optimal control problem, namely that where the increase of entropy is used as a criterion to be minimised. To illustrate these ideas a hybrid model of a simple thermodynamic system with a liquid-vapour phase transition is presented; the system-theoretic properties of this model are analysed and a hybrid optimal control problem is formulated.