Doctoral seminars

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Friday, December 15, 16:00-17:00 inCelestijnenlaan 200 S00.05, 3001 Heverlee

Stabilisation of time-delay systems via nonsmooth optimisation

By: Joris Vanbiervliet, Scientific Computing Group, Department of Computerscience, K.U.Leuven

Abstract:

The stabilisation of time-delay systems with a finite number of free parameters is a problem that typically arises in the design of fixed-order controllers. As time-delay systems exhibit infinitely many characteristic roots, a full assignment of the spectrum is impossible. Most methods attempt to solve the stabilisation problem by trying to satisy a certain type of stabilisibility conditions. Because these conditions are in general sufficient, but not necessary, the system may however be stabilisible although the conditions cannot be satisfied.

Our approach is to directly minimise the real part of the rightmost characteristic root, or spectral abscissa, in function of the parameters to be tuned. Stabilisation is then achieved as soon as this objective function becomes negative. The spectral abscissa is in general a nonsmooth and nonconvex function, precluding the use of standard optimisation methods. Instead, we use a recently developed bundle gradient optimisation algorithm which has already been successfully applied to fixed-order controller design problems for systems of ordinary differential equations.

In dealing with systems of time-delay type, we extend the use of this algorithm to infinite-dimensional systems. This is realised by combining the optimisation method with advanced numerical algorithms to efficiently and accurately compute the rightmost characteristic roots of such time-delay systems. Furthermore, the optimisation procedure is adapted, enabling it to perform a local stabilisation along a branch of steady state solutions of a nonlinear discretised PDE system with a time-delay.