Multiobjective Robust Control via Youla Parametrization

Abstract

Using Youla Parametrization and Linear Matrix Inequalities (LMI) a Multiobjective Robust Control (MRC) design for continuous linear time invariant (LTI) systems with bounded uncertainties is described. The design objectives can be a combination of H ∞-, H2-performances, constraints on the control signal, etc.. Based on an initial stabilizing controller all stabilizing controllers for the uncertain system can be described by the Youla parametrization. Given this representation, all objectives can be formulated by independent Lyapunov functions, increasing the degree of freedom for the control design.

Structured linear fractional parametric controller H<inf>∞</inf> design and its applications

“…Let first define the integral operator and K ∈ R n K n∆nu×n K n∆ny matrix as : With reference to the loop of the above code, the first line corresponds to the evaluation of the ∆ block at p j , the second, to the evaluation of K(s, p j ) and the third/fourth to the concatenation of the F l (T(s, p j ), F u (F u K, 1 s I n K ), ∆ j )) in the structure Ttot. Note also that Klfj*Wk is added to ensure controller stability and a given roll off dictated by W K , as in (12). Finally, the above problem is solved through the hinfstruct function as: [Kopt,gamma,info] = hinfstruct(Ttot); This leads to the K matrix which cans then be used to construct K(s, p) easily.…”

“…To be complete, a stability (and bandwidth) constrain is also added to the problem with W K = 10 −1 s/100+1 , in (12). Then, the procedure exposed in Section 2 is applied for L = {10, 12.5, 15, 17.5, 20} (i.e.…”

“…Moreover, the Youla parametrization also provides a framework to this aim (see e.g. [12] for more details). For additional information on theses subjects, reader is invited to refer to the many results of e.g.…”

Robust H∞ Controller Design for Aircraft Lateral Dynamics using Multi-objective Optimization and Genetic Algorithms

“…To solve the mixed H 2 /H ∞ control problem two different approaches have been used; the first one uses the Youla parameterization of the controller (Scherer 1995, Neering et al 2006 and the second one (Scherer et al, 1997) introduces a dependence in the objectives, making the optimization a single objective problem. Based on the former approach some authors have looked for a way to further optimize their controller; for example, (Feng et.…”