Since W > 0 and Q > 0 this is a convex quadratic program in z parameterized by p. Convexity guarantees that a global solution can be found. The optimal solution z*(p) is a continuous piecewise linear function z*(p) defined on any subset,

of the parameter space. Moreover, an exact representation of this piecewise linear function can be computed off-line using multi-parametric QP algorithms (T0ndel and Johansen, 2003b) or the Matlab Multi-Parametric Toolbox (MPT) by Kvasnica, Grieder and Baotic (2004). Consequently, it is not necessary to solve the QP (1.36) in real time for the current value of T and the parameters fmin, fmax and ยก3 , if they are allowed to vary.

In fact it suffices to evaluate the known piecewise linear function z*(p) as a function of the given parameter vector p which can be done efficient with a small amount of computations. For details on the implementation aspects of the mp-QP algorithm; see Johansen et al. (2003) and references therein. An on-line control allocation algorithm is presented in T0ndel et al. (2003a).

Learn Photoshop Now

Learn Photoshop Now

This first volume will guide you through the basics of Photoshop. Well start at the beginning and slowly be working our way through to the more advanced stuff but dont worry its all aimed at the total newbie.

Get My Free Ebook

Post a comment