Robust Control via Sequential Semidefinite Programming

Abstract

Multi-objective H ∞ /H ∞ -synthesis with structured control laws is discussed and used as a means to enhance robustness of the system in the presence of real parametric uncertainty.

Local and superlinear convergence of a primal-dual interior point method for nonlinear semidefinite programming

“…Thus, by using the operator svec and the symmetrized Kronecker product, the Newton equations (7)(8)(9) are represented by the form…”

“…Kocvara and Stingl also developed a computer code PENNON. Fares, Noll and Apkarian [7], Correa and Ramirez [5], Freund, Jarre and Vogelbusch [8] dealt with algorithms which used the sequential linear SDP method. Kanzow, Nagel, Kato and Fukushima [10] presented a successive linearization method with a trust region-type globalization strategy.…”

“…However, in our knowledge, there are few researches on local behavior of interior point methods for nonlinear SDP problems. Existing literatures on local convergence properties include [7] and [8] for the superlinear and quadratic convergence properties of SQP type methods, and Sun, Sun and Zhang [24] for the linear convergence property of the augmented Lagrangian method. Stingl [22] also discussed the local behavior of the augmented Lagrangian method.…”

A successive SDP-NSDP approach to a robust optimization problem in finance

“…To our knowledge, there only exist some specialized solvers for particular NSDPs (see e.g. SLMSDP [17], PENBMI [18], IPCTR [23][24][25], SSDP [8]). On the other hand, for the solution of linear SDPs and SOCPs a lot of solvers are freely available over the Internet (e.g.…”

Second-Order Nonsmooth Optimization for H Synthesis

“…In response, various new design methods have been proposed since the late 1990s, including methods from global optimization [6,7,34,37], matrix inequality constrained nonlinear programming [5,14,24,25,36], augmented Lagrangian methods [13,30], eigenvalue optimization [1][2][3]19], and others. Presently we discuss a new strategy for H ∞ output feedback control synthesis, which has several advantages over existing approaches, because it avoids the use of Lyapunov variables.…”