By Laurent El Ghaoui, Silviu-Iulian Niculescu
Linear matrix inequalities (LMIs) have lately emerged as worthwhile instruments for fixing a few keep an eye on difficulties. This ebook offers an up to date account of the LMI process and covers themes akin to contemporary LMI algorithms, research and synthesis matters, nonconvex difficulties, and functions. It additionally emphasizes functions of the strategy to parts except regulate.
The easy inspiration of the LMI technique up to the mark is to approximate a given keep an eye on challenge through an optimization challenge with linear goal and so-called LMI constraints. The LMI procedure results in an effective numerical resolution and is very fitted to difficulties with doubtful information and a number of (possibly conflicting) necessities.
Since the early Nineties, with the improvement of interior-point equipment for fixing LMI difficulties, the LMI procedure has received elevated curiosity. One good thing about this system is its skill to deal with huge sessions of regulate difficulties through effective numerical instruments. This strategy is largely appropriate, not just on top of things yet additionally in different parts the place uncertainty arises. LMI recommendations offer a universal language for plenty of engineering difficulties. Notions now renowned in keep watch over, reminiscent of uncertainty and robustness, are getting used in different parts by using LMIs. this method is very beautiful for commercial purposes. it really is like minded for the improvement of CAD instruments that aid engineers remedy research and synthesis difficulties.
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Extra resources for Advances in linear matrix inequality methods in control
8 explores some perspectives and challenges that lie ahead. 1 Decision problems with uncertain data Decision problems Many engineering analysis and design problems can be seen as decision problems. In control engineering, one must decide which controller gains to choose in order to satisfy the desired specifications. This decision involves several trade-offs. ). 3) minimize /o(x) subject to x € #, fi(x) < 0, i = 1,... , fp are given scalar-valued functions of the decision vector x G Rm, and X is a subset of R m .
2 Interval calculus A basic problem in interval computations is the following. We are given a function f from R/ to Rm and a set confidence V for 6 € R* in the form of a product of intervals.
1 LMIs in combinatorial optimization SDPs are now recognized as yielding very efficient relaxations for (hard) combinatorial problems . 4. ) In turn, the SDP relaxations open up interesting perspectives for handling combinatorial problems with uncertain data, in view of the tools developed for the robust SDP. We illustrate this via a simple example. Consider the NP-hard problem where W is a given symmetric matrix. When W assumes some special structure, the above problem is known in the combinatorial optimization literature as "the maximum cut" (MAX-CUT) problem [161, 154].
Advances in linear matrix inequality methods in control by Laurent El Ghaoui, Silviu-Iulian Niculescu