• Home
  • Linear Programming
  • Advances in Linear Matrix Inequality Methods in Control by Laurent El Ghaoui, Silviu-Iulian Niculescu PDF

Advances in Linear Matrix Inequality Methods in Control by Laurent El Ghaoui, Silviu-Iulian Niculescu PDF

By Laurent El Ghaoui, Silviu-Iulian Niculescu

ISBN-10: 0898714389

ISBN-13: 9780898714388

Linear matrix inequalities (LMIs) have lately emerged as important instruments for fixing a few keep an eye on difficulties. This ebook offers an up to date account of the LMI approach and covers subject matters akin to contemporary LMI algorithms, research and synthesis matters, nonconvex difficulties, and purposes. It additionally emphasizes functions of the strategy to parts except regulate. the elemental thought of the LMI process on top of things is to approximate a given regulate challenge through an optimization challenge with linear goal and so-called LMI constraints. The LMI process results in a good numerical answer and is especially suited for issues of doubtful information and a number of (possibly conflicting) requirements.

Show description

Read or Download Advances in Linear Matrix Inequality Methods in Control (Advances in Design and Control) PDF

Similar linear programming books

Read e-book online Mathematics in Industrial Problems: Part 4 PDF

This is often the fourth quantity within the sequence "Mathematics in commercial Prob­ lems. " the inducement for those volumes is to foster interplay among and arithmetic on the "grass roots"; that's, on the point of spe­ cific difficulties. those difficulties come from undefined: they come up from versions constructed by means of the commercial scientists in ventures directed on the manufac­ ture of recent or more desirable items.

Vasile Dragan, Toader Morozan, Adrian-Mihail Stoica's Mathematical Methods in Robust Control of Linear Stochastic PDF

This moment version of Mathematical tools within the strong regulate of Linear Stochastic structures features a huge variety of contemporary ends up in the keep watch over of linear stochastic platforms. extra in particular, the recent effects provided are: - A unified and summary framework for Riccati kind equations coming up within the stochastic keep watch over- balance and keep an eye on difficulties for structures perturbed by way of homogeneous Markov approaches with endless variety of states- combined H2/ H∞ keep watch over challenge and numerical strategies- Linear differential equations with optimistic evolution on ordered Banach areas with purposes for stochastic platforms together with either multiplicative white noise and Markovian jumps represented by means of a Markov chain with countable endless set of states- Kalman filtering for stochastic structures topic either to country based noise and Markovian jumps- H∞ lowered order filters for stochastic platforms The e-book will entice graduate scholars, researchers in complex keep an eye on engineering, finance, mathematical structures concept, utilized likelihood and stochastic tactics, and numerical research.

Download e-book for kindle: Variational Methods: Applications to Nonlinear Partial by Michael Struwe

Variational difficulties are a part of our classical cultural history. The ebook supplies an creation to variational equipment and provides on review of parts of present examine during this box. specific subject matters incorporated are the direct equipment together with reduce semi-continuity effects, the compensated compactness technique, the focus compactness strategy, Ekeland's variational precept, and duality equipment or minimax equipment, together with the mountain move theorems, index conception, perturbation thought, linking and extensions of those concepts to non-differentiable functionals and functionals outlined on convex units - and restrict situations.

Extra resources for Advances in Linear Matrix Inequality Methods in Control (Advances in Design and Control)

Sample text

Ben Tal and Nemirovski consider a truss topology design problem with uncertainty on the loading forces [41, 40]. In a more recent work [42], they introduce and study the complexity of robust optimality problems in the sense defined above in the context of convex optimization. Their approach is based on ellipsoidal bounds for the perturbation. 5) belong to the class of min-max problems. To attack them, we can thus use a versatile technique, called Lagrange relaxation, that enables us to approximate a set of complicated constraints by a "more tractable" set.

The above problem is convex; however, it is in general very difficult to solve (NP-hard; see [154, 323]). Checking if a given candidate solution x is robustly feasible is already very difficult in general. Our objective is to find lower bounds on this problem in the form of SDP. 4. 24). The variables in this SDP are x (the original decision variable) and 5 (the "multiplier" matrix). 14)), the approximation is exact. 16 El Ghaoui and Niculescu A special case: Robust linear programming (LP) Consider the LP Assume that the a^'s and 6i's are subject to unstructured perturbations.

Another purpose of this chapter is to open the method to other areas. In our presentation, we have tried to give an "optimization point of view" of the method in an effort to put it in perspective with classical relaxation methods. This effort is mainly motivated by the belief that the approach could be useful in many other fields, especially regarding robustness issues. This topic of robustness is receiving renewed attention in the field of optimization, as demonstrated by a series of recent papers [42, 127, 39].

Download PDF sample

Advances in Linear Matrix Inequality Methods in Control (Advances in Design and Control) by Laurent El Ghaoui, Silviu-Iulian Niculescu

by John

Rated 4.44 of 5 – based on 15 votes