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

By Laurent El Ghaoui, Silviu-Iulian Niculescu

Linear matrix inequalities (LMIs) have lately emerged as priceless instruments for fixing a few keep watch over difficulties. This booklet offers an up to date account of the LMI process and covers themes comparable to fresh LMI algorithms, research and synthesis matters, nonconvex difficulties, and functions. It additionally emphasizes purposes of the tactic to parts except keep watch over. the elemental notion of the LMI approach up to speed is to approximate a given keep an eye on challenge through an optimization challenge with linear goal and so-called LMI constraints. The LMI approach results in an effective numerical resolution and is very fitted to issues of doubtful facts and a number of (possibly conflicting) requisites.

Show description

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

Similar linear programming books

Flexible Shift Planning in the Service Industry: The Case of Physicians in Hospitals

The booklet offers new rules to version and clear up the versatile shift making plans challenge of team of workers staff within the carrier undefined. First, a brand new modeling technique is proposed that calls for shifts to be generated implicitly instead of utilising a predefined set of shift forms like 3 8-hour or 12-hour shifts to hide various forecast call for.

Duality principles in nonconvex systems

Encouraged via functional difficulties in engineering and physics, drawing on quite a lot of utilized mathematical disciplines, this booklet is the 1st to supply, inside of a unified framework, a self-contained entire mathematical concept of duality for common non-convex, non-smooth platforms, with emphasis on equipment and purposes in engineering mechanics.

The obstacle problem (Publications of the Scuola Normale Superiore)

The fabric offered the following corresponds to Fermi lectures that i used to be invited to bring on the Scuola Normale di Pisa within the spring of 1998. The concern challenge is composed in learning the homes of minimizers of the Dirichlet vital in a website D of Rn, between all these configurations u with prescribed boundary values and costrained to stay in D above a prescribed difficulty F.

Additional info for Advances in Linear Matrix Inequality Methods in Control (Advances in Design and Control)

Sample text

To find the new iterate, two steps are taken. In the predictor step, we seek to approach the optimum, that is, to satisfy ZF = 0. In the corrector step, we seek to return close to the central path by ensuring ZF = fj,I. The search directions 6x, 6Z for each step (predictor and corrector) are computed by linearization of the constraint ZF = 0 (predictor) or ZF = p,I (corrector) around the current value of (x,Z). Each step thus gives rise to a linear system in the elements of 6x, 6Z. Note that ZF can be linearized in a number of ways, depending on the specific method used.

Even this approach, however, is limited by the size of linear systems that can be solved. In what follows, we briefly describe primal-dual path-following methods, following Kojima et al. [233]. 35) are both strictly feasible, then we may write the optimality conditions where £ is an affine subspace: We can interpret the above conditions as complementarity conditions over the positive semidefinite cone, similar to those arising in LP [233]. The convexity of the original SDP is transported here into a property of monotonicity of £, which is crucial for the algorithm outlined below to converge globally.

3 El Ghaoui and Niculescu Examples Let us now show how the above tools can be used to describe compactly a wide array of uncertain matrices and dynamical systems. To simplify our description, we take the operator point of view mentioned previously. Matrices The above framework covers the case when some (matrix) data occurring in the robust decision problem is affected by a perturbation vector <5, in an algebraic manner, and the vector 6 is unknown-but-bounded. Consider, for example, an "uncertain matrix" M(£), where M is an algebraic function of vector <5, and 6 is unknown-but-bounded in the maximum-norm sense.

Download PDF sample

Rated 4.07 of 5 – based on 35 votes