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 helpful instruments for fixing a couple of keep watch over difficulties. This e-book offers an up to date account of the LMI procedure and covers themes comparable to contemporary LMI algorithms, research and synthesis matters, nonconvex difficulties, and functions. It additionally emphasizes functions of the tactic to parts except regulate. the elemental suggestion of the LMI technique up to the mark is to approximate a given keep an eye on challenge through an optimization challenge with linear target and so-called LMI constraints. The LMI strategy ends up in a good numerical resolution and is very fitted to issues of doubtful info and a number of (possibly conflicting) standards.

Show description

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

Best linear programming books

Linear Programming and its Applications

Within the pages of this article readers will locate not anything lower than a unified therapy of linear programming. with out sacrificing mathematical rigor, the most emphasis of the publication is on types and functions. crucial sessions of difficulties are surveyed and provided by way of mathematical formulations, by way of answer tools and a dialogue of numerous "what-if" situations.

Methods of Mathematical Economics: Linear and Nonlinear Programming, Fixed-Point Theorems (Classics in Applied Mathematics, 37)

This article makes an attempt to survey the middle matters in optimization and mathematical economics: linear and nonlinear programming, keeping apart airplane theorems, fixed-point theorems, and a few in their applications.

This textual content covers simply topics good: linear programming and fixed-point theorems. The sections on linear programming are established round deriving equipment according to the simplex set of rules in addition to the various commonplace LP difficulties, resembling community flows and transportation challenge. I by no means had time to learn the part at the fixed-point theorems, yet i believe it will possibly turn out to be valuable to investigate economists who paintings in microeconomic conception. This part offers 4 diversified proofs of Brouwer fixed-point theorem, an explanation of Kakutani's Fixed-Point Theorem, and concludes with an evidence of Nash's Theorem for n-person video games.

Unfortunately, an important math instruments in use through economists at the present time, nonlinear programming and comparative statics, are slightly pointed out. this article has precisely one 15-page bankruptcy on nonlinear programming. This bankruptcy derives the Kuhn-Tucker stipulations yet says not anything in regards to the moment order stipulations or comparative statics results.

Most most probably, the unusual choice and assurance of themes (linear programming takes greater than half the textual content) easily displays the truth that the unique version got here out in 1980 and in addition that the writer is absolutely an utilized mathematician, no longer an economist. this article is worthy a glance if you'd like to appreciate fixed-point theorems or how the simplex set of rules works and its purposes. glance in different places for nonlinear programming or newer advancements in linear programming.

Planning and Scheduling in Manufacturing and Services

This booklet makes a speciality of making plans and scheduling purposes. making plans and scheduling are sorts of decision-making that play a major position in such a lot production and companies industries. The making plans and scheduling services in a firm ordinarily use analytical strategies and heuristic tips on how to allocate its constrained assets to the actions that experience to be performed.

Optimization with PDE Constraints

This ebook offers a latest creation of pde limited optimization. It presents an actual practical analytic therapy through optimality stipulations and a cutting-edge, non-smooth algorithmical framework. additionally, new structure-exploiting discrete recommendations and big scale, essentially correct purposes are provided.

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

Sample text

We may distinguish the following: • A robust feasibility problem, where we seek a vector x that belongs to • A robust optimality problem, defined as Here, we seek to minimize the worst-case value of the objective fo(x, A) over the set of robustly feasible solutions. ) Parameter-scheduled synthesis. In such a problem, we allow the decision vector to be a function of the perturbation. In this case, we assume that the decision vector is not finite dimensional but evolves in a set X of functions (of the perturbation A).

Robustness out of control 29 The problem is to find a u e U, if any, such that for every XQ € AQ, the resulting output satisfies y £ y. If the state-space matrices are exactly known, the problem is equivalent to a simple linear program. In the case when the state-space matrices are uncertain, the robust counterpart can be approximated using the robust decision methodology. In terms of optimization, this versatile framework gives rise to challenging large-scale problems. One way to avoid the curse of dimensionality is to construct ellipsoids of confidence for the future state and optimize (over a few time steps) the control vector.

1 Basic idea The basic idea of the LMI method is to formulate a given problem as an optimization problem with linear objective and linear matrix inequality (LMI) constraints. An LMI constraint on a vector x e Rm is one of the form where the symmetric matrices Fj = F? G R JVxJV , i = 0,... ,m, are given. The minimization problem where c € R m , and F > 0 means the matrix F is symmetric and positive semidefinite, is called a semidefinite program (SDP). The above framework is particularly attractive for the following reasons.

Download PDF sample

Rated 4.75 of 5 – based on 19 votes