The Rank One Mixed μ Problem and 'Kharitonov-Type' Analysis

The general mixed μ problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed μ problem. We show that for this case the mixed μ problem is equivalent to its upper bound (which is convex), and it can in fact be computed easily (and exactly). This special case is shown to be equivalent to the so called "affine parameter variation" problem (for a polynomial with perturbed coefficients) which has been examined in detail in the literature, and for which several celebrated "Kharitonov-type" results have been proven

Properties of the mixed μ problem and its bounds

Upper and lower bounds for the mixed μ problem have recently been developed, and here we examine the relationship of these bounds to each other and to μ. A number of interesting properties are developed and the implications of these properties for the robustness analysis of linear systems and the development of practical computation schemes are discussed. In particular we find that current techniques can only guarantee easy computation for large problems when μ equals its upper bound, and computational complexity results prohibit this possibility for general problems. In this context we present some special cases where computation is easy and make some direct comparisons between mixed μ and “Kharitonov-type” analysis methods

Antibacterial surface modification of titanium implants in orthopaedics

The use of biomaterials in orthopaedics for joint replacement, fracture healing and bone regeneration is a rapidly expanding field. Infection of these biomaterials is a major healthcare burden, leading to significant morbidity and mortality. Furthermore, the cost to healthcare systems is increasing dramatically. With advances in implant design and production, research has predominately focussed on osseointegration; however, modification of implant material, surface topography and chemistry can also provide antibacterial activity. With the increasing burden of infection, it is vitally important that we consider the bacterial interaction with the biomaterial and the host when designing and manufacturing future implants. During this review, we will elucidate the interaction between patient, biomaterial surface and bacteria. We aim to review current and developing surface modifications with a view towards antibacterial orthopaedic implants for clinical applications

Controller Design with Real Parametric Uncertainty

A number of techniques have been developed in recent years for the analysis and design of controllers which are robust with respect to structured complex uncertainty. In particular the complex μ synthesis procedure has been successfully applied to a number of engineering problems. However the presence of real parametric uncertainty in the problem description substantially complicates matters, so that standard complex μ synthesis techniques are no longer adequate. In this paper we develop a procedure to tackle the mixed (real and complex) μ synthesis problem. This procedure involves a "D,G-K iteration" between computing the mixed μ upper bound and solving an H∞ optimal control problem, and has guaranteed convergence to a local minimum of the (nonconvex) problem. The procedure has been implemented in software, and several controller designs are compared with the corresponding complex μ synthesis designs

Computational complexity of μ calculation

The structured singular value μ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems

Implications for the U.S. of Anglo-French Defense Cooperation

The paper analyzes, from a predominantly UK perspective, the implications for the U.S. of the November 2, 2010, Anglo-French Defence Cooperation Treaty. The current pressures on British and French defence budgets were the primary driving force behind this cooperative effort. London and Paris have made steps toward improving joint efforts in a number of areas, with defence acquisition and industrial cooperation being prominent. In the UK, there appears to be strong political support at the highest levels, which has permeated to lower levels in the bureaucracy, while the UK defence industry appears to be cautiously optimistic about future business opportunities. The impact of enhanced Anglo-French cooperation on the U.S. would appear to be largely favourable for Washington. Rather than providing a basis for weakened UK attention to the U.S., as some fear, the efforts by London and Paris will potentially generate greater national military capability from scarce resources and could serve as a vehicle for broader European efforts to enhance their defence capabilities. While multinational European military development projects are viewed with scepticism in the UK, the Anglo-French arrangement could strengthen the prospects for bilateral projects in which other European states may elect to participate

Computation of µ with real and complex uncertainties

The robustness analysis of system performance is one of the key issues in control theory, and one approach is to reduce this problem to that of computing the structured singular value, mu . When real parametric uncertainty is included, then mu must be computed with respect to a block structure containing both real and complex uncertainties. It is shown that mu is equivalent to a real eigenvalue maximization problem, and a power algorithm is developed to solve this problem. The algorithm has the property that mu is (almost) always an equilibrium point of the algorithm, and that whenever the algorithm converges a lower bound for mu results. This scheme has been found to have fairly good convergence properties. Each iteration of the scheme is very cheap, requiring only such operations as matrix-vector multiplications and vector inner products, and the method is sufficiently general to handle arbitrary numbers of repeated real scalars, repeated complex scalars, and full complex blocks

Accurate prediction of gene feedback circuit behavior from component properties

A basic assumption underlying synthetic biology is that analysis of genetic circuit elements, such as regulatory proteins and promoters, can be used to understand and predict the behavior of circuits containing those elements. To test this assumption, we used time‐lapse fluorescence microscopy to quantitatively analyze two autoregulatory negative feedback circuits. By measuring the gene regulation functions of the corresponding repressor–promoter interactions, we accurately predicted the expression level of the autoregulatory feedback loops, in molecular units. This demonstration that quantitative characterization of regulatory elements can predict the behavior of genetic circuits supports a fundamental requirement of synthetic biology