Robust pole assignment in systems subject to structured perturbations

The problem of robust pole assignment by feedback in a linear, multivariable, time-invariant system which is subject to structured perturbations is investigated. A measure of robustness, or sensitivity, of the poles to a given class of perturbations is derived, and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Robust control system design for generalized state-space systems

Robustness in multi-variable control system design requires that the solution to the design problem be insensitive to perturbations in the system data. In this paper we discuss measures of robustness for generalized state-space, or descriptor, systems and describe algorithmic techniques for optimizing robustness for various applications.

Robust pole assignment and optimal stability margins

A robust pole assignment by linear state feedback is achieved in state-space representation by selecting a feedback which minimises the conditioning of the assigned eigenvalues of the closed-loop system. It is shown here that when this conditioning is minimised, a lower bound on the stability margin in the frequency domain is maximised.

Algorithms for Robust Pole Assignment in Singular Systems

The solution of the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil. A robustness measure is defined, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.

A verification framework for interannual-to-decadal predictions experiments

Decadal predictions have a high profile in the climate science community and beyond, yet very little is known about their skill. Nor is there any agreed protocol for estimating their skill. This paper proposes a sound and coordinated framework for verification of decadal hindcast experiments. The framework is illustrated for decadal hindcasts tailored to meet the requirements and specifications of CMIP5 (Coupled Model Intercomparison Project phase 5). The chosen metrics address key questions about the information content in initialized decadal hindcasts. These questions are: (1) Do the initial conditions in the hindcasts lead to more accurate predictions of the climate, compared to un-initialized climate change projections? and (2) Is the prediction model’s ensemble spread an appropriate representation of forecast uncertainty on average? The first question is addressed through deterministic metrics that compare the initialized and uninitialized hindcasts. The second question is addressed through a probabilistic metric applied to the initialized hindcasts and comparing different ways to ascribe forecast uncertainty. Verification is advocated at smoothed regional scales that can illuminate broad areas of predictability, as well as at the grid scale, since many users of the decadal prediction experiments who feed the climate data into applications or decision models will use the data at grid scale, or downscale it to even higher resolution. An overall statement on skill of CMIP5 decadal hindcasts is not the aim of this paper. The results presented are only illustrative of the framework, which would enable such studies. However, broad conclusions that are beginning to emerge from the CMIP5 results include (1) Most predictability at the interannual-to-decadal scale, relative to climatological averages, comes from external forcing, particularly for temperature; (2) though moderate, additional skill is added by the initial conditions over what is imparted by external forcing alone; however, the impact of initialization may result in overall worse predictions in some regions than provided by uninitialized climate change projections; (3) limited hindcast records and the dearth of climate-quality observational data impede our ability to quantify expected skill as well as model biases; and (4) as is common to seasonal-to-interannual model predictions, the spread of the ensemble members is not necessarily a good representation of forecast uncertainty. The authors recommend that this framework be adopted to serve as a starting point to compare prediction quality across prediction systems. The framework can provide a baseline against which future improvements can be quantified. The framework also provides guidance on the use of these model predictions, which differ in fundamental ways from the climate change projections that much of the community has become familiar with, including adjustment of mean and conditional biases, and consideration of how to best approach forecast uncertainty.

Making robust policy decision using global biodiversity indicators

In order to influence global policy effectively, conservation scientists need to be able to provide robust predictions of the impact of alternative policies on biodiversity and measure progress towards goals using reliable indicators. We present a framework for using biodiversity indicators predictively to inform policy choices at a global level. The approach is illustrated with two case studies in which we project forwards the impacts of feasible policies on trends in biodiversity and in relevant indicators. The policies are based on targets agreed at the Convention on Biological Diversity (CBD) meeting in Nagoya in October 2010. The first case study compares protected area policies for African mammals, assessed using the Red List Index; the second example uses the Living Planet Index to assess the impact of a complete halt, versus a reduction, in bottom trawling. In the protected areas example, we find that the indicator can aid in decision-making because it is able to differentiate between the impacts of the different policies. In the bottom trawling example, the indicator exhibits some counter-intuitive behaviour, due to over-representation of some taxonomic and functional groups in the indicator, and contrasting impacts of the policies on different groups caused by trophic interactions. Our results support the need for further research on how to use predictive models and indicators to credibly track trends and inform policy. To be useful and relevant, scientists must make testable predictions about the impact of global policy on biodiversity to ensure that targets such as those set at Nagoya catalyse effective and measurable change.