Robust pole assignment in linear state feedback

Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.

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 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.

Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.

On computational algorithms for pole assignment

A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct procedures do not necessarily produce robust solutions to the problem, however, in the sense that the assigned poles are insensitive to perturbalions in the closed-loop system. This difficulty is illustrated here with results from a recent algorithm presented in this TRANSACTIONS and its causes are examined. A measure of robustness is described, and techniques for testing and improving robustness are indicated.

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.

What determines the out-of-home placement of children in the USA?

Using NCANDS data of US child maltreatment reports for 2009, logistic regression, probit analysis, discriminant analysis and an artificial neural network are used to determine the factors which explain the decision to place a child in out-of-home care. As well as developing a new model for 2009, a previous study using 2005 data is replicated. While there are many small differences, the four estimation techniques give broadly the same results, demonstrating the robustness of the results. Similarly, apart from age and sexual abuse, the 2005 and 2009 results are roughly similar. For 2009, child characteristics (particularly child emotional problems) are more important than the nature of the abuse and the situation of the household; while caregiver characteristics are the least important. All these models have low explanatory power.

Challenges in identifying factors which determine the placement of children in care? An international review

Placing a child in out-of-home care is one of the most important decisions made by professionals in the child care system, with substantial social, psychological, educational, medical and economic consequences. This paper considers the challenges and difficulties of building statistical models of this decision by reviewing the available international evidence. Despite the large number of empirical investigations over a 50 year period, a consensus on the variables associated with this decision is hard to identify. In addition, the individual models have low explanatory and predictive power and should not be relied on to make placement decisions. A number of reasons for this poor performance are offered, and some ways forwards suggested. This paper also aims to facilitate the emergence of a coherent and integrated international literature from the disconnected and fragmented empirical studies. Rather than one placement problem, there are many slightly different problems, and therefore it is expected that a number of related sub-literatures will emerge, each concentrating on a particular definition of the placement problem.

Precision placement of fertiliser for optimising the early nutrition of vegetable crops: a review of the implications for the yield and quality of crops, and their nutrient use efficiency

The research outlined in this paper highlights the importance of the early nutrition of vegetable crops, and its long-term effects on their subsequent growth and development. Results are also presented to demonstrate how the nutrient supply during the establishment stages of young seedlings and transplants can be enhanced by targeting fertiliser to a zone close to their developing roots. Three different precision fertiliser placement techniques are compared for this purpose: starter, band or side-injected fertiliser. The use of each of these methods consistently produced the same (or greater) yields at lower application rates than those from conventional broadcast applications, increasing the apparent recovery of N, P and K, and the overall efficiency of nutrient use, while reducing the levels of residual nutrients in the soil. Starter fertilisers also advanced the maturity of some crops, and enhanced produce quality by increasing the proportions of the larger and/or more desirable marketable grades. The benefits of the different placement techniques are illustrated with selected examples from research at Warwick HRI using different vegetable crops, including lettuce, onion and carrot.