Output feedback optimal control with contraints

In Chapters 1 through 9 of the book (with the exception of a brief discussion on observers and integral action in Section 5.5 of Chapter 5) we considered constrained optimal control problems for systems without uncertainty, that is, with no unmodelled dynamics or disturbances, and where the full state was available for measurement. More realistically, however, it is necessary to consider control problems for systems with uncertainty. This chapter addresses some of the issues that arise in this situation. As in Chapter 9, we adopt a stochastic description of uncertainty, which associates probability distributions to the uncertain elements, that is, disturbances and initial conditions. (See Section 12.6 for references to alternative approaches to model uncertainty.) When incomplete state information exists, a popular observer-based control strategy in the presence of stochastic disturbances is to use the certainty equivalence [CE] principle, introduced in Section 5.5 of Chapter 5 for deterministic systems. In the stochastic framework, CE consists of estimating the state and then using these estimates as if they were the true state in the control law that results if the problem were formulated as a deterministic problem (that is, without uncertainty). This strategy is motivated by the unconstrained problem with a quadratic objective function, for which CE is indeed the optimal solution (˚Astr¨om 1970, Bertsekas 1976). One of the aims of this chapter is to explore the issues that arise from the use of CE in RHC in the presence of constraints. We then turn to the obvious question about the optimality of the CE principle. We show that CE is, indeed, not optimal in general. We also analyse the possibility of obtaining truly optimal solutions for single input linear systems with input constraints and uncertainty related to output feedback and stochastic disturbances.We first find the optimal solution for the case of horizon N = 1, and then we indicate the complications that arise in the case of horizon N = 2. Our conclusion is that, for the case of linear constrained systems, the extra effort involved in the optimal feedback policy is probably not justified in practice. Indeed, we show by example that CE can give near optimal performance. We thus advocate this approach in real applications.

An Introduction to Constrained Control

An ubiquitous problem in control system design is that the system must operate subject to various constraints. Although the topic of constrained control has a long history in practice, there have been recent significant advances in the supporting theory. In this chapter, we give an introduction to constrained control. In particular, we describe contemporary work which shows that the constrained optimal control problem for discrete-time systems has an interesting geometric structure and a simple local solution. We also discuss issues associated with the output feedback solution to this class of problems, and the implication of these results in the closely related problem of anti-windup. As an application, we address the problem of rudder roll stabilization for ships.

Optimization of complex QoS-aware service compositions

In Service-oriented Architectures, business processes can be realized by composing loosely coupled services. The problem of QoS-aware service composition is widely recognized in the literature. Existing approaches on computing an optimal solution to this problem tackle structured business processes, i.e., business processes which are composed of XOR-block, AND-block, and repeat loop orchestration components. As of yet, OR-block and unstructured orchestration components have not been sufficiently considered in the context of QoS-aware service composition. The work at hand addresses this shortcoming. An approach for computing an optimal solution to the service composition problem is proposed considering the structured orchestration components, such as AND/XOR/OR-block and repeat loop, as well as unstructured orchestration components.

Optimization approaches for the design of additively manufactured scaffolds

Scaffolds play a pivotal role in tissue engineering, promoting the synthesis of neo extra-cellular matrix (ECM), and providing temporary mechanical support for the cells during tissue regeneration. Advances introduced by additive manufacturing techniques have significantly improved the ability to regulate scaffold architecture, enhancing the control over scaffold shape and porosity. Thus, considerable research efforts have been devoted to the fabrication of 3D porous scaffolds with optimized micro-architectural features. This chapter gives an overview of the methods for the design of additively manufactured scaffolds and their applicability in tissue engineering (TE). Along with a survey of the state of the art, the Authors will also present a recently developed method, called Load-Adaptive Scaffold Architecturing (LASA), which returns scaffold architectures optimized for given applied mechanical loads systems, once the specific stress distribution is evaluated through Finite Element Analysis (FEA).

Interaction of psychosocial risk factors explain increased neck problems among female office workers

This study investigated the relationship between psychosocial risk factors and (1) neck symptoms and (2) neck pain and disability as measured by the neck disability index (NDI). Female office workers employed in local private and public organizations were invited to participate, with 333 completing a questionnaire. Data were collected on various risk factors including age, negative affectivity, history of previous neck trauma, physical work environment, and task demands. Sixty-one percent of the sample reported neck symptoms lasting greater than 8 days in the last 12 months. The mean NDI of the sample was 15.5 out of 100, indicating mild neck pain and disability. In a hierarchical multivariate logistic regression, low supervisor support was the only psychosocial risk factor identified with the presence of neck symptoms. Similarly, low supervisor support was the only factor associated with the score on the NDI. These associations remained after adjustment for potential confounders of age, negative affectivity, and physical risk factors. The interaction of job demands, decision authority, and supervisor support was significantly associated with the NDI in the final model and this association increased when those with previous trauma were excluded. Interestingly, and somewhat contrary to initial expectations, as job demands increased, high decision authority had an increasing effect on the NDI when supervisor support was low.

Accurately defining the reference condition for summary biotic metrics: A comparison of four approaches

Protocols for bioassessment often relate changes in summary metrics that describe aspects of biotic assemblage structure and function to environmental stress. Biotic assessment using multimetric indices now forms the basis for setting regulatory standards for stream quality and a range of other goals related to water resource management in the USA and elsewhere. Biotic metrics are typically interpreted with reference to the expected natural state to evaluate whether a site is degraded. It is critical that natural variation in biotic metrics along environmental gradients is adequately accounted for, in order to quantify human disturbance-induced change. A common approach used in the IBI is to examine scatter plots of variation in a given metric along a single stream size surrogate and a fit a line (drawn by eye) to form the upper bound, and hence define the maximum likely value of a given metric in a site of a given environmental characteristic (termed the 'maximum species richness line' - MSRL). In this paper we examine whether the use of a single environmental descriptor and the MSRL is appropriate for defining the reference condition for a biotic metric (fish species richness) and for detecting human disturbance gradients in rivers of south-eastern Queensland, Australia. We compare the accuracy and precision of the MSRL approach based on single environmental predictors, with three regression-based prediction methods (Simple Linear Regression, Generalised Linear Modelling and Regression Tree modelling) that use (either singly or in combination) a set of landscape and local scale environmental variables as predictors of species richness. We compared the frequency of classification errors from each method against set biocriteria and contrast the ability of each method to accurately reflect human disturbance gradients at a large set of test sites. The results of this study suggest that the MSRL based upon variation in a single environmental descriptor could not accurately predict species richness at minimally disturbed sites when compared with SLR's based on equivalent environmental variables. Regression-based modelling incorporating multiple environmental variables as predictors more accurately explained natural variation in species richness than did simple models using single environmental predictors. Prediction error arising from the MSRL was substantially higher than for the regression methods and led to an increased frequency of Type I errors (incorrectly classing a site as disturbed). We suggest that problems with the MSRL arise from the inherent scoring procedure used and that it is limited to predicting variation in the dependent variable along a single environmental gradient.

Two dynamic discrete choice estimation problems and simulation method solutions

This paper considers two problems that frequently arise in dynamic discrete choice problems but have not received much attention with regard to simulation methods. The first problem is how to simulate unbiased simulators of probabilities conditional on past history. The second is simulating a discrete transition probability model when the underlying dependent variable is really continuous. Both methods work well relative to reasonable alternatives in the application discussed. However, in both cases, for this application, simpler methods also provide reasonably good results.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

Part 2. MOO methods for multidisciplinary design using parallel evolutionary algorithms, game theory and hierarchical topology. (Part 2.) Numerical aspects and implementation of model test cases

These lecture notes describe the use and implementation of a framework in which mathematical as well as engineering optimisation problems can be analysed. The foundations of the framework and algorithms described -Hierarchical Asynchronous Parallel Evolutionary Algorithms (HAPEAs) - lie upon traditional evolution strategies and incorporate the concepts of a multi-objective optimisation, hierarchical topology, asynchronous evaluation of candidate solutions , parallel computing and game strategies. In a step by step approach, the numerical implementation of EAs and HAPEAs for solving multi criteria optimisation problems is conducted providing the reader with the knowledge to reproduce these hand on training in his – her- academic or industrial environment.

RF plasma sputtering deposition of hydroxyapatite bioceramics : synthesis, performance, and biocompatibility

Hydroxyapatite (HA) coatings have numerous applications in orthopedics and dentistry, owing to their excellent ability to promote stronger implant fixation and faster bone tissue ingrowth and remodeling. Thermal plasma spray and other plasma-assisted techniques have recently been used to synthesize various calcium phosphate-based bioceramics. Despite notable recent achievements in the desired stoichiometry, phase composition, mechanical, structural, and bio-compatible properties, it is rather difficult to combine all of the above features in a single coating. For example, many existing plasma-sprayed HA coatings fall short in meeting the requirements of grain size and crystallinity, and as such are subject to enhanced resorption in body fluid. On the other hand, relatively poor interfacial bonding and stability is an obstacle to the application of the HA coatings in high load bearing Ti6Al4V knee joint implants. Here, we report on an alternative: a plasma-assisted, concurrent, sputtering deposition technique for high performance biocompatible HA coatings on Ti6Al4V implant alloy. The plasma-assisted RF magnetron co-sputtering deposition method allows one to simultaneously achieve most of the desired attributes of the biomimetic material and overcome the aforementioned problems. This article details the film synthesis process specifications, extensive analytical characterization of the material's properties, mechanical testing, simulated body fluid assessments, biocompatibility and cytocompatibility of the HA-coated Ti6Al4V orthopedic alloy. The means of optimization of the plasma and deposition process parameters to achieve the desired attributes and performance of the HA coating, as well as future challenges in clinical applications are also discussed.

Series in vector spherical harmonics : an efficient tool for solution of nonlinear problems in spherical plasmas

The series expansion of the plasma fields and currents in vector spherical harmonics has been demonstrated to be an efficient technique for solution of nonlinear problems in spherically bounded plasmas. Using this technique, it is possible to describe the nonlinear plasma response to the rotating high-frequency magnetic field applied to the magnetically confined plasma sphere. The effect of the external magnetic field on the current drive and field configuration is studied. The results obtained are important for continuous current drive experiments in compact toruses. © 2000 American Institute of Physics.

Using enterprise information architecture methods to model wicked problems in information systems design research

Design Science is the process of solving ‘wicked problems’ through designing, developing, instantiating, and evaluating novel solutions (Hevner, March, Park and Ram, 2004). Wicked problems are described as agent finitude in combination with problem complexity and normative constraint (Farrell and Hooker, 2013). In Information Systems Design Science, determining that problems are ‘wicked’ differentiates Design Science research from Solutions Engineering (Winter, 2008) and is a necessary part of proving the relevance to Information Systems Design Science research (Hevner, 2007; Iivari, 2007). Problem complexity is characterised as many problem components with nested, dependent and co-dependent relationships interacting through multiple feedback and feed-forward loops. Farrell and Hooker (2013) specifically state for wicked problems “it will often be impossible to disentangle the consequences of specific actions from those of other co-occurring interactions”. This paper discusses the application of an Enterprise Information Architecture modelling technique to disentangle the wicked problem complexity for one case. It proposes that such a modelling technique can be applied to other wicked problems and can lay the foundations for proving relevancy to DSR, provide solution pathways for artefact development, and aid to substantiate those elements required to produce Design Theory.

Wicked problems in designing open online learning

This paper will report on the “wicked” problems encountered when designing an online course with bounded content in an unbounded learning environment. It will describe the dilemmas faced and decisions made by academics in an Australian university challenged by an institutional initiative to design radical, disruptive learning experiences making use of readily available online media. This bounded/unbounded environment demands new roles for instructors in adopting innovative pedagogies and teaching and learning strategies. It also creates changing and challenging roles for course designers as they deal with ill-defined parameters and unknown audiences. In this paper, we propose a novel methodology for making curricular decisions in ill-defined spaces.