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.

Managing Research Data: Mechanical testing and modelling of bone-implant constructs

Presentation by Dr Caroline Grant, Science & Engineering Faculty, IHBI, at Managing your research data seminar, 2012

On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.

Design, characterisation and in vivo testing of a new, adjustable stiffness, external fixator for the rat femur

Very little is known about the infl uence of the mechanical environment on the healing of large segmental defects. This partly reflects the lack of standardised, well characterised technologies to enable such studies. Here we report the design, construction and characterisation of a novel external fixator for use in conjunction with rat femoral defects. This device not only imposes a predetermined axial stiffness on the lesion, but also enables the stiffness to be changed during the healing process. The main frame of the fi xator consists of polyethylethylketone with titanium alloy mounting pins. The stiffness of the fi xator is determined by interchangeable connection elements of different thicknesses. Fixators were shown to stabilise 5 mm femoral defects in rats in vivo for at least 8 weeks during unrestricted cage activity. No distortion or infections, including pin infections, were noted. The healing process was simulated in vitro by inserting into a 5 mm femoral defect, materials whose Young’s moduli approximated those of the different tissues present in regenerating bone. These studies confirmed that, although the external fixator is the major determinant of axial stiffness during the early phase of healing, the regenerate within the lesion subsequently dominates this property. There is much clinical interest in altering the mechanics of the defect to enhance bone healing. Our data suggest that, if alteration of the mechanical environment is to be used to modulate the healing of large segmental defects, this needs to be performed before the tissue properties become dominant.

Dilemmatic spaces : high-stakes testing and the possibilities of collaborative knowledge work to generate learning innovations

This paper examines collaborative researcher-practitioner knowledge work around assessment data in culturally diverse, low- socioeconomic school communities in Queensland, Australia. Specifically, the paper draws on interview accounts about the work of a bridging knowledge flows between a local university and a cluster of schools. We draw on Bernstein’s (2000) concept of recontextualisation to explore the processes of knowledge mediation in dialogues around student assessment data to design instructional innovations. We argue that critical policy studies need to explore the complex ways in which neoliberal education policies are enacted in local sites. Moreover, we suggest that an analysis of collaborative knowledge work designed to improve student learning outcomes in low-socioeconomic school communities necessitates attention to the principles regulating knowledge flows across boundaries. In addition, it necessitates attention to the ways in which mediators navigate dilemmatic spaces, anxieties and affects/feelings in order to generate innovative learning designs in the current global context of high-stakes national testing and accountability regimes.

Performance-based structural fire design and testing of structures

Fire incident in buildings is common in Hong Kong and this could lead to heavy casualties due to its high population density, so the fire safety design of the framed structure is an important research topic. This paper describes a computer tool for determination of capacity of structural safety against various fire scenarios and the well-accepted second-order direct plastic analysis is adopted for simulation of material yielding and buckling. A computer method is developed to predict structural behaviour of bare steel framed structures at elevated temperatures but the work can be applied to structures made of other materials. These effects of thermal expansion and material degradation due to heating are required to be considered in order to capture the actual behavior of the structure under fire. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. Several numerical and experimental verifications of framed structures are presented and compared against solutions by other researchers. The proposed method allows us to adopt the truly performance-based structural fire analysis and design with significant saving in cost and time.

A framework for testing robust autonomy of UAS during design and certification

As the number of Uninhabited Airborne Systems (UAS) proliferates in civil applications, industry is increasingly putting pressure on regulation authorities to provide a path for certification and allow UAS integration into regulated airspace. The success of this integration depends on developments in improved UAS reliability and safety, regulations for certification, and technologies for operational performance and safety assessment. This paper focusses on the last topic and describes a framework for quantifying robust autonomy of UAS, which quantifies the system's ability to either continue operating in the presence of faults or safely shut down. Two figures of merit are used to evaluate vehicle performance relative to mission requirements and the consequences of autonomous decision making in motion control and guidance systems. These figures of merit are interpreted within a probabilistic framework, which extends previous work in the literature. The valuation of the figures of merit can be done using stochastic simulation scenarios during both vehicle development and certification stages with different degrees of integration of hardware-in-the-loop simulation technology. The objective of the proposed framework is to aid in decision making about the suitability of a vehicle with respect to safety and reliability relative to mission requirements.

Damping structure selection in nonlinear ship manoeuvring models

This paper presents the application of a statistical method for model structure selection of lift-drag and viscous damping components in ship manoeuvring models. The damping model is posed as a family of linear stochastic models, which is postulated based on previous work in the literature. Then a nested test of hypothesis problem is considered. The testing reduces to a recursive comparison of two competing models, for which optimal tests in the Neyman sense exist. The method yields a preferred model structure and its initial parameter estimates. Alternatively, the method can give a reduced set of likely models. Using simulated data we study how the selection method performs when there is both uncorrelated and correlated noise in the measurements. The first case is related to instrumentation noise, whereas the second case is related to spurious wave-induced motion often present during sea trials. We then consider the model structure selection of a modern high-speed trimaran ferry from full scale trial data.

Modeling nitrous oxide emissions from irrigated agriculture : testing DayCent with high-frequency measurements

A unique high temporal frequency dataset from an irrigated cotton-wheat rotation was used to test the agroecosystem model DayCent to simulate daily N2O emissions from sub-tropical vertisols under different irrigation intensities. DayCent was able to simulate the effect of different irrigation intensities on N2O fluxes and yield, although it tended to overestimate seasonal fluxes during the cotton season. DayCent accurately predicted soil moisture dynamics and the timing and magnitude of high fluxes associated with fertilizer additions and irrigation events. At the daily scale we found a good correlation of predicted vs. measured N2O fluxes (r2 = 0.52), confirming that DayCent can be used to test agricultural practices for mitigating N2O emission from irrigated cropping systems. A 25 year scenario analysis indicated that N2O losses from irrigated cotton-wheat rotations on black vertisols in Australia can be substantially reduced by an optimized fertilizer and irrigation management system (i.e. frequent irrigation, avoidance of excessive fertiliser application), while sustaining maximum yield potentials.

Applying and testing design for intuitive interaction

Various tools have been developed to assist designers in making interfaces easier to use although none yet offer a complete solution. Through previous work we have established that intuitive interaction is based on past experience. From this we have developed theory around intuitive interaction, a continuum and a conceptual tool for intuitive use. We then trialled our tool. Firstly, one designer used the tool to design a camera. Secondly, seven groups of postgraduate students re-designed various products using our tool. We then chose one of these - a microwave – and prototyped the new and original microwave interfaces on a touchscreen. We tested them on three different age groups. We found that the new design was more intuitive and rated by participants as more familiar. Therefore, design interventions based on our intuitive interaction theory can work. Work is ongoing to develop the tool further.

Biological performance of a polycaprolactone-based scaffold plus recombinant human morphogenetic protein-2 (rhBMP-2) in an ovine thoracic interbody fusion model

PURPOSE. We develop a sheep thoracic spine interbody fusion model to study the suitability of polycaprolactone-based scaffold and recombinant human bone morphogenetic protein-2 (rhBMP-2) as a bone graft substitute within the thoracic spine. The surgical approach is a mini- open thoracotomy with relevance to minimally invasive deformity correction surgery for adolescent idiopathic scoliosis. To date there are no studies examining the use of this biodegradable implant in combination with biologics in a sheep thoracic spine model. METHODS. In the present study, six sheep underwent a 3-level (T6/7, T8/9 and T10/11) discectomy with randomly allocated implantation of a different graft substitute at each of the three levels; (i) calcium phosphate (CaP) coated polycaprolactone-based scaffold plus 0.54μg rhBMP-2, (ii) CaP coated PCL- based scaffold alone or (iii) autograft (mulched rib head). Fusion was assessed at six months post-surgery. RESULTS. Computed Tomographic scanning demonstrated higher fusion grades in the rhBMP-2 plus PCL- based scaffold group in comparison to either PCL-based scaffold alone or autograft. These results were supported by histological evaluations of the respective groups. Biomechanical testing revealed significantly higher stiffness for the rhBMP-2 plus PCL- based scaffold group in all loading directions in comparison to the other two groups. CONCLUSION. The results of this study demonstrate that rhBMP-2 plus PCL- based scaffold is a viable bone graft substitute, providing an optimal environment for thoracic interbody spinal fusion in a large animal model.

Исследования и испытания алгоритмов автоматической пилотажно-навигационной системы малогабаритного беспилотного летательного аппарата = Research and testing of automatic navigation management system’s algorithms for small unmanned aerial vehicle

В статье представлено развитие принципа построения автоматической пилотажно-навигационной системы (АПНС) для беспилотного летательного аппарата (БЛА). Принцип заключается в синтезе комплексных систем управления БПЛА не только на основе использования алгоритмов БИНС, но и алгоритмов, объединяющих в себе решение задач формирования и отработки сформированной траектории резервированной системой управления и навигации. Приведены результаты аналитического исследования и данные летных экспериментов разработанных алгоритмов АПНС БЛА, обеспечивающих дополнительное резервирование алгоритмов навигации и наделяющих БЛА новым функциональной способностью по выходу в заданную точку пространства с заданной скоростью в заданный момент времени с учетом атмосферных ветровых возмущений. Предложена и испытана методика идентификации параметров воздушной атмосферы: направления и скорости W ветра. Данные летных испытаний полученного решения задачи терминальной навигации демонстрируют устойчивую работу синтезированных алгоритмов управления в различных метеоусловиях. The article presents a progress in principle of development of automatic navigation management system (ANMS) for small unmanned aerial vehicle (UAV). The principle defines a development of integrated control systems for UAV based on tight coupling of strap down inertial navigation system algorithms and algorithms of redundant flight management system to form and control flight trajectory. The results of the research and flight testing of the developed ANMS UAV algorithms are presented. The system demonstrates advanced functional redundancy of UAV guidance. The system enables new UAV capability to perform autonomous multidimensional navigation along waypoints with controlled speed and time of arrival taking into account wind. The paper describes the technique for real-time identification of atmosphere parameters such as wind direction and wind speed. The flight test results demonstrate robustness of the algorithms in diverse meteorological conditions.

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

Minimum cost of transport in human running is not ubiquitous

Purpose This study explores recent claims that humans exhibit a minimum cost of transport (CoTmin) for running which occurs at an intermediate speed, and assesses individual physiological, gait and training characteristics. Methods Twelve healthy participants with varying levels of fitness and running experience ran on a treadmill at six self-selected speeds in a discontinuous protocol over three sessions. Running speed (km[middle dot]hr-1), V[spacing dot above]O2 (mL[middle dot]kg-1[middle dot]km-1), CoT (kcal[middle dot]km-1), heart rate (beats[middle dot]min-1) and cadence (steps[middle dot]min-1) were continuously measured. V[spacing dot above]O2 max was measured on a fourth testing session. The occurrence of a CoTmin was investigated and its presence or absence examined with respect to fitness, gait and training characteristics. Results Five participants showed a clear CoTmin at an intermediate speed and a statistically significant (p < 0.05) quadratic CoT-speed function, while the other participants did not show such evidence. Participants were then categorized and compared with respect to the strength of evidence for a CoTmin (ClearCoTmin and NoCoTmin). The ClearCoTmin group displayed significantly higher correlation between speed and cadence; more endurance training and exercise sessions per week; than the NoCoTmin group; and a marginally non-significant but higher aerobic capacity. Some runners still showed a CoTmin at an intermediate speed even after subtraction of resting energy expenditure. Conclusion The findings confirm the existence of an optimal speed for human running, in some but not all participants. Those exhibiting a COTmin undertook a higher volume of running, ran with a cadence that was more consistently modulated with speed, and tended to be aerobically fitter. The ability to minimise the energetic cost of transport appears not to be ubiquitous feature of human running but may emerge in some individuals with extensive running experience.