Certain nonlinear partially observable stochastic optimal controlproblems with explicit control laws equivalent to LEQG/LQG problems

This paper is concerned with partially observed stochastic optimal control problems when nonlinearities enter the dynamics of the unobservable state and the observations as gradients of potential functions. Explicit representations for the information state are derived in terms of a finite number of sufficient statistics. Consequently, the partially observed problem is recast as one of complete information with a new state generated by a modified version of the Kalman filter. When the terminal cost is quadratic in the unobservable state and includes the integral of the nonlinearities, the optimal control laws are explicitly computed, similar to linear-exponential-quadratic-Gaussian (LEQG) and linear-quadratic-Gaussian (LQG) tracking problems. The results are applicable to filtering and control of Hamiltonian systems     

Modeling wireless fading channels via stochastic differential equations: identification and estimation based on noisy measurements

This paper is concerned with modeling and identification of wireless channels using noisy measurements. The models employed are governed by stochastic differential equations (SDEs) in state space form, while the identification method is based on the expectation-maximization (EM) algorithm and Kalman filtering. The algorithm is tested against real channel measurements. The results presented include state space models for the channels, estimates of inphase and quadrature components, and estimates of the corresponding Doppler power spectral densities (DPSDs), from sample noisy measurements. Based on the available measurements, it is concluded that state space models of order two are sufficient for wireless flat fading channel characterization.     

A computational method for the LU decomposition of rectangularmatrices and its implications to the realization of 2-D digital filters

The realization of 2-D digital filters based on the lower-upper triangular decomposition of the coefficient matrix is investigated. A numerical method based on the QA decomposition, which has some important characteristics, is proposed for reaching the LU structure. The coefficients in the final LU structure have values favorable to fixed-point arithmetic implementation. Furthermore, the QR structure can be used for the realization and possesses good numerical characteristics in terms of the approximate decomposition scheme. The symmetry in the impulse response coefficient matrix of an octagonally symmetric 2-D FIR filter is utilized to reduce the computational effort spent in the decomposition and the total number of multipliers in the final realization structure     

A variable neighborhood descent heuristic for the problem of makespan minimisation on unrelated parallel machines with setup times

The NP-hard problem of scheduling jobs on unrelated parallel machines, in the presence of machine-dependent and sequence-dependent setup times, with the objective of minimizing the makespan, is considered. A variable neighborhood descent search algorithm, hybridized with mathematical programming elements, is presented and its performance is evaluated on a large set of benchmark problem instances. The extensive computational experiments show that the proposed algorithm outperforms previously proposed methods in terms of solution quality as well as computation time.     

Stochastic nonlinear minimax dynamic games with noisy measurements

This note is concerned with nonlinear stochastic minimax dynamic games which are subject to noisy measurements. The minimizing players are control inputs while the maximizing players are square-integrable stochastic processes. The minimax dynamic game is formulated using an information state, which depends on the paths of the observed processes. The information state satisfies a partial differential equation of the Hamilton-Jacobi-Bellman (HJB) type. The HJB equation is employed to characterize the dissipation properties of the system, to derive a separation theorem between the design of the estimator and the controller, and to introduce a certainty-equivalence principle along the lines of Whittle. Finally, the separation theorem and the certainty-equi. valence principle are applied to solve the linear-quadratic-Gaussian minimax game. The results of this note generalize the L/sup 2/-gain of deterministic systems to stochastic analogs; they are related to the controller design of stochastic systems which employ risk-sensitive performance criteria, and to the controller design of deterministic systems which employ minimax performance criteria.     

Decentralized optimality conditions of stochastic differential decision problems via Girsanov’s measure transformation

In this paper, we apply two methods to derive necessary and sufficient decentralized optimality conditions for stochastic differential decision problems with multiple Decision Makers (DMs), which aim at optimizing a common pay-off, based on the notions of decentralized global optimality and decentralized person-by-person (PbP) optimality. Method 1: We utilize the stochastic maximum principle to derive necessary and sufficient conditions which consist of forward and backward Stochastic Differential Equations (SDEs), and conditional variational Hamiltonians, conditioned on the information structures of the DMs. The sufficient conditions for decentralized PbP optimality are local conditions, closely related to the necessary conditions for decentralized PbP optimality. However, under certain convexity condition on the Hamiltonian, and a global version of the sufficient conditions for decentralized PbP optimality, we show decentralized global optimality. Method 2: We utilize the value processes of decentralized PbP optimal policies, we relate them to solutions of backward SDEs, we identify sufficient conditions for decentralized PbP optimality, and we show these are precisely those derived via the maximum principle. For both methods, as usual, we utilize Girsanov’s theorem to transform the initial decentralized stochastic optimal decision problems, to equivalent decentralized stochastic optimal decision problems on a reference probability space, in which the controlled process and the information processes which generate part of the information structures of the DMs, are independent of any of the decisions.     

Amphiphilic drug interactions with model cellular membranes are influenced by lipid chain-melting temperature

Small-molecule amphiphilic species such as many drug molecules frequently exhibit low-to-negligible aqueous solubility, and generally have no identified transport proteins assisting their distribution, yet are able to rapidly penetrate significant distances into patient tissue and even cross the blood–brain barrier. Previous work has identified a mechanism of translocation driven by acid-catalysed lipid hydrolysis of biological membranes, a process which is catalysed by the presence of cationic amphiphilic drug molecules. In this study, the interactions of raclopride, a model amphiphilic drug, were investigated with mixtures of biologically relevant lipids across a range of compositions, revealing the influence of the chain-melting temperature of the lipids upon the rate of acyl hydrolysis.     

Characterisation of a uranium ore using multiple X-ray diffraction based methods

Uranium bearing ores are often a complex mixture of minerals and compounds, a number of which are not of economic importance and are commonly referred to as gangue materials. In order to improve the efficiency of the dissolution stage of the overall uranium extraction process, a greater understanding of the minerals and compounds present in the ore is required. A greater knowledge of the gangue materials present is important as they can influence various aspects of the dissolution process such as providing potential adsorption sites for aqueous uranium species and through influencing the equilibrium of reactions involving aqueous uranium species. In this study the mineralogy of a uranium ore was investigated using a range of X-ray diffraction (XRD) based methods including in situ high temperature XRD and XRD using a synchrotron beam line. The results obtained from standard XRD (Cu Kα), high temperature XRD and synchrotron XRD (16.534 keV) were compared and a number of minerals were identified. The improved spatial resolution and intensity of the synchrotron data allowed for superior phase identification of a variety of minerals where standard X-ray techniques gave inconclusive results.     

Optimization of the photovoltaic thermal (PV/T) collector absorber

In an effort to reduce the cost of conventional fin and tube photovoltaic thermal (PV/T) collectors a novel mathematical analysis was developed which determines the optimum absorber plate configuration having the least material content and thus cost, whilst maintaining high collection efficiency.The analysis was based on the “low-flow” concept whose advantages include: improved system performance, smaller pump (less expensive with lower power consumption), smaller diameter tubes requiring lower thickness and thus cost of insulation, less construction power and time for the optimum absorber configuration.From the optimization methodology developed it was found that very thin fins (typically 50 μm) and small tubes (of 1.65 mm inside diameter for the risers, in the header and riser arrangement and 4.83 mm for the serpentine arrangement), with a tube spacing of 62 mm and 64 mm (both corresponding to 97% fin efficiency) and a mass of 1.185 kg/m² and 2.140 kg/m², respectively, can be used. This optimum serpentine absorber plate contains 40.50% less material content and mass, as compared to the serpentine prototype proposed by others. In one such design a mass of 3.596 kg/m² was used (with 10 mm diameter tubes, 95 mm tube spacing and 200 μm thick absorber).To predict the performance of the determined optimum configurations, a steady-state model (using the EES code) was developed. To validate the steady-state model two prototypes, one in Header and Riser and the other in Serpentine configuration, were built and tested. It was found from the experiments that there is a good agreement between the computational and the experimental results. Moreover, it was found that optimum PV/T configurations do indeed have thermal and electrical performance comparable to non-optimum ones of greater mass and cost.     

Information states in stochastic control and filtering: a Liealgebraic theoretic approach

The purpose of the paper is two-fold: (i) to introduce the sufficient statistic algebra which is responsible for propagating the sufficient statistics, or information state, in the optimal control of stochastic systems and (ii) to apply certain Lie algebraic methods and gauge transformations, widely used in nonlinear control theory and quantum physics, to derive new results concerning finite dimensional controllers. This enhances our understanding of the role played by the sufficient statistics. The sufficient statistic algebra enables us to determine a priori whether there exist finite-dimensional controllers; it also enables us to classify all finite-dimensional controllers. Relations to minimax dynamic games are delineated