Induced rational approximations of transcendental curves

A novel technique for the construction of positive weight high-precision rational approximations to a class of transcendental curves is presented. The approximations are induced from the rational parametrisations of the circle. The previously published rational parametrisations of the circle are not suited to the induction process and the new parametrisations are constructed in the paper for the purpose. Explicit rational approximations of a number of transcendental curves are then given. The work is a development of the authors’ previous work on induced rational parametrisations of special algebraic curves.     

Finite dimensional approximations for a class of infinite dimensional time optimal control problems

ABSTRACT

In this work, we study the numerical approximation of the solutions of a class of abstract parabolic time optimal control problems with unbounded control operator. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the optimal time and the optimal controls of the approximate time optimal problems converge (in appropriate norms) to the optimal time and to the optimal controls of the original problem. In order to prove our main theorem, we provide a nonsmooth data error estimate for abstract parabolic systems.     

Squared and absolute errors in optimal approximation of nonlinear systems

Optimal squared error and absolute error-based approximation problems for static polynomial models of nonlinear, discrete-time, systems are studied in detail. These problems have many similarities with other linear-in-the-parameters approximation problems, such as with optimal approximation problems for linear time-invariant models of linear and nonlinear systems. Nonprobabilistic signal analysis is used.Close connections between the studied approximation problems and certain classical topics in approximation theory, such as optimal L₂(−1,1) and L₁(−1,1) approximation, are established by analysing conditions under which sample averages of static nonlinear functions of the input converge to appropriate Riemann integrals of the static functions. These results should play a significant role in the analysis of corresponding system identification and model validation problems. Furthermore, these results demonstrate that optimal modelling based on the absolute error can offer advantages over squared error-based modelling. Especially, modelling problems in which some signals possess heavy tails can benefit from absolute value-based signal and error analysis.     

Convergence of semidiscrete approximations to optimal control problems in hilbert spaces: A counterexample

In this paper we give and discuss a counterexample related to the approximation of non-quadratic optimal control problems for linear distributed parameter systems. More precisely, we show that the assumption (1.7), which has been proved in a previous paper to be sufficient, is also necessary for the convergence (at least in the most general setting of the problem).     

A BSDE approach to a risk-based optimal investment of an insurer

We discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer’s risk process is modeled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth. The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. It leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases.     

Bandwidth allocation and scheduling of networked control systems with exponential and quadratic approximations

This paper investigates bandwidth allocation and scheduling of networked control systems (NCSs) with nonlinear-programming techniques. The bandwidth utilization (BU) is defined in terms of sampling frequency. An exponential and a quadratic approximation are formulated to describe system performance versus the sampling frequencies. The optimal sampling frequencies are obtained by solving the approximations with Karush–Kuhn–Tucker (KKT) conditions. Experimental results verify the effectiveness of the proposed approximations and scheduling algorithms. The two approximations could find an optimal BU of an NCS with a given sequence of plants and maximize the total BU up to 98% of the total available bandwidth.     

Polynomial time algorithm for an optimal stable assignment with multiple partners

This paper considers the many-to-many version of the stable marriage problem where each man and woman has a strict preference ordering on the members of the opposite sex that he or she considers acceptable. Further, each man and woman wishes to be matched to as many acceptable partners as possible, up to his or her specified quota. In this setup, a polynomial time algorithm for finding a stable matching that minimizes the sum of partner ranks across all men and women is provided. It is argued that this sum can be used as an optimality criterion for minimizing total dissatisfaction if the preferences over partner-combinations satisfy a no-complementarities condition. The results in this paper extend those already known for the one-to-one version of the problem.     

Comparisons of optimal release policies for software systems

In a software product management, it is an important problem to determine the optimal release timing which minimizes the total expected cost incurred in both testing and operation phases. In this paper, we compare the performance between two kinds of software release methods, which are referred to as the T-policy and the N-policy. Based on the existing software reliability growth models, we formulate the expected cost functions and derive analytically the optimal policies under these control methods. Also, we derive a criterion for which control methods should be adopted. Finally, in numerical examples, we calculate the optimal release policies for several cost parameters.     

A generalised optimal linear quadratic tracker with universal applications. Part 2: discrete-time systems

Contrastive to Part 1, Part 2 presents a generalised optimal linear quadratic digital tracker (LQDT) with universal applications for the discrete-time (DT) systems. This includes (1) a generalised optimal LQDT design for the system with the pre-specified trajectories of the output and the control input and additionally with both the input-to-output direct-feedthrough term and known/estimated system disturbances or extra input/output signals; (2) a new optimal filter-shaped proportional plus integral state-feedback LQDT design for non-square non-minimum phase DT systems to achieve a minimum-phase-like tracking performance; (3) a new approach for computing the control zeros of the given non-square DT systems; and (4) a one-learning-epoch input-constrained iterative learning LQDT design for the repetitive DT systems.     

Combining features of negative correlation learning with mixture of experts in proposed ensemble methods

Both theoretical and experimental studies have shown that combining accurate neural networks (NNs) in the ensemble with negative error correlation greatly improves their generalization abilities. Negative correlation learning (NCL) and mixture of experts (ME), two popular combining methods, each employ different special error functions for the simultaneous training of NNs to produce negatively correlated NNs. In this paper, we review the properties of the NCL and ME methods, discussing their advantages and disadvantages. Characterization of both methods showed that they have different but complementary features, so if a hybrid system can be designed to include features of both NCL and ME, it may be better than each of its basis approaches. In this study, two approaches are proposed to combine the features of both methods in order to solve the weaknesses of one method with the strength of the other method, i.e., gated-NCL (G-NCL) and mixture of negatively correlated experts (MNCE). In the first approach, G-NCL, a dynamic combiner of ME is used to combine the outputs of base experts in the NCL method. The suggested combiner method provides an efficient tool to evaluate and combine the NCL experts by the weights estimated dynamically from the inputs based on the different competences of each expert regarding different parts of the problem. In the second approach, MNCE, the capability of a control parameter for NCL is incorporated in the error function of ME, which enables the training algorithm of ME to efficiently adjust the measure of negative correlation between the experts. This control parameter can be regarded as a regularization term added to the error function of ME to establish better balance in bias–variance–covariance trade-offs and thus improves the generalization ability. The two proposed hybrid ensemble methods, G-NCL and MNCE, are compared with their constituent methods, ME and NCL, in solving several benchmark problems. The experimental results show that our proposed methods preserve the advantages and alleviate the disadvantages of their basis approaches, offering significantly improved performance over the original methods.     

Subjective perceptions and ergonomics evaluation of a liquid cooled garment worn under protective ensemble during an intermittent treadmill exercise

While a personal protective equipment (PPE) ensemble effectively provides workers with protection from occupational hazards, working in a vapour-resistant ensemble increases the risk of heat illness/injuries and physiological burdens. The purpose of this study was to investigate the effect of body cooling via a liquid-cooled garment (LCG) underneath a PPE ensemble on perceived thermal strain, physiological responses and ergonomics during an intermittent treadmill exercise in warm environmental conditions. The results of the present study indicated that the concomitant wearing of LCG underneath the PPE ensemble significantly reduced subjective perception of heat and alleviated overall increase in body temperature and heart rate while no impact of wearing LCG on ergonomic features was found. The extension of the present findings to practical applications in occupational settings requires further research on a LCG system design and performance evaluations while the LCG is incorporated within the PPE ensemble.

Statement of Relevance: Implementation of a LCG underneath PPE for body cooling was investigated, focusing on its impact on individuals' perceived thermal strain, physiological responses and ergonomics. The findings of the present study indicated that body cooling via a wearable LCG underneath PPE significantly alleviated both perceived thermal and physiological strain in uncompensable heat stress condition.     

Convexity and convex approximations of discrete-time stochastic control problems with constraints

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost subject to probabilistic constraints. We study the convexity of a finite-horizon optimization problem in the case where the control policies are affine functions of the disturbance input. We propose an expectation-based method for the convex approximation of probabilistic constraints with polytopic constraint function, and a Linear Matrix Inequality (LMI) method for the convex approximation of probabilistic constraints with ellipsoidal constraint function. Finally, we introduce a class of convex expectation-type constraints that provide tractable approximations of the so-called integrated chance constraints. Performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example.     

Towards the optimal control of Markov chains with constraints

An optimal control problem with constraints is considered on a finite interval for a non-stationary Markov chain with a finite state space. The constraints are given as a set of inequalities. The optimal solution existence is proved under a natural assumption that the set of admissible controls is non-empty. The stochastic control problem is reduced to a deterministic one and it is shown that the optimal solution satisfies the maximum principle, moreover it can be chosen within a class of Markov controls. On the basis of this result an approach to the numerical solution is proposed and its implementation is illustrated by examples.     

Maximum principle for the optimal control of an ablation-transpiration cooling system with free final time and phase constraints

This paper is concerned with an optimal control problem of an abhtion-transpiration cooling control system with Stefan-Signorini boundary condition. As the continuation of the authors＇previous paper, the Dubovits Rii-Milyutin fimctional approach is again adopted in investigation of the Pontryagin＇ s maximun principle of the system. The necessary optimality condition is presented for the problem with free final horizon and phase constraints.     

Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise

We provide convergence rates for space approximations of semi-linear stochastic differential equations with multiplicative noise in a Hilbert space. The space approximations we consider are spectral Galerkin and finite elements, and the type of convergence we consider is almost sure uniform convergence, i.e. pathwise convergence. The proofs are based on a recent perturbation result for such equations.     

Kinematic analysis and optimal design of a novel 1T3R parallel manipulator with an articulated travelling plate

Driven by the requirements of the large-scale component assemblage for the docking platform, this paper proposes a novel one-translational-three-rotational (1T3R) parallel manipulator with an articulated travelling plate, which can provide high stiffness and good accuracy performances in the assemblage. The underlying architecture of this manipulator is briefly addressed with emphasis on the practical realization of the articulated travelling plate. On the basis of the kinematic analysis of the 1T3R parallel manipulator, its optimal design considering the force and motion transmissibility is carried out, in which the generalized virtual power transmissibility of this manipulator is defined. This paper aims at laying a solid theoretical and technical foundation for the prototype design and manufacture of the 1T3R parallel manipulator.     

An efficient algorithm for optimal control of PWA systems with polyhedral performance indices

We present an algorithm for the computation of explicit optimal control laws for piecewise affine (PWA) systems with polyhedral performance indices. The algorithm is based on dynamic programming (DP) and represents an extension of ideas initially proposed in Kerrigan and Mayne [(2003). Optimal control of constrained, piecewise affine systems with bounded disturbances. In Proceedings of the 41st IEEE conference on decision and control, Las Vegas, Nevada, USA, December], and Baoti? et al. [(2003). A new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index. In Proceedings of European control conference, Cambridge, UK, September]. Specifically, we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off-line computations. An extensive case study is provided, which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature.     

An error bound for infinite approximations of queueing networks with large finite stations under RSRD protocol

Queueing networks with stations having finite but relatively large buffers are studied. The protocol is the repetitive service random destination (RSRD) protocol. A simple infinite product approximation is suggested to evaluate the system. An analytic error bound is established for the accuracy of this approximation. This error bound is shown to be of the order of the steady state probability to exceed the buffer limits computed by product form expressions for the infinite system. This probability can often be thought as being quite small and thus provides a practical error bound. Some numerical support is provided. To establish the error bound, a new method consisting of introducing an intermediate model is used. This approach seems of interest for wider application to obtain error bounds.     

Improving the prediction of petroleum reservoir characterization with a stacked generalization ensemble model of support vector machines

The ensemble learning paradigm has proved to be relevant to solving most challenging industrial problems. Despite its successful application especially in the Bioinformatics, the petroleum industry has not benefited enough from the promises of this machine learning technology. The petroleum industry, with its persistent quest for high-performance predictive models, is in great need of this new learning methodology. A marginal improvement in the prediction indices of petroleum reservoir properties could have huge positive impact on the success of exploration, drilling and the overall reservoir management portfolio. Support vector machines (SVM) is one of the promising machine learning tools that have performed excellently well in most prediction problems. However, its performance is a function of the prudent choice of its tuning parameters most especially the regularization parameter, C. Reports have shown that this parameter has significant impact on the performance of SVM. Understandably, no specific value has been recommended for it. This paper proposes a stacked generalization ensemble model of SVM that incorporates different expert opinions on the optimal values of this parameter in the prediction of porosity and permeability of petroleum reservoirs using datasets from diverse geological formations. The performance of the proposed SVM ensemble was compared to that of conventional SVM technique, another SVM implemented with the bagging method, and Random Forest technique. The results showed that the proposed ensemble model, in most cases, outperformed the others with the highest correlation coefficient, and the lowest mean and absolute errors. The study indicated that there is a great potential for ensemble learning in petroleum reservoir characterization to improve the accuracy of reservoir properties predictions for more successful explorations and increased production of petroleum resources. The results also confirmed that ensemble models perform better than the conventional SVM implementation.