Nonlinear dynamical systems of trajectory design for 3D horizontal well and their optimal controls

AbstractThe trajectory design of horizontal well is a optimal control problem of nonlinear multistage dynamical system. It is often sought using trial-and-error methods, but these methods depend on experience of designers and workers. In this paper, we create new optimal control model of nonlinear dynamical system for the trajectory design of horizontal well. Several properties are discussed. Uniform design method is used to choose the initial points in the feasible region. We demonstrate how to decompose the feasible region into finite subregions in which improved Hook–Jeeves algorithm is employed to search optimal solution. Finally, the feasible optimization algorithm is constructed to find the optimal solution of the system. Several results show the validity of our algorithm. This is preferable, since our method is independent of the experience

Stochastic optimal control and algorithm of the trajectory of horizontal wells

AbstractThis paper presents a nonlinear, multi-phase and stochastic dynamical system according to engineering background. We show that the stochastic dynamical system exists a unique solution for every initial state. A stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. This model can be converted into a parametric nonlinear stochastic programming by integrating the state equation. It is discussed here that the local optimal solution depends in a continuous way on the parameters. A revised Hooke–Jeeves algorithm based on this property has been developed. Computer simulation is used for this paper, and the numerical results illustrate the validity and efficiency of the algorithm

Modeling nonlinear stochastic kinetic system and stochastic optimal control of microbial bioconversion process in batch culture

In this paper, we analyze a stochastic model representing batch fermentation in the process of glycerol bio-dissimilation to 1,3-propanediol by klebsiella pneumoniae. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. Thus, based on the nonlinear deterministic dynamical system of glycerol bioconversion to 1,3-propanediol in batch culture, we present the stochastic version of the batch fermentation process driven by a five-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness and Markov property of solutions. Moveover a stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. Finally we present computer simulation for the stochastic system by using Stochastic Euler–Maruyama scheme. Compared with the results from the deterministic system, numerical results reveal the peculiar role of stochasticity in the dynamical responses of the batch culture

Vector measure as controls for explicit nonlinear impulsive system of fed-batch culture

AbstractIn this paper, we consider an optimal control problem of microbial fermentation process in which glycerol is converted to 1,3-propanediol by Klebsiella pneumoniae in fed-batch culture. During the period of reaction, the variation of pH value is monitored to determine glycerol replenishment quantity, guaranteeing that microorganism can always keep growing fast under enough nutrition. Every time pH value is lower than seven, the quantity of glycerol added is such that pH value returns seven again. Glycerol is poured into reactor at discrete time instant and the quantity is controllable. The problem is to determine for each discrete time instant the glycerol quantity to add and maximize the final concentration of 1,3-propanediol. We present a controlled explicit nonlinear impulsive dynamical system of fed-batch culture with state independent vector measures as controls and study the existence, uniqueness, boundedness, continuous dependence and Gâteaux differentiability of its solution with respect to controls. We then propose a multiple objective programming model and demonstrate the regularity of cost functionals and weak compactness of admissible control set. Finally we discuss the existence of optimal control and implement a hybrid particle swarm optimization algorithm to solve the model optimally. Computational results are presented on a numerical example

Semi-blind source extraction algorithm for fetal electrocardiogram based on generalized autocorrelations and reference signals

AbstractBlind source extraction (BSE) has become one of the promising methods in the field of signal processing and analysis, which only desires to extract “interesting” source signals with specific stochastic property or features so as to save lots of computing time and resources. This paper addresses BSE problem, in which desired source signals have some available reference signals. Based on this prior information, we develop an objective function for extraction of temporally correlated sources. Maximizing this objective function, a semi-blind source extraction fixed-point algorithm is proposed. Simulations on artificial electrocardiograph (ECG) signals and the real-world ECG data demonstrate the better performance of the new algorithm. Moreover, comparisons with existing algorithms further indicate the validity of our new algorithm, and also show its robustness to the estimated error of time delay

Improvement of k-means Clustering Algorithm for Analyzing the Morphology of Ice Ridge Sails

An improved k-means clustering algorithm is proposed after analyzing the disadvantages of the traditional k-means algorithm. The cluster centers are initialized by combining the sample mean and standard deviation, the optimal cluster centers are searched by the hybridizing particle swarm optimization and traditional k-means algorithm, and the criterion function is improved during the iteration process to search the optimal number of clusters. The theory analysis and experimental results show that the improved algorithm not only avoids the local optima, also has greater searching capability than the traditional algorithm. This improved algorithm is used to analyze the morphology of the ridge sail (the upper surface of ice ridges). The comparison with the measured data shows that the influences of the geographical locations and the growing environments on the formation of ice ridges can be perfectly reflected by the clustered results

Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification

We present a fuzzy version of the Garman-Kohlhagen (FG-K) formula for pricing European currency option based on the extension principle. In order to keep consistent with the real market, we assume that the interest rate, the spot exchange rate, and the volatility are fuzzy numbers in the FG-K formula. The conditions of a basic proposition about the fuzzy-valued functions of fuzzy subsets are modified. Based on the modified conditions and the extension principle, we prove that the fuzzy price obtained from the FG-K formula for European currency option is a fuzzy number. To simplify the trade, the weighted possibilistic mean (WPM) value with a weighting function is adopted to defuzzify the fuzzy price to a crisp price. The numerical example shows our method makes the α-level set of fuzzy price smaller, which decreases the fuzziness. The example also indicates that the WPM value has different approximation effects to real market price by taking different values of weighting parameter in the weighting function. Inspired by this example, we provide a method, which can identify the optimal parameter

Thermal Diffusivity Identification of Distributed Parameter Systems to Sea Ice

A method of optimal control is presented as a numerical tool for solving the sea ice heat transfer problem governed by a parabolic partial differential equation. Taken the deviation between the calculated ice temperature and the measurements as the performance criterion, an optimal control model of distributed parameter systems with specific constraints of thermal properties of sea ice was proposed to determine the thermal diffusivity of sea ice. Based on sea ice physical processes, the parameterization of the thermal diffusivity was derived through field data. The simulation results illustrated that the identified parameterization of the thermal diffusivity is reasonably effective in sea ice thermodynamics. The direct relation between the thermal diffusivity of sea ice and ice porosity is physically significant and can considerably reduce the computational errors. The successful application of this method also explained that the optimal control model of distributed parameter systems in conjunction with the engineering background has great potential in dealing with practical problems

Asymptotical stability of a nonlinear non-differentiable dynamic system in microbial continuous cultures

Abstract In this paper, we consider a nonlinear non-differentiable dynamic system in microbial continuous cultures involving all possible metabolic pathways of the inhibition mechanisms of 3-hydroxypropionaldehyde onto the cell growth and the transport systems of glycerol and 1,3-PD across the cell membrane. First, the existence of the equilibrium point of the system proved. And by numerical calculation, the equilibrium point of the system is obtained. Subsequently, we derive the local bounded properties of the Jacobian, tensor and Hessian matrices of the system. Finally, the local asymptotical stability of the system at equilibrium point is proved