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This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to canonical constraints, where the fractional-order derivatives are expressed in the Caputo sense. To solve the problem by discretization scheme, an explicit numerical integration technique is proposed for solving the fractional-order system, and the trapezoidal rule is introduced to approximate the cost functional. Then, the gradients of the resulting cost and constraint functions are derived. On the basis of this result, we develop a gradient-based optimization algorithm to numerically solve the discretized problem. Finally, numerical results of several non-trivial examples are provided to illustrate the applicability and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method is developed for solving a class of delay fractional optimal control problems involving nonlinear time-delay systems and subject to state inequality constraints. The fractional derivatives in this class of problems are described in the sense of Caputo, and they can be of different orders. First, we propose a numerical integration scheme for the fractional time-delay system and prove that the convergence rate of the numerical solution to the exact one is of second order based on Taylor expansion and linear interpolation. This gives rise to a discrete-time optimal control problem. Then, we derive the gradient formulas of the cost and constraint functions with respect to the decision variables and present a gradient computation procedure. On this basis, a gradient-based optimization algorithm is developed to solve the resulting discrete-time optimal control problem. Finally, several example problems are solved to demonstrate the effectiveness of the developed solution approach. [ABSTRACT FROM AUTHOR]

BACKGROUND: Previous studies revealed that DEP domain containing 1 (DEPDC1) is involved in the carcinogenesis and progression of several types of human cancer. However the role of DEPDC1 in gastric cancer has not been studied. OBJECTIVE: The objective of this study was to study the expression and pathophysiological function of DEPDC1 in gastric cancer. METHODS: DEPDC1 expression in gastric adenocarcinoma cells was examined with Western blot and qRT-PCR. Clinical pathological features of patients were determined by immunohistochemistry. The effect of DEPDC1 expression on cell proliferation was studied by in vitro cell proliferation assay; and cell cycle influence was assessed by flow cytometry. Survival curves were plotted using Kaplan-Meier. RESULTS: DEPDC1 was overexpressed in gastric adenocarcinoma tissues compared with the paired adjacent normal gastric tissues, in accordance with mRNA level downloaded from GEPIA database. DEPDC1 expression level was significantly associated with cancer metastasis and differentiation. DEPDC1 upregulation caused cell cycle accelerating from G1 to S phase, and it was correlated with poorer overall survival. CONCLUSION: Therefore, DEPDC1 upregulation in gastric adenocarcinoma is associated with tumor development and poor clinical outcomes of the patients, implying DEPDC1 might be a potential therapeutic target against gastric cancer. [ABSTRACT FROM AUTHOR]

• A novel nonlinear time-varying delay system is proposed for microbial batch process. • An optimal state-delay control problem is presented to determine the unknown delay function. • Effectiveness of the developed numerical solution approach is analysed. In this paper, we consider optimal control problem involving a time-varying state-delay system arising in 1,3-propanediol microbial batch process. The dynamic system in this problem includes unknown time-varying delay function and unknown kinetic parameters. To optimally determine the unknown delay function and unknown kinetic parameters in the system, the weighted least-squares error between the computed values and experimental data is minimized subject to path constraints. By parameterizing the delay function with piecewise quadratic basis functions, the optimal state-delay control problem is approximated by a sequence of parameter optimization problems. Furthermore, an exact penalty method is utilized to transform these parameter optimization problems into the ones only with box constraints. On this basis, a modified differential evolution algorithm is developed to solve the resulting optimization problems. Finally, numerical results are presented to verify the effectiveness of the developed solution approach. [ABSTRACT FROM AUTHOR]

This paper considers optimal control of glycerol producing 1,3-propanediol (1,3-PD) in batch process with uncertain time-delay and kinetic parameters. Based on a dynamic system with uncertain time-delay and kinetic parameters describing the batch process, we propose a robust bi-objective optimal control model, in which 1,3-PD productivity and glycerol consumption rate, and their semi-relative sensitivities with respect to the uncertain parameters are all involved in the vector objective. The control variables in this problem are the initial concentrations of biomass and glycerol and the terminal time of the process. Then, by introducing auxiliary time-delay systems and performing a time-scaling transformation, we transform the robust bi-objective optimal control problem into an equivalent bi-objective optimal control problem in standard form. Furthermore, we convert the equivalent optimal control problem into a sequence of solvable single-objective optimal control problems by using the normalized normal constraint method together with the constraint transcription technique. To solve each of the resulting optimal control problems, we develop a novel gradient-based solution method. Finally, numerical results are provided to verify the effectiveness of the proposed solution approach. [ABSTRACT FROM AUTHOR]

Highlights • A distributionally robust parameter identification model is proposed for time-delay systems. • The problem is transformed to a single-level optimization problem. • A gradient-based optimization method is developed to solve the transformed problem. Abstract In this paper, we consider a parameter identification problem involving a time-delay dynamical system, in which the measured data are stochastic variable. However, the probability distribution of this stochastic variable is not available and the only information we have is its first moment. This problem is formulated as a distributionally robust parameter identification problem governed by a time-delay dynamical system. Using duality theory of linear optimization in a probability space, the distributionally robust parameter identification problem, which is a bi-level optimization problem, is transformed into a single-level optimization problem with a semi-infinite constraint. By applying problem transformation and smoothing techniques, the semi-infinite constraint is approximated by a smooth constraint and the convergence of the smooth approximation method is established. Then, the gradients of the cost and constraint functions with respect to time-delay and parameters are derived. On this basis, a gradient-based optimization method for solving the transformed problem is developed. Finally, we present an example, arising in practical fermentation process, to illustrate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider estimation problems involving a class of nonlinear systems characterized by two non-standard attributes: (i) such systems evolve over multiple stages; and (ii) the dynamics in each stage involve unknown time-delays and unknown system parameters. These unknown quantities are to be estimated such that a least-squares error function between the system output and a set of noisy measurement data from a real plant is minimized. We first present the classical parameter estimation formulation, where the expectation of the error function is regarded as the cost function. However, in practice, there exists uncertainty in the distribution of the measurement data. The optimal parameter estimate should be able to withstand this uncertainty. Accordingly, we propose a new parameter estimation formulation, in which the cost function is the variance of the error function and the constraint indicates an allowable sacrifice from the optimal expectation value of the classical parameter estimation problem. For these two estimation problems, we show that the gradients of their cost functions and the constraint function with respect to the time-delays and system parameters can be computed through solving a set of auxiliary time-delay systems in conjunction with the governing multistage time-delay system, simultaneously. On this basis, we develop gradient-based optimization algorithms to determine the unknown time-delays and system parameters. Finally, we consider two example problems to illustrate the effectiveness and applicability of our proposed algorithms. [ABSTRACT FROM AUTHOR]

Maximization of productivity and minimization of consumption are two top priorities for biotechnological industry. In this paper, we model a fed-batch process as a nonlinear switched time-delay system. Taking the productivity of target product and the consumption rate of substrate as the objective functions, we present a multi-objective optimization problem involving the nonlinear switched time-delay system and subject to continuous state inequality constraints. To solve the multi-objective optimization problem, we first convert the problem into a sequence of single-objective optimization problems by using convex weighted sum and normal boundary intersection methods. A gradient-based single-objective solver incorporating constraint transcription technique is then developed to solve these single-objective optimization problems. Finally, a numerical example is provided to verify the effectiveness of the numerical solution approach. Numerical results show that the normal boundary intersection method in conjunction with the developed single-objective solver is more favourable than the convex weighted sum method. [ABSTRACT FROM AUTHOR]

This paper considers the three-dimensional path planning problem for horizontal oil wells. The decision variables in this problem are the curvature, tool-face angle and switching points for each turn segment in the path, and the optimization objective is to minimize the path length and target error. The optimal curvatures, tool-face angles and switching points can be readily determined using existing gradient-based dynamic optimization techniques. However, in a real drilling process, the actual curvatures and tool-face angles will inevitably deviate from the planned optimal values, thus causing an unexpected increase in the target error. This is a critical challenge that must be overcome for successful practical implementation. Accordingly, this paper introduces a sensitivity function that measures the rate of change in the target error with respect to the curvature and tool-face angle of each turn segment. Based on the sensitivity function, we propose a new optimization problem in which the switching points are adjusted to minimize target error sensitivity subject to continuous state inequality constraints arising from engineering specifications, and an additional constraint specifying the maximum allowable increase in the path length from the optimal value. Our main result shows that the sensitivity function can be evaluated by solving a set of auxiliary dynamic systems. By combining this result with the well-known time-scaling transformation, we obtain an equivalent transformed problem that can be solved using standard nonlinear programming algorithms. Finally, the paper concludes with a numerical example involving a practical path planning problem for a Ci-16-Cp146 well. [ABSTRACT FROM AUTHOR]

In this paper, a computational method is proposed for solving a class of fractional optimal control problems subject to canonical constraints of equality and inequality. Fractional derivatives are described in the Atangana–Baleanu-Caputo sense, and their fractional orders can be different. To solve this problem, we present a discretization scheme based on the trapezoidal rule and a novel numerical integration technique. Then, the gradient formulas of the cost and constraint functions with respect to the decision variables are derived. Furthermore, a gradient-based optimization algorithm for solving the discretized optimal control problem is developed. Finally, the applicability and effectiveness of the proposed algorithm are verified through three non-trivial example problems. [ABSTRACT FROM AUTHOR]

• A numerical integration scheme is proposed to solve the fractional pantograph-delay systems. • A gradient computation procedure is presented for computing the gradients of the cost function. • A gradient optimization is developed for fractional pantograph-delay optimal control problems. In this paper, we consider optimal control of nonlinear fractional-order systems with multiple pantograph-delays, where the fractional-order derivatives are expressed in the Caputo sense. For this problem, we first propose an explicit integration scheme to numerically solve the nonlinear fractional-order system with multiple pantograph-delays and approximate the cost functional using the trapezoidal rule. This yields a series of nonlinear parameter optimization problems. Then, we derive gradients of the cost functions in the resulting problems. Furthermore, we present a gradient-based optimization approach to solve the fractional pantograph-delay optimal control problem. Finally, we validate the proposed solution approach by solving three numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider a three-dimensional horizontal well’s path planning problem, where the well’s path evolves as a combination of several constant-curvature smooth turn segments. The problem is formulated as an optimal switching control problem subject to continuous state inequality constraints. By applying the time-scaling transformation and constraint transcription in conjunction with local smooth approximation technique, the optimal switching control problem is approximated by a sequence of optimal parameter selection problems with only box constraints, each of which is solvable by gradient-based optimization techniques. The optimal path planning problems of the wells Ci-16-Cp146 and Jin27 in Liaohe oil field are solved to demonstrate the applicability of the approach proposed. [ABSTRACT FROM AUTHOR]

Abstract: The main control goal in fed-batch fermentation is to get a high concentration of production. In this paper, a new nonlinear dynamical system, in which the feed rate of glycerol is the control function and the switching instants between the batch and feed processes are the variables, is proposed to formulate the fed-batch fermentation process of glycerol bioconversion to 1,3-propanediol (1,3-PD). To maximize the concentration of 1,3-PD at the terminal time, an optimal control model involving the nonlinear system and subject to the continuous state constraints and the control constraint is presented. To seek the optimal solution of the constrained optimal control problem, the control parametrization enhancing transform together with the constraint transcription technique is first used to convert the constrained optimal control problem into a sequence of mathematical programming problems. An improved Particle Swarm Optimization is subsequently constructed to solve the resultant mathematical programming problem. Numerical results show that, by employing the obtained optimal strategy, 1,3-PD concentration at the terminal time can be increased considerably. [Copyright &y& Elsevier]

In this article, we propose a controlled nonlinear dynamical system with variable switching instants, in which the feeding rate of glycerol is regarded as the control function and the moments between the batch and feeding processes as switching instants, to formulate the fed-batch fermentation of glycerol bioconversion to 1,3-propanediol (1,3-PD). Some important properties of the proposed system and its solution are then discussed. Taking the concentration of 1,3-PD at the terminal time as the cost functional, we establish an optimal control model involving the controlled nonlinear dynamical system and subject to continuous state inequality constraints. The existence of the optimal control is also proved. A computational approach is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that, by employing the optimal control strategy, the concentration of 1,3-PD at the terminal time can be increased considerably. [ABSTRACT FROM PUBLISHER]

A nonlinear dynamical system, in which the feed rates of glycerol and alkali are taken as the control functions, is first proposed to formulate the fed-batch culture of 1,3-propanediol (1,3-PD) production. To maximize the 1,3-PD concentration at the terminal time, a constrained optimal control model is then presented. A solution approach is developed to seek the optimal feed rates based on control vector parametrization method and improved differential evolution algorithm. The proposed methodology yielded an increase by 32.17% of 1,3-PD concentration at the terminal time. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers modelling and optimization of a microbial fed-batch fermentation process. A switched system with variable switching instants is proposed to describe the fermentation process of glycerol bioconversion to 1,3-propanediol (1,3-PD). Taking the concentration of 1,3-PD at the terminal time as the cost function and the switching instants as optimization variables, an optimization model involving switched system and subject to continuous state inequality constraints is then presented. By introducing a time-scaling transform, the optimization model is transcribed into an equivalent one with parameters and fixed switching instants. A computational approach to seek the optimal solution is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that, by employing the optimal switching instants, the concentration of 1,3-PD can be increased considerably compared with previous results. [Copyright &y& Elsevier]

Abstract: The mathematical model and optimal control of microbial fed-batch fermentation is considered in this paper. Since it is decisive for increasing the productivity of 1,3-propanediol (1,3-PD) to optimize the feeding rate of glycerol and the switching instants between the batch and feeding processes in the fermentation process, we propose a new nonlinear dynamical system to formulate the process. In the system, the switching instants are variable and the feed rate of glycerol is regarded as the control function. Some important properties of the proposed system and its solution are then discussed. To maximize the concentration of 1,3-PD at the terminal time, an optimal control model involving the proposed system and subject to continuous state inequality constraints is established. The existence of the optimal control of the model is also proved. Finally, a computational approach is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that the concentration of 1,3-PD at the terminal time can be increased considerably. [ABSTRACT FROM AUTHOR]

Abstract: The goal of planning a horizontal well path is to obtain a trajectory that arrives at a given target subject to various constraints. In this paper, the optimal control problem subject to a nonlinear multistage dynamical system (NMDS) for horizontal well paths is investigated. Some properties of the multistage system are proved. In order to derive the optimality conditions, we transform the optimal control problem into one with control constraints and inequality-constrained trajectories by defining some functions. The properties of these functions are then discussed and optimality conditions for optimal control problem are also given. Finally, an improved simplex method is developed and applied to the optimal design for well Ci-16-Cp146 in Oil Field of Liaohe, and the numerical results illustrate the validity of both the model and the algorithm. [Copyright &y& Elsevier]

Abstract: Flux balance analysis (FBA) is an effective tool in the analysis of metabolic network. It can predict the flux distribution of engineered cells, whereas the accurate prediction depends on the reasonable objective function. In this work, we propose two nonlinear bilevel programming models on anaerobic glycerol metabolism in Klebsiella pneumoniae (K. pneumoniae) for 1,3-propanediol (1,3-PD) production. One intends to infer the metabolic objective function, and the other is to analyze the robustness of the objective function. In view of the models’ characteristic an improved genetic algorithm is constructed to solve them, where some techniques are adopted to guarantee all chromosomes are feasible and move quickly towards the global optimal solution. Numerical results reveal some interesting conclusions, e.g., biomass production is the main force to drive K. pneumoniae metabolism, and the objective functions, which are obtained in term of several different groups of flux distributions, are similar. [Copyright &y& Elsevier]

• A constrained fractional optimal control problem with free terminal time is considered. • The problem is transformed based on time-scaling transformation and numerical integration scheme. • A novel gradient-based optimization is developed to solve the transformed optimization problem. The main purpose of this work is to develop a numerical solution method for solving a class of nonlinear free final time fractional optimal control problems. This problem is subject to equality and inequality constraints in canonical forms, and the orders in the fractional system can be different. For this problem, we first show that, by a time-scaling transformation, the problem can be transformed into an equivalent fractional optimal control problem with fixed final time. We then discretize the transformed fractional optimal control problem by a second-order one-point numerical integration scheme and the trapezoidal rule. Furthermore, we derive the gradient formulae of the cost and constraint functions with respect to decision variables and propose a numerical procedure for calculating these gradients. On this basis, a gradient-based optimization algorithm is developed for solving the resulting problem. Finally, numerical simulations of three example problems illustrate the effectiveness of the developed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a nonlinear piecewise smooth dynamical system of the trajectory of deviated wells according to engineering background. An optimal control model is established and the necessary conditions for optimality are proved via maximum principle. The optimal control problem is solved by a revised Hooke–Jeeves algorithm. The uniform design technique has been incorporated into the revised Hooke–Jeeves algorithm to handle the multimodal function. Computer simulation is used for this paper, and the numerical example illustrates the validity and efficiency of the algorithm. The procedure demonstrates its advantages in practical applications in Liaohe Oil Field. [Copyright &y& Elsevier]

This study aimed at exploring HOXB13 expression and function in gastric cancer (GC), and the underlying molecular mechanism. HOXB13 and fat mass and obesity-associated protein (FTO) expression in GC and non-GC tissues of GC patients were analyzed using Gene Expression Profiling Interactive Analysis (GEPIA) and verified by quantitative reverse transcription-polymerase chain reaction (RT-qPCR) and western blotting. The regulatory relationship between FTO and HOXB13 was verified via RT-qPCR, methylated RNA immunoprecipitation sequencing (MeRIP-seq), and double luciferase reporter gene assay. The effects of HOXB13 and FTO on proliferation, invasion, and migration of GC cells were studied using EdU and Transwell assays. HOXB13 and FTO expression was abnormally high in GC tissues and cell lines, with no significant correlation between HOXB13 and FTO expression and the prognosis of GC patients. Inhibiting FTO expression in GC cells decreased HOXB13 methylation and upregulated HOXB13 expression. Inhibiting HOXB13 and FTO expression suppressed GC cell proliferation, migration, and invasion. Decreased HOXB13 expression suppressed PI3K/AKT/mTOR signaling pathway activity, while atypical HOXB13 expression promoted it. A probable downstream target of HOXB13 was insulin-like growth factor 1 receptor (IGF-1R); a decrease in IGF-1R relieved GC cell migration, invasion, and proliferation and inhibited PI3K/AKT/mTOR signaling pathway activity promoted by atypical HOXB13 expression. HOXB13 and FTO expression is elevated in GC. FTO suppresses HOXB13 methylation; FTO and HOXB13 expression promotes GC cell proliferation, migration, and invasion. HOXB13 expression intensifies GC invasion through PI3K/AKT/mTOR signaling via IGF-1R. HOXB13 and associated signaling pathways can be effective targets for GC therapy. [ABSTRACT FROM AUTHOR]

The high mortality of colorectal cancer (CRC) patients and the limitations of conventional tumor-node-metastasis (TNM) stage emphasized the necessity of exploring hub genes closely related to carcinogenesis and prognosis in CRC. The study is aimed at identifying hub genes associated with carcinogenesis and prognosis for CRC. We identified and validated 212 differentially expressed genes (DEGs) from six Gene Expression Omnibus (GEO) datasets and the Cancer Genome Atlas (TCGA) database. We investigated functional enrichment analysis for DEGs. The protein-protein interaction (PPI) network was constructed, and hub modules and genes in CRC carcinogenesis were extracted. A prognostic signature was developed and validated based on Cox proportional hazards regression analysis. The DEGs mainly regulated biological processes covering response to stimulus, metabolic process, and affected molecular functions containing protein binding and catalytic activity. The DEGs played important roles in CRC-related pathways involving in preneoplastic lesions, carcinogenesis, metastasis, and poor prognosis. Hub genes closely related to CRC carcinogenesis were extracted including six genes in model 1 (CXCL1, CXCL3, CXCL8, CXCL11, NMU, and PPBP) and two genes and Metallothioneins (MTs) in model 2 (SLC26A3 and SLC30A10). Among them, CXCL8 was also related to prognosis. An eight-gene signature was proposed comprising AMH, WBSCR28, SFTA2, MYH2, POU4F1, SIX4, PGPEP1L, and PAX5. The study identified hub genes in CRC carcinogenesis and proposed an eight-gene signature with good reproducibility and robustness at the molecular level for CRC, which might provide directive significance for treatment selection and survival prediction. [ABSTRACT FROM AUTHOR]

Cyclophilin J (CYPJ) is a new member of the peptidyl-prolyl cis/trans-isomerase (PPIase) identified with upregulated expression in human glioma. However, the biological function of CYPJ remained unclear. We aimed to study the role of CYPJ in hepatocellular carcinoma (HCC) carcinogenesis and its therapeutic potential. We determined the expression of CYPJ in HCC/adjacent normal tissues using Western blot, Northern blot and semi-quantitative RT-PCR, analyzed the biochemical characteristics of CYPJ, and resolved the 3D-structure of CYPJ/Cyclosporin A (CsA) complex. We also studied the roles of CYPJ in cell cycle, cyclin D1 regulation, in vitro and in vivo tumor growth. We found that CYPJ expression was upregulated in over 60% HCC tissues. The PPIase activity of CYPJ could be inhibited by the widely used immunosuppressive drug CsA. CYPJ was found expressed in the whole cell of HCC with preferential location at the cell nucleus. CYPJ promoted the transition of cells from G1 phase to S phase in a PPIase-dependent manner by activating cyclin D1 promoter. CYPJ overexpression accelerated liver cell growth in vitro (cell growth assay, colony formation) and in vivo (xenograft tumor formation). Inhibition of CYPJ by its inhibitor CsA or CYPJ-specific RNAi diminished the growth of liver cancer cells in vitro and in vivo. In conclusion, CYPJ could facilitate HCC growth by promoting cell cycle transition from G1 to S phase through the upregulation of cyclin D1. Suppression of CYPJ could repress the growth of HCC, which makes CYPJ a potential target for the development of new strategies to treat this malignancy. [ABSTRACT FROM AUTHOR]