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Clinical biomedical applications of genomic technologies are extensive and provide possibilities to enhance healthcare covering the span of medical talents. Genome disorder prediction is an important issue in biomedical research. Genome disorders cause multivariate diseases such as cancer, dementia, diabetes, Leigh syndrome, etc. Existing machine and deep learning-based methods were introduced to forecast genome disorders. However, the genome prediction outcomes were not sufficient. To address this issue, propose a new method called Quadratic Feynman Polynomial Interpolated and Vector Nearest Centroid-based (QFPI-VNC) for acutely predicting the genome disorder with improved sensitivity and specificity. First, we utilized medical data about children from a public genomes dataset and applied it to Linear Quadratic and Feynman Kac Genome filtering to obtain computationally efficient filtered results. Next, the results are fed to the Concordance Correlated Polynomial Interpolation with the purpose of extracting genome wide data in an accurate manner. Finally, the features extracted are fused and fed to the Support Vector and Nearest Centroid model for genome disorder prediction. Experimental investigations of the proposed method employing the genome dataset confirm that the performance of the proposed method is prospective and in the scope of acceptance with relative to state-of-the-art methods in terms of convergence speed, recognition rate, sensitivity, and specificity. Results suggest that the QFPI-VNC method produces the best performance with a higher genome disease detection rate by 14%, accuracy by 11%, sensitivity by 14% specificity by 12%, and lesser convergence speed by 29% than compared to state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Abstract Clinical biomedical applications of genomic technologies are extensive and provide possibilities to enhance healthcare covering the span of medical talents. Genome disorder prediction is an important issue in biomedical research. Genome disorders cause multivariate diseases such as cancer, dementia, diabetes, Leigh syndrome, etc. Existing machine and deep learning-based methods were introduced to forecast genome disorders. However, the genome prediction outcomes were not sufficient. To address this issue, propose a new method called Quadratic Feynman Polynomial Interpolated and Vector Nearest Centroid-based (QFPI-VNC) for acutely predicting the genome disorder with improved sensitivity and specificity. First, we utilized medical data about children from a public genomes dataset and applied it to Linear Quadratic and Feynman Kac Genome filtering to obtain computationally efficient filtered results. Next, the results are fed to the Concordance Correlated Polynomial Interpolation with the purpose of extracting genome wide data in an accurate manner. Finally, the features extracted are fused and fed to the Support Vector and Nearest Centroid model for genome disorder prediction. Experimental investigations of the proposed method employing the genome dataset confirm that the performance of the proposed method is prospective and in the scope of acceptance with relative to state-of-the-art methods in terms of convergence speed, recognition rate, sensitivity, and specificity. Results suggest that the QFPI-VNC method produces the best performance with a higher genome disease detection rate by 14%, accuracy by 11%, sensitivity by 14% specificity by 12%, and lesser convergence speed by 29% than compared to state-of-the-art methods.

This paper presents a successive approximation method for decentralized strategy design in the large-scale linear quadratic (LQ) Gaussian game. The strategy consists of transforming the original mean field game (MFG) problem into solving decoupled ordinary differential equations (ODEs) whose numerical solutions are obtained by a new two-loop iteration algorithm. It should be noted that we employ the augmented model technique and the LQ framework to derive these low-dimensional solvable ODEs, which is the cornerstone of constructing the decentralized ε -Nash strategy. In addition, the quadratic ODEs contained therein are approximately solved for by a sequence of iterative linear ordinary differential equations (LODEs) with guaranteed convergence. A numerical example is given to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Aiming at the objective uncertainty, subjective uncertainty, and extreme events may be in a dynamic system simultaneously. This paper focuses on the differential game problem of a linear quadratic jump uncertain stochastic system. The system is described by both a jump uncertain differential equation and a stochastic differential equation. The principle of optimality and equation of optimality are established. Then, a differential game model based on linear quadratic jump uncertain stochastic system is constructed. Furthermore, Nash equilibrium are discussed by using the obtained equation. Finally, its application in the dynamic investment decision of enterprises is given, and numerical simulations are performed. This approach offers a new method for quantitative analysis in future studies.

This paper considers a linear‐quadratic mean field control problem involving a major agent and N minor agents. We aim to optimize a social cost as a weighted sum of the individual costs under decentralized information. Firstly, the forward‐backward stochastic difference equations (FBSDEs) are obtained for this problem by variational analysis. Then, by decoupling the FBSDEs, we design the decentralized control laws, which are further shown to be asymptotically optimal. [ABSTRACT FROM AUTHOR]

In this paper, various modern model based optimal control methods (as well as one model-free or data-driven) are applied to the dynamical positioning problem of vessels, i.e. we seek to control the surge, sway and yaw motion, using the thrusters and propellers, subject to environmental disturbances, i.e. wind and current. The low-frequency part of Balchen's nonlinear vessel model is selected for these tests.

The paper aims to develop a new method for the design of hybrid multivariable automatic control systems. We determine a hybrid control system as a system that includes two different types of parallel operating controllers. The paper's aim is achieved by solving the following tasks. The first task is to develop a method for the design of hybrid control systems. Investigated systems include PI controllers and a linear-quadratic controller. The second task is to investigate the resulting control system. The investigation is based on direct quality indicators, robustness, and fragility analyses. The most significant result of the paper is the development of a method for the tuning of a linear-quadratic controller, which should work with the decentralized control system in parallel. BLT (Biggest Log Modulus) method is used for decentralized control system tuning. BLT is a well-known method of PI controller detuning. The idea of BLT is to ensure the robustness of multivariable control systems tuned by Ziegler Nichols's rules. The proposed method for the design of the control system is not complicated. The possibility of correcting the tunings of decentralized controllers remains. Design of the new hybrid automatic control system for the distillation plant made using the developed method. The analysis of the dynamic properties of the designed control system showed that the use of a parallel linear-quadratic controller provides a small percentage of overshoot in the control by the reference and high accuracy of stabilizing the values of controlled variables at the largest disturbances. At the same time, the robustness does not decrease and the control system remains fragile, i.e., it is possible to change the settings of the controllers without significant loss of robustness. [ABSTRACT FROM AUTHOR]

The second-order systems can capture the dynamics of a vast majority of industrial processes. However, the existence of uncertainty in second-order approximation of such processes is inevitable because the approximation may not be accurate or the operating condition changes, resulting in performance degradation or even instability. This article aims at designing a novel robust proportional–integral–derivative controller for the uncertain second-order delay-free and time-delay systems in an optimal manner. The method is simple, effective, and can efficiently improve the performance of the uncertain systems. The approach is based on the linear quadratic theory, in which by adding a new matrix in the quadratic cost function regarding the uncertainties, the stability of the perturbed system is guaranteed and proven for both time-delay and delay-free second-order cases. The comparison with the recent works in the literature supports the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

We investigate a class of zero-sum linear-quadratic stochastic differential games on a finite time horizon governed by slow and fast state equations. The slow-fast nature of the problem can be leveraged to reformulate the associated generalized Riccati equation as a deterministic singular perturbation problem. In doing so, we show that as the evolutionary speed of the slow and fast processes diverge, the existence of a solution to the associated generalized Riccati equation is guaranteed by the existence of a solution to a decoupled pair of differential and algebraic Riccati equations with a reduced order of dimensionality. Furthermore, we are able to formulate a pair of asymptotic estimates to the value function of the game problem by constructing an approximate feedback strategy and observing the limiting value function. [ABSTRACT FROM AUTHOR]

This paper studies two types of linear quadratic (LQ) optimal control models for multistage uncertain random systems. The first model is an LQ model with additive noises, while the second model is an LQ model with both multiplicative noises and additive noises. Chance theory is a useful tool to deal with the analysis of indeterminacy including both uncertainty and randomness. Based on Bellman's principle and chance theory, the recurrence equations are presented for settling such optimal control problems. Then, by applying recurrence equations, the analytical expressions are derived for solving both the optimal objective function and optimal control strategies of the LQ models. Meanwhile, an application and a numerical example are provided to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights for the state and control in the costs. The authors employ a rescaling approach to derive a low dimensional Riccati ordinary differential equation (ODE) system, which characterizes a necessary and sufficient condition for asymptotic solvability. The rescaling technique is further used for performance estimates, establishing an O(1/N)-Nash equilibrium for the obtained decentralized strategies. [ABSTRACT FROM AUTHOR]

This paper investigates an infinite-horizon linear quadratic stochastic optimal control (LQSOC) problem with state- and control-dependent noises, in which two system matrices are unknown. First, a deterministic system is introduced and a relationship among its system trajectory, its control and the matrices to be solved is formulated. Subsequently, based on the deterministic system, an adaptive dynamic programming (ADP) algorithm is established to tackle the LQSOC problem. Then, the convergence analysis is presented by proving the equivalence between the proposed algorithm and an existing policy iteration algorithm. Finally, the effectiveness of the obtained algorithm is verified by a perturbed turbocharged diesel engine optimal control design example. [ABSTRACT FROM AUTHOR]

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La prescription de la dose en radiothérapie est actuellement basée sur des abaques qui ne prennent pas en compte la complexité de la relation patient/dose/effet. Leurs performances prédictives tant sur l'efficacité anti-tumorale que sur la toxicité peuvent être améliorées par l'utilisation de modèles radiobiologiques. C'est dans cette optique qu'ont été développés les modèles de calculs TCP (Tumor Control Probability) et NTCP (Normal Tissue Complication Probability). Leur construction comporte plusieurs étapes importantes utiles à comprendre. La première étape est basée sur les modèles radiobiologiques permettant de définir de manière plus ou moins complexe des taux de cellules survivantes après irradiation. Deux étapes supplémentaires sont nécessaires pour convertir la dose physique en dose biologique équivalente, notamment en dose biologique équivalente à 2 Gy (EQD 2) ; d'une part, pour prendre en compte l'effet du fractionnement de la dose, tant pour le volume cible que les organes à risque, et d'autre part, pour réaliser sa conversion en une dose uniforme qui permet de modéliser l'effet produit par une dose hétérogène sur un organe (dose uniforme équivalente généralisée (gEUD) de Niemierko). Enfin, les modèles radiobiologiques de prédiction des effets cliniques transforment les doses en probabilités de contrôle tumoral (TCP) ou de toxicité (NTCP) en recourant aux paramètres qui rendent compte des caractéristiques radiobiologiques des tissus en question. L'utilisation de ces modèles est encore limitée en pratique courante mais comme les logiciels de radiothérapie en propose l'utilisation, il est important d'en connaître les conditions d'application. In radiotherapy, the dose prescription is currently based on discretized dose-effects records that do not take into fully account for the complexity of the patient-dose-response relationship. Their predictive performance on both anti-tumour efficacy and toxicity can be optimized by integrating radiobiological models. It is with this in mind that the calculation models TCP (Tumor Control Probability) and NTCP (Normal Tissue Complication Probability) have been developed. Their construction involves several important steps that are necessary and important to understand. The first step is based on radiobiological models allowing to calculate according to more or less complexity the rate of surviving cells after irradiation. Two additional steps are required to convert the physical dose into an equivalent biological dose, in particular a 2 Gy equivalent biological dose (EQD2): first to take into account the effect of the fractionation of the dose for both the target volume and the organs at risk; second to convert an heterogeneous dose to an organ into an homogeneous dose having the same effect (Niemierko generalized equivalent uniform dose (gEUD)). Finally, the process of predicting clinical effects based on radiobiological models transform doses into tumour control (TCP) or toxicity (NTCP) probabilities using parameters that reflect the radiobiological characteristics of the tissues in question. The use of these models in current practice is still limited, but since the radiotherapy softwares increasingly integrate them, it is important to know the principle and limits of application of these models. [ABSTRACT FROM AUTHOR]

In this paper, the ride performance of a vehicle with active suspension and Linear Quadratic Gaussian (LQG) controller has been studied and is compared to the performances of a traditional passive suspension system. The study includes variables that are related to a passenger’s comfort: vertical position, vertical velocity, pitch angle, pitch velocity, roll angle, and roll velocity. The performances of the two systems are evaluated by maximum values and root mean square (RMS) of the variables when riding on a sinusoidal road profile. The simulation results show that the vehicle with active suspension and LQG controller performs better than passive suspension system where the maximum values decrease by 85.77%, 92.73%, 50.31% 86.83%, 89.41%, 43.28%, and RMS values decrease by 88.59%, 92.36%, 42.99%, 87.61%, 90.85%, and 42.79% for vertical position, vertical velocity, pitch angle, pitch velocity, roll angle, and roll velocity, respectively. [ABSTRACT FROM AUTHOR]

Proximity operations offer aggregate capability for a spacecraft operating in close proximity to another spacecraft, to perform on-orbit satellite servicing, or to a space object to perform debris removal. To utilize a spacecraft performing such advanced maneuvering operations and perceiving of the relative motion of a foreign spacecraft, these trajectories must be modeled accurately based on the coupled translational and rotational dynamics models. This paper presents work towards exploiting the dual-quaternion representations of spacecraft relative dynamics for proximity operations and developing a sub-optimal control law for efficient and robust maneuvers. A linearized model using dual-quaternions for the proximity operation was obtained, and its stability was verified using Monte Carlo simulations for the linear quadratic regulator solution. A sub-optimal control law using generalized higher order feedback gains in dual-quaternion form was developed based on small error approximations for the proximity operation and also verified through Monte Carlo simulations. Necessary information needed to understand the theory behind the use of the dual-quaternion is also overviewed within this paper, including the validity of using the dual-quaternions against their Cartesian or quaternion equivalents.

Lightweight optical mirrors usually play key roles in aerospace and optical structural systems applied to space telescopes, radars, solar collectors, communication antennas, etc. Due to their high flexibility and low damping properties, external excitations such as orbital maneuver may induce unexpected oscillations and thus reduce their working performance. Active vibration control is therefore essential for the lightweight optical mirror systems. In this spirit, a lightweight mirror structronic system with a linear quadratic optimal controller is presented. The mirror is modeled as a membrane plate with pretension and distributed polyvinylidene fluoride sensors and actuators. The sensing sensitivity of the piezoelectric (PVDF) sensors and the modal actuation factor of the PVDF actuators are derived. The state-space equations are established and the feedback control gains between sensing and control signals are obtained. Sensor and actuator of different shape, size, and position are employed to actively control the first four natural modes of the mirror. The influences of mode order, pretension, and the two weighting factors Q and R on the control performance are also investigated. Analytical results in this paper could guide the design and layout of the PZT sensor and actuator on lightweight membrane plate mirrors. [ABSTRACT FROM AUTHOR]

In this paper, a linear quadratic (LQ) optimal control model is studied for a multistage uncertain random system. First, recurrence equations are presented for this model based on Bellman's Principle. Second, analytical expressions are derived for solving both the optimal objective function and the optimal control strategy of the model. Finally, an example is given to illustrate our results. [ABSTRACT FROM AUTHOR]