Affine Model Research Articles

Observer-Based Output Feedback Control of Nonlinear 2-D Systems via Fuzzy-Affine Models

Through Takagi-Sugeno fuzzy affine models, the observer-based output feedback control of discrete-time nonlinear two-dimensional systems is investigated, where the two-dimensional system information evolves dynamically along two independent directions. A piecewise fuzzy affine observer is designed to estimate the unmeasurable system states, and two enhanced observer-based piecewise output feedback control approaches are then developed. By making sufficient use of Young’s matrix inequality with its variant, novel and less conservative observer-based piecewise output feedback controller design results are proposed via piecewise quadratic Lyapunov functions. Simulation studies on a doubly-indexed nonlinear process are provided to illustrate the effectiveness of the developed approaches.

Nominal U.S. Treasuries Embed Liquidity Premiums, Too: An Affine Model of the Term Structure

Nominal U.S. Treasuries Embed Liquidity Premiums, Too: An Affine Model of the Term Structure

Explicit Model Predictive Based Fault Tolerant Control for Turboshaft Engine System

In order to tackle the faults of turboshaft engine-rotor systems and the real time implementation difficulty of traditional model predictive control methods, an explicit model predictive (EMPC) fault-tolerant control algorithm is designed based on an active fault-tolerant control scheme that implicitly detects the faults and adjusts the control law online. The proposed real time control algorithm can achieve good control command tracking performance and, at the same time, guarantee limit protection of turboshaft engine-rotor system. Firstly, to start with the algorithm, a dynamic system model library and a fault monitoring mechanism are established, in which the dynamic system model library contains sets of piecewise affine models (PWA) of normal engine mode and modes with faults. Secondly, the EMPC fault-tolerant controller is derived and designed for each sub-model in the modes of dynamic model library. Through the transformation and derivation of the traditional model predictive controller of turboshaft engine-rotor system, the explicit solution of its fault-tolerant controller is obtained. With the explicit solution which is in the form of state feedback control for each partition, controller gains can be designed off-line. Finally, the online engine control process is completed by searching the corresponding controller gain based on engine state, which improves the real-time performance of the control system. The effectiveness of the method for engine systems with modeled or un-modeled compressor faults and the robustness of the algorithm are verified by simulations.

Locally Nonlinear Affine Verification for Multisensor Image Matching

Matching local features between two overlapped images is a fundamental task in photogrammetry and remote sensing. However, images acquired by multiple sensors often differ substantially in properties, thus posing a great challenge to the robustness and flexibility of feature matching methods. In this article, we propose a locally non-linear affine verification (LAV) method for robust multisensor image matching. The main idea of the LAV is the development of a nonlinear regression formulation that practically models the nonlinear deviation of a real surface around a point from its tangent plane during affine verification. Specifically, we start by selecting a restricted set of reliable and well-distributed putative matches as the matching seeds and assign them with neighbors to construct search spaces. In each search space, the regression seeks the smoothest affine model consistent with the latent correct matches, thereby deriving a set of affine parameters to verify correspondence hypotheses for true matches. The verification can be extended to all nearest neighbor matches to discover additional inlier matches. Evaluation on multisensor image datasets with different extents of variations in viewpoint, scale, illumination, and appearance shows that the proposed LAV consistently outperforms existing methods. LAV can achieve a considerable number of high-quality matches, in cases where existing methods provide few or no correct matches.

Deep multiple affinity model for proposal-free single instance segmentation

Deep multiple affinity model for proposal-free single instance segmentation

Artificial Intelligence for Stability Control of Actuated In–Wheel Electric Vehicles with CarSim® Validation

This paper presents an active controller for electric vehicles in which active front steering and torque vectoring are control actions combined to improve the vehicle driving safety. The electric powertrain consists of four independent in–wheel electric motors situated on each corner. The control approach relies on an inverse optimal controller based on a neural network identifier of the vehicle plant. Moreover, to minimize the number of sensors needed for control purposes, the authors present a discrete–time reduced–order state observer for the estimation of vehicle lateral and roll dynamics. The use of a neural network identifier presents some interesting advantages. Notably, unlike standard strategies, the proposed approach avoids the use of tire lateral forces or Pacejka’s tire parameters. In fact, the neural identification provides an input–affine model in which these quantities are absorbed by neural synaptic weights adapted online by an extended Kalman filter. From a practical standpoint, this eliminates the need of additional sensors, model tuning, or estimation stages. In addition, the yaw angle command given by the controller is converted into electric motor torques in order to ensure safe driving conditions. The mathematical models used to describe the electric machines are able to reproduce the dynamic behavior of Elaphe M700 in–wheel electric motors. Finally, quality and performances of the proposed control strategy are discussed in simulation, using a CarSim® full vehicle model running through a double–lane change maneuver.

INFLATION, CENTRAL BANK AND SHORT-TERM INTEREST RATES: A NEW MODEL WITH CALIBRATION TO MARKET DATA

In this paper, we propose a new model for the joint evolution of the inflation rate, the Central Bank official interest rate and the short-term interest rate. Our model takes into account the fact that the Central Bank interest rate changes at random times, inflation is measured at fixed, regular times, while the short-term interest rate evolves essentially continuously. We derive the valuation equation for a contingent claim and show that it has a unique solution. The payoff may depend on all three economic factors of the model and the discount factor is allowed to include inflation. Our model is not an affine model. Although in some special cases the solution of the valuation equation might admit a closed form, in general it has to be solved numerically. This can be done efficiently by the algorithm that we provide. Taking as a benchmark the model of [H. W. Ho, H. H. Huang & Y. Yildirim (2014) Affine model of inflation-indexed derivatives and inflation risk premium, European Journal of Operational Research 235, 159–169], we show that our model performs better on European market data from 2008 to 2015. Our model uses many fewer parameters than the benchmark model: This is advantageous from the numerical point of view and suggests that our model describes the behavior of the economic factors more closely.

An Extension of the Five‐factor Affine Term Structure Model: Predicting Future Bond Returns*

AbstractWe investigate time‐varying risk premia in Korean government bonds using a five‐factor affine model. The model generates nearly perfectly fitted yields and estimates the bonds’ expected returns with more precision than the four‐factor model. We also find the statistically significant predictive power of the model for future bond returns using forward rates from cross‐sectional and time‐series regressions. The predictive power varies in time for bonds with different maturities and reverts to the mean values for short‐ and long‐term bonds, while showing a sign of momentum for medium‐term bonds. In out‐of‐sample exercises, the predictive power is even enhanced when volatility increases.

Affine arbitrage-free yield net models with application to the euro debt crisis

We develop a parsimonious class of affine arbitrage-free yield net models for consistent bond pricing across maturities and issuers of different risk levels. Containing a core curve and multiple peripheral curves, the yield net is spanned by three layers of factors: base factors spanning all curves, and common and individual spread factors. Under the arbitrage-free assumption, we prove a parsimonious solution to the risk-neutral process that guarantees joint identification of parameters and latent states. By using a Bayesian estimation method with a marginal Metropolis–Hastings algorithm and specification tests based on MCMC output, we apply the model to weekly treasury yields of Germany, Italy, Spain, and Greece from 2009 to 2016. The results show that the extracted common credit risk is a level factor in spread, and market liquidity risk is a slope factor. Further, the net structure helps reconstruct the Greek yield curve even with only its 10-year yield available throughout the sample.

A point cloud-based deep learning strategy for protein–ligand binding affinity prediction

There is great interest to develop artificial intelligence-based protein-ligand binding affinity models due to their immense applications in drug discovery. In this paper, PointNet and PointTransformer, two pointwise multi-layer perceptrons have been applied for protein-ligand binding affinity prediction for the first time. Three-dimensional point clouds could be rapidly generated from PDBbind-2016 with 3772 and 11327 individual point clouds derived from the refined or/and general sets, respectively. These point clouds (the refined or the extended set) were used to train PointNet or PointTransformer, resulting in protein-ligand binding affinity prediction models with Pearson correlation coefficients R = 0.795 or 0.833 from the extended data set, respectively, based on the CASF-2016 benchmark test. The analysis of parameters suggests that the two deep learning models were capable to learn many interactions between proteins and their ligands, and some key atoms for the interactions could be visualized. The protein-ligand interaction features learned by PointTransformer could be further adapted for the XGBoost-based machine learning algorithm, resulting in prediction models with an average Rp of 0.827, which is on par with state-of-the-art machine learning models. These results suggest that the point clouds derived from PDBbind data sets are useful to evaluate the performance of 3D point clouds-centered deep learning algorithms, which could learn atomic features of protein-ligand interactions from natural evolution or medicinal chemistry and thus have wide applications in chemistry and biology.

On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approach

Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results.

Study on Multi-Model Soft Sensor Modeling Method and Its Model Optimization for the Fermentation Process of Pichia pastoris.

The problems that the key biomass variables in Pichia pastoris fermentation process are difficult measure in real time; this paper mainly proposes a multi-model soft sensor modeling method based on the piecewise affine (PWA) modeling method, which is optimized by particle swarm optimization (PSO) with an improved compression factor (ICF). Firstly, the false nearest neighbor method was used to determine the order of the PWA model. Secondly, the ICF-PSO algorithm was proposed to cooperatively optimize the number of PWA models and the parameters of each local model. Finally, a least squares support vector machine was adopted to determine the scope of action of each local model. Simulation results show that the proposed ICF-PSO-PWA multi-model soft sensor modeling method accurately approximated the nonlinear features of Pichia pastoris fermentation, and the model prediction accuracy is improved by 4.4884% compared with the weighted least squares vector regression model optimized by PSO.

Amino acid environment affinity model based on graph attention network.

Proteins are engines involved in almost all functions of life. They have specific spatial structures formed by twisting and folding of one or more polypeptide chains composed of amino acids. Protein sites are protein structure microenvironments that can be identified by three-dimensional locations and local neighborhoods in which the structure or function exists. Understanding the amino acid environment affinity is essential for additional protein structural or functional studies, such as mutation analysis and functional site detection. In this study, an amino acid environment affinity model based on the graph attention network was developed. Initially, we constructed a protein graph according to the distance between amino acid pairs. Then, we extracted a set of structural features for each node. Finally, the protein graph and the associated node feature set were set to input the graph attention network model and to obtain the amino acid affinities. Numerical results show that our proposed method significantly outperforms a recent 3DCNN-based method by almost 30%.

Quantitative prediction model for affinity of drug\u2013target interactions based on molecular vibrations and overall system of ligand-receptor

BackgroundThe study of drug–target interactions (DTIs) affinity plays an important role in safety assessment and pharmacology. Currently, quantitative structure–activity relationship (QSAR) and molecular docking (MD) are most common methods in research of DTIs affinity. However, they often built for a specific target or several targets, and most QSAR and MD methods were based either on structure of drug molecules or on structure of receptors with low accuracy and small scope of application. How to construct quantitative prediction models with high accuracy and wide applicability remains a challenge. To this end, this paper screened molecular descriptors based on molecular vibrations and took molecule-target as a whole system to construct prediction models with high accuracy-wide applicability based on dissociation constant (Kd) and concentration for 50% of maximal effect (EC50), and to provide reference for quantifying affinity of DTIs.ResultsAfter comprehensive comparison, the results showed that RF models are optimal models to analyze and predict DTIs affinity with coefficients of determination (R2) are all greater than 0.94. Compared to the quantitative models reported in literatures, the RF models developed in this paper have higher accuracy and wide applicability. In addition, E-state molecular descriptors associated with molecular vibrations and normalized Moreau-Broto autocorrelation (G3), Moran autocorrelation (G4), transition-distribution (G7) protein descriptors are of higher importance in the quantification of DTIs.ConclusionThrough screening molecular descriptors based on molecular vibrations and taking molecule-target as whole system, we obtained optimal models based on RF with more accurate-widely applicable, which indicated that selection of molecular descriptors associated with molecular vibrations and the use of molecular-target as whole system are reliable methods for improving performance of models. It can provide reference for quantifying affinity of DTIs.

External-memory Dictionaries in the Affine and PDAM Models

Storage devices have complex performance profiles, including costs to initiate IOs (e.g., seek times in hard drives), parallelism and bank conflicts (in SSDs), costs to transfer data, and firmware-internal operations. The Disk-access Machine (DAM) model simplifies reality by assuming that storage devices transfer data in blocks of size B and that all transfers have unit cost. Despite its simplifications, the DAM model is reasonably accurate. In fact, if B is set to the half-bandwidth point, where the latency and bandwidth of the hardware are equal, then the DAM approximates the IO cost on any hardware to within a factor of 2. Furthermore, the DAM model explains the popularity of B-trees in the 1970s and the current popularity of B ɛ -trees and log-structured merge trees. But it fails to explain why some B-trees use small nodes, whereas all B ɛ -trees use large nodes. In a DAM, all IOs, and hence all nodes, are the same size. In this article, we show that the affine and PDAM models, which are small refinements of the DAM model, yield a surprisingly large improvement in predictability without sacrificing ease of use. We present benchmarks on a large collection of storage devices showing that the affine and PDAM models give good approximations of the performance characteristics of hard drives and SSDs, respectively. We show that the affine model explains node-size choices in B-trees and B ɛ -trees. Furthermore, the models predict that B-trees are highly sensitive to variations in the node size, whereas B ɛ -trees are much less sensitive. These predictions are born out empirically. Finally, we show that in both the affine and PDAM models, it pays to organize data structures to exploit varying IO size. In the affine model, B ɛ -trees can be optimized so that all operations are simultaneously optimal, even up to lower-order terms. In the PDAM model, B ɛ -trees (or B-trees) can be organized so that both sequential and concurrent workloads are handled efficiently. We conclude that the DAM model is useful as a first cut when designing or analyzing an algorithm or data structure but the affine and PDAM models enable the algorithm designer to optimize parameter choices and fill in design details.

Machine learning based model linearization of a wind turbine for power regulation

ABSTRACT Wind turbine systems exhibit highly nonlinear dynamics influenced by the aerodynamic torque induced in the wind turbine blades and thrust force on the turbine structure due to the wind flow. This paper presents a system identification approach to approximate the nonlinear wind turbine model. A clustering-based piecewise affine system identification technique is utilized to construct an affine multiple-model that is valid for the power regulation region of a wind turbine. A comprehensive study is performed to validate the accuracy and performance of the developed model. The piecewise affine model identified in this paper can be widely used for advanced control systems design and the security assessment of the power grid.

Influence of SiO2 Nanoparticles and Surfactants on Extraction Efficiency: Sensitivity Analysis

AbstractThe improvement of mass transfer in liquid‐liquid extraction systems of pulsed packed columns has recently attracted much attention. The influence of nanoparticle and surfactant concentration on hydrodynamic characteristics and the mass transfer coefficient in the liquid phase were evaluated. The addition of nanoparticles increases the diffusion and mass transfer, but they are not stable in this system. One possibility to improve the sustainability of nanoparticles is the simultaneous application of a surfactant and nanoparticles. A slightly higher concentration of surfactant resulted in a significant improvement in extraction efficiency. The Newman, Krong, and Hendlos theories and chemical affinity model were applied to study the mass transfer in the chemical system with and without nanoparticles.

Volatility Bursts: A Discrete-Time Option Model with Multiple Volatility Components

Abstract I propose an affine discrete-time model, called Vector Autoregressive Gamma with volatility Bursts (VARG-B) in which volatility experiences, in addition to frequent and small changes, periods of sudden and extreme movements generated by a latent factor which evolves according to the Autoregressive Gamma Zero process. A key advantage of the discrete-time specification is the possibility of estimating the model using Kalman Filter techniques. Moreover, the VARG-B model leads to a fully analytic conditional Laplace transform which boils down to a closed-form option pricing formula. When estimated on S&P500 index options and returns, the new model provides more accurate option pricing and modeling of the IV surface compared with some alternative models.

Convertible bond valuation with regime switching

We present a valuation formula for convertible bonds with regime-switching market conditions by decomposing the convertible bond into a coupon-bearing bond and the American-type exchange option. A coupon-bearing bond component is modeled with a four-factor model: a two-factor affine model for the risk-free rate and a two-factor affine model with stochastic volatility for the credit spreads on the coupon-bearing bond component. We also derive a new valuation formula for the American-type exchange option component.

Sliding Mode Control-Based Autonomous Control of a Tri-rotor Unmanned Aerial Vehicle

A nonlinear control technique for autonomous control of a tri-rotor unmanned aerial vehicle is presented in this paper. First, a comprehensive mathematical model is developed using the Newton–Euler approach for a tri-rotor, which is found to be highly nonlinear and coupled. Then, the equivalent input affine model is extracted by applying a suitable transformation. Finally, the sliding mode control for trajectory tracking is chosen which is immune to matched external disturbances, parametric uncertainties, and modeling errors. The proposed controller performance has been verified for appropriate inputs under wind disturbances using MATLAB, and the simulation results are presented.