Linearized Research Articles

Implementation Method of the Robot Adaptation to Contact Interaction Mode Changes Using Deep Fully Connected Neural Networks

Purpose of research. The present paper conserns the problem of using reaction predictors in the control system of bipedal walking robots. The main advantage of using predictors is the ability to exclude unknown reaction forces from the dynamics equations and, consequently, from the robot control problem statements based on the model. An additional advantage of predictor setting of control tasks is also discussed in the paper, namely the possibility of its use to predict changes in contact interaction modes, such as slipping motion or foot lifting from the supporting surface.Methods. The following methods are used in the research: the method of dynamics of multi-mass systems is necessary for developing a mathematical model of the behavior of a walking robot and describing its contact interaction with the support surface, the method of neural networks is used to develop a predictor that allows one to forecast the values of reactions between the robot’s foot and the surface.Results. The paper shows that there is a connection between the frequencies of the harmonic components of robot movements (the ratio p of these frequencies in the experiment and the training sample) and the quality of reactions predictor operation of the support surface. This indicates the importance of applying a representative spectrum of walking robot movement frequencies in forming a training sample, and the poor generalizability of the predictor in relation to movement frequency.Conclusion. The paper has considered the use of a reaction predictor to identify the possibility of changing the mode of contact interaction, based on the measurement of discrepancies between local linearizations for various discrete steps. The results obtained in this work will be used in the development of a motion control system for a bipedal walking robot, which allows the device to adapt to the parameters of the support surface on which the movement occurs.

Trapping characteristics of magnetic rod-like particles flowing in a cylindrical pipe by means of a non-uniform magnetic field (Brownian dynamics simulations)

We have elucidated the feasibility of trapping magnetic rod-like particles that flow in a cylindrical pipe in terms of a non-uniform magnetic field. We have performed Brownian dynamics (BD) simulations in order to clarify the influence that various factors have on the attachment or trapping characteristics of magnetic rod-like particles to the poles. The employment of a local linearisation approximation enables us to apply the BD method that was fully-developed for a simple shear flow to the present Hagen-Poiseuille flow. In the case of a sufficiently small magnetic interaction between the particles, numerous rod-like particles may attach to the magnetic poles if the influence of a non-uniform magnetic field is sufficiently more dominant than that of the flow field, otherwise, the particles flow away along the centreline of the cylindrical pipe. If the magnetic interactions are sufficiently more dominant than both the flow field and the non-uniform magnetic field, the particles aggregate to form densely-packed clusters that flow away along the centreline area of the pipe without being trapped at the poles. In the situation of insufficient magnetic interactions, thin chain-like clusters may be formed from several anchored particles trapped to the poles and incline in the downstream direction.

Numerical spectral examination of EMHD mixed convective flow of second-grade nanofluid towards a vertical Riga plate using an advanced version of the revised Buongiorno’s nanofluid model

Present communication aims to determine the impact of Cattaneo–Christov model and convective boundary on second-grade nanofluid flow alongside a Riga pattern. Zero mass flux is accounted at the solid surface of Riga pattern such that the fraction of nanoparticles maintains itself on strong retardation. The impact of Lorentz forces generated by Riga pate is also an important aspect of the study. The governing nonlinear problem is converted into ordinary problems via suitably adjusted transformations. Spectral local linearization method has been incorporated to find the solutions of the nonlinear problems. Variation in horizontal movement of the nanofluid, thermal distribution and concentration distribution of the nanoparticles has been noted for various fluid parameters. The results are plotted graphically. Outcomes indicate that the horizontal movement gains enhancement for elevated values of modified Hartman factor. Thermal state of the nanofluid and concentration of nanoparticles receive reduction for incremental values of relaxation time parameters. Numerical results for skin friction and heat flux have been reported in tabular form. The CPU run time and residual error are obtained to check the efficiency of the method used for finding the solution.

A bi-level programing for wildfire self-evacuation network design

A non-linear bi-level problem is suggested in this paper for wildfire self-evacuation planning, the upper problem of which includes binary variables and the lower problem includes continuous variables. In this model, the upper problem selects a number of links and adds them to the available evacuation network. It, moreover, predicts the traffic balance, and the time window of the links in the lower problem. A part of the objective function in the bi-level problem is non-linear which is linearized with a linear approximation method that does not require binary variables. Then the linear bi-level model is reformulated as a non- linear single level problem. This model is linearized and transferred into Mixed Integer Programing. The model is then used for the real case study of the Beechworth fire in 2009. The resulted outputs of the model are beneficial in planning design schemes for emergency evacuation to use the maximum potential of the available transportation network.

Active vibration control of nonlinear stiffened FG cylindrical shell under periodic loads

Active control of nonlinear vibration of stiffened functionally graded (SFG) cylindrical shell is studied in this paper. The system is subjected to axial and transverse periodic loads in the presence of thermal uncertainty. The material composition is considered to be continuously graded in the thickness direction, also these properties depend on temperature. The relations of straindisplacement are derived based on the classical shell theory and the von Karman equations. For modeling the stiffeners on the cylindrical shell surface, the smeared stiffener technique is used. The Galerkin method is used to discretize the partial differential equations of motion. Some comparisons are made to validate the SFG model. For suppression of the nonlinear vibration, the linear and nonlinear control strategies are applied. For control objectives, the piezoelectric actuator is attached to the external surface of the shell and the thin ring piezoelectric sensor is attached to the middle internal surface of shell. The effect of PID, feedback linearization and sliding mode control on the suppression of vibration for SFG cylindrical shell is presented.

Models and linearizations for the Traveling Car Renter with Passengers

Models and linearizations for the Traveling Car Renter with Passengers

Autonomous Steering of Concentric Tube Robots via Nonlinear Model Predictive Control

This article presents a model predictive controller (MPC) developed for the autonomous steering of concentric tube robots (CTRs). State-of-the-art CTR control relies on differential kinematics developed by local linearization of the CTRs mechanics model and cannot explicitly handle constraints on robot's joint limits or unstable configurations commonly known as snapping points. The proposed nonlinear MPC explicitly considers constraints on the robot configuration space (i.e., joint limits) and the robot's workspace (i.e., mixed boundary conditions on robot curvature). Additionally, the MPC calculates control decisions by optimizing the model-based predictions of future robot configurations. This way, it avoids configurations it cannot recover from, i.e., joint limits, singular configurations, and snapping. The proposed controller is evaluated via simulations and experimental studies with a variety of trajectories of increasing complexity. Simulation results demonstrate the capability of MPC to avoid singularities while satisfying robot mechanical constraints. Experimental results demonstrate that our solution enables following of trajectories unattainable by state-of-the-art controllers with mean error corresponding to $1\%$ of robot arclength.

Wind-tolerant optimal closed loop controller design for a domestic atmospheric research airship

Airships are inherently sensitive to random atmospheric disturbances that could potentially make their data gathering and observation missions a formidable task. In this context robust closed loop feedback controllers are important. The present study is therefore focused on optimal feedback controller design of an indigenous domestically designed airship (DA) for added robustness against atmospheric disturbances. While the general airship six degrees of freedom (6DoF) governing equations of motion are mathematically nonlinear, one often needs to resort to local linearization methods to benefit from proven linear closed loop controller (CLC) design approaches. In this sense an optimal linear quadratic regulator/tracker (LQR/LQT) seems to be a viable alternative for DA control purposes whose implementation relies on local linearization of the 6DoF nonlinear equations around the instantaneous airship trajectory. In order to demonstrate the capabilities of the proposed CLC design against external turbulences, a random wind profile over the DA hull is assumed and the airship behavior is analyzed in regulation as well as the tracking mode. The results show that the proposed CLC design complies with the all mission requirements and adequately reduces the impact of environmental random wind fluctuations. Given the small computational time required for control gain and command determination within the LQR/LQT algorithm against the DA mission flight time, the proposed CLC can be utilized online as a feedback control strategy while the airship is performing any physical atmospheric experiment.

Returns and volume

PurposeThe relationship between returns and trading volume is central in financial economics because it has both a theoretical interest and important practical implications with regard to the structure of financial markets and the level of speculation activity. The aim of this study is to provide new insights into the association between returns and trading volume by investigating their kernel (instantaneous) causality. The empirical analysis relies on time series data from 22 commodities futures markets (agricultural, energy and metals) in the USA.Design/methodology/approachNon-parametric (local linear) regressions are applied to daily data on returns and on trading activity; generalized correlation measures are computed and their differences are subjected to formal statistical testing.FindingsThe results suggest that raw returns are likely to kernel-cause volume and volume is likely to kernel-cause price volatility. The patterns of causal order are generally in line with what is stipulated by the relevant theory, they provide guidance for model specification and they appear to explain the empirical evidence on temporal (lag-lead) causality between the same pairs of variables obtained in earlier works.Originality/valueThe concept of kernel causality has very recently become a part of the toolkit for econometric/statistical analysis. To the best of the author’s knowledge, this is the first study that relies on the notion of kernel (instantaneous) causality to provide new evidence on a relationship that is of keen interest to investors, professional economists and policymakers.

A Novel Numerical Procedure for Simulating Steady MHD Convective Flows of Radiative Casson Fluids over a Horizontal Stretching Sheet with Irregular Geometry under the Combined Influence of Temperature-Dependent Viscosity and Thermal Conductivity

A novel mathematical computing analysis for steady magnetohydrodynamic convective flows of radiative Casson fluids moving over a nonlinearly elongating elastic sheet with a nonuniform thickness is established successfully in this numerical exploration. Also, the significance of an externally applied magnetic field with space-dependent strength on the development of MHD convective flows of Casson viscoplastic fluids is evaluated thoroughly by including the momentous influence of linear thermal radiation along with the temperature-dependent viscosity and thermal conductivity effects. By combining the assumption of the low-inducing magnetic field with the boundary layer approximations, the governing partial differential equations monitoring the current flow model are transmuted accordingly into a set of nonlinear coupled ordinary differential equations by invoking appropriate similarity transformations. Moreover, these derived differential equations are resolved numerically by utilizing a new innovative GDQLLM algorithm integrating the local linearization technique with the generalized differential quadrature method. On the other hand, the behaviours of velocity and temperature fields are deliberated properly through various graphical illustrations and different sets of flow parameters. However, the accurate datasets generated for the skin friction coefficient and local Nusselt number are presented separately in tabular displays, whose physical insights are discussed comprehensively via the slope linear regression method (SLRM). As main results, it is demonstrated that the higher values of the Casson viscoplastic parameter reduce significantly the fluid velocity within the boundary layer region, while a partial reverse tendency is observed near the stretching sheet as long as the wall thickness parameter is increased. Besides the previously mentioned hydrodynamical features, it is also depicted that the thermal field throughout the medium is enhanced considerably with the elevating values of these parameters.

Autonomous Vehicle Trajectory Following: A Flatness Model Predictive Control Approach With Hardware-in-the-Loop Verification

Trajectory following of autonomous vehicle is a challenging task because of the multiple constraints imposed on the plant. Therefore, Model Predictive Control (MPC) is becoming prevail in vehicle motion control as it can explicitly handle system constraints. However, MPC, grounded in real-time iterative optimization, entails a considerable computational burden for current electronic control units. To mitigate the MPC execution load, a popular strategy is to linearize the original (nonlinear) system around the current working point and then design a Linear Time-Varying MPC (LTVMPC). Nevertheless, the successive linearization introduces extra modeling errors, which may impair the control performance. Indeed, if the plant model satisfies the `differential flatness' condition, it can be exactly linearized to the Brunovsky's canonical form. In contrast to the LTV model, this newly appeared linear form reserves all the nonlinear features of the native plant model. Based on this equivalent linear system, a Flatness Model Predictive Controller (FMPC) can be formulated. FMPC on the one hand, improves the control performance over an LTVMPC because it avoids extra modeling errors from the local linearization. On the other hand, it entails a much lighter computational load versus a nonlinear MPC thanks to its linear nature. Real-time simulations conducted on a hardware-in-the-loop system indicate the advantages of the proposed FMPC in autonomous vehicle trajectory following.

Observer-Based Sampled-Data Model-Free Adaptive Control for Continuous-Time Nonlinear Nonaffine Systems With Input Rate Constraints

A sampled-data model-free adaptive control (SMFAC) strategy is proposed for continuous-time nonlinear nonaffine systems with input rate constraints. By using differential and integral mean value theorems as two basic mathematic tools, a sampled-data local dynamic linearization method is proposed at first to transform the continuous-time nonlinear nonaffine model into a sampled-data nonlinear affine I/O model, including a linear parametric term affined to the control input and a nonlinear uncertainty term. On this basis, we consequently propose an observer-based SMFAC (ObSMFAC) scheme, including a sampled-data parameter estimator to estimate the unknown partial derivatives and a sampled-data observer to estimate the residual nonlinear uncertainty, respectively. Note that the sampling period is incorporated explicitly in the proposed ObSMFAC which enhances the control performance by reducing its negative influence on the system stability. The constraint on the input rate is also considered in the control law as the transition condition of the input updating algorithms. The convergence of the proposed ObSMFAC is proved by using the contraction mapping principle. The simulation study demonstrates the theoretical results.

Feedback Linearization-Based Perimeter Controllers for Oversaturated Regions

This paper concerns the perimeter control problem in the oversaturated region. The road network system is a nonlinear system. However, the existing achievements in the perimeter control setting are obtained by partially linearizing the system model around the point of interest, which is a local linearization and probably leads to lower traffic performances. To this end, a feedback linearization-based proportional and integral perimeter controller is developed to regulate the overall traffic state towards the desired accumulation state. Theoretical analysis demonstrates that the proposed feedback linearization-based control method can guarantee the exponentially asymptotic convergence of the protected road network state to the desired one. To evaluate the proposed methodology, extensive simulation tests are conducted, in which the proposed controller is compared with the existing proportional and integral control strategy. The results indicate that the proposed feedback linearization-based proportional and integral perimeter controller can: (i) relieve the overall congestion in the urban network; and (ii) enhance the traffic performance in terms of the cumulative throughput and the mean speed.

Study of Activation Energy on the Movement of Gyrotactic Microorganism in a Magnetized Nanofluids Past a Porous Plate

The present study deals with the swimming of gyrotactic microorganisms in a nanofluid past a stretched surface. The combined effects of magnetohydrodynamics and porosity are taken into account. The mathematical modeling is based on momentum, energy, nanoparticle concentration, and microorganisms’ equation. A new computational technique, namely successive local linearization method (SLLM), is used to solve nonlinear coupled differential equations. The SLLM algorithm is smooth to establish and employ because this method is based on a simple univariate linearization of nonlinear functions. The numerical efficiency of SLLM is much powerful as it develops a series of equations which can be subsequently solved by reutilizing the data from the solution of one equation in the next one. The convergence was improved through relaxation parameters in the study. The accuracy of SLLM was assured through known methods and convergence analysis. A comparison of the proposed method with the existing literature has also been made and found an excellent agreement. It is worth mentioning that the successive local linearization method was found to be very stable and flexible for resolving the issues of nonlinear magnetic materials processing transport phenomena.

APPROXIMATE SOLUTIONS OF SOME NONLINEAR PROBLEMS FOR THE MONGE-AMPERE EQUATIO

Due to numerous applications in various fields of science, including gas dynamics, meteorology, differential geometry, and others, the Monge – ampere equation is one of the most intensively studied equations of nonlinear mathematical physics.In this report, we study a nonlinear boundary value problem for the inhomogeneous Monge-ampere equation, the right part of which contains power nonlinearities in derivatives and arbitrary nonlinearity from the desired function.Based on linearization, the studied boundary value problems are reduced to a system of ordinary first-order differential equations with initial conditions that depend on the parameter.Methods for constructing exact and approximate solutions of some boundary value problems for the Monge-ampere equation are proposed.Using the Mathcad software package, numerical implementation of methods for constructing approximate solutions of the obtained systems of ordinary differential equations with a parameter is performed.Three-dimensional graphs of exact and approximate solutions of the problems under consideration in the Grafikus service are constructed.

Numerical Investigation on the Swimming of Gyrotactic Microorganisms in Nanofluids through Porous Medium over a Stretched Surface

In this article, the effects of swimming gyrotactic microorganisms for magnetohydrodynamics nanofluid using Darcy law are investigated. The numerical results of nonlinear coupled mathematical model are obtained by means of Successive Local Linearization Method. This technique is based on a simple notion of the decoupling systems of equations utilizing the linearization of the unknown functions sequentially according to the order of classifying the system of governing equations. The linearized equations, that developed a sequence of linear differential equations along with variable coefficients, were solved by employing the Chebyshev spectral collocation method. The convergence speed of the SLLM technique can be willingly upgraded by successive applying over relaxation method. The comparison of current study with available published literature has been made for the validation of obtained results. It is found that the reported numerical method is in perfect accord with the said similar methods. The results are displayed through tables and graphs.

Modulated rapid load pull system for the emulation of envelope tracking power amplifiers

This Letter presents a novel characterisation system that is able to fully emulate a complete envelope tracking power amplifier (ET-PA) environment, with modulated impedance synthesis and dynamic supply voltage generation while using industry-standard modulated signals and digital pre-distortion. The system is used to characterise a 10 W GaN device and provide impedance control over the signal and distortion bandwidths, in response to a 10 MHz long-term evolution signal. A National Instruments PXI-based measurement system is utilised to apply tracking signals to a bespoke supply modulator and successfully improve the average power added efficiency by ~18 percentage points. Three different shaping functions are implemented, and their efficiency and linearity performance evaluated. In addition, digital pre-distortion (DPD) is used to linearise the PA while operating with the three different tracking trajectories. Experimental results demonstrate that when applying shaping functions, a trade-off needs to be made between efficiency and linearity. Even though a constant gain shaping function provides lower efficiency, it achieves good raw linearity performance without DPD, which is a good option if local linearisation is not available. This novel system is a useful tool in the design of ET-PAs, to more completely investigate the performance of the device.

Strong convergence of a stochastic Rosenbrock-type scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear part is stronger than the linear part, usually called stochastic dominated transport equations. Most standard numerical schemes lose their good stability properties on such equations, including the current linear implicit Euler method. We discretize the SPDE in space by the finite element method and propose a novel scheme called stochastic Rosenbrock-type scheme for temporal discretization. Our scheme is based on the local linearization of the semi-discrete problem obtained after space discretization and is more appropriate for such equations. We provide a strong convergence of the new fully discrete scheme toward the exact solution for multiplicative and additive noise and obtain optimal rates of convergence. Numerical experiments to sustain our theoretical results are provided.

Differential Evolution Optimized a Second-Order Divided Difference Particle Filter

In order to improve the estimation accuracy of particle filter algorithm in a nonlinear system state estimation problem, a new algorithm based on the second-order divided difference filter to generate the proposed distribution and the differential evolution algorithm for resampling is proposed. The second-order divided difference based on Strling’s interpolation formula is used to generate approximations to nonlinear dynamics, which avoids the evaluation of the Jacobian derivative matrix and is easy to implement. Cholesky factorization is used to ensure the positive definiteness of the covariance matrix. The truncated errors of the local linearization are reduced to a certain extent, and the approximation degree of the proposed distribution to the posterior probability of the system state is improved. The differential evolution algorithm is used to replace the traditional resampling algorithm, which effectively mitigates the problem of particle degradation. Monte Carlo simulation experiments show the effectiveness of the new algorithm.

Monotonicity, linearity and symmetry in the price volatility–volume relationship

PurposeThis paper aims to investigate the contemporaneous link between price volatility and trading volume in the futures markets of energy.Design/methodology/approachNon-parametric (local linear) regression models and formal statistical tests are used to assess monotonicity, linearity and symmetry. The data are daily price and volumes from five futures markets (West Texas Intermediate, Brent, gasoline, heating oil and natural gas) in the USA.FindingsTrading volume and price volatility have, in all markets, a strong nonlinear relation to each other. There are violations of monotonicity locally but not globally. The qualitative nature of the price shocks may have implications for the trading activity locally.Originality/valueTo the authors’ best knowledge, this is the first manuscript that investigates simultaneously and formally all the three important issues (i.e. monotonicity, linearity and asymmetry) for the price volatility–volume relationship using a highly flexible nonparametric approach.