Approximate Dynamic Model Research Articles

An approximate dynamic model of double-sided LCC resonant converter in wireless power transmission based on average current model

Wireless Power Transmission (WPT) system could realize a non-contact power transmission through the air gap weak magnetic coupling. This paper aims at analyzing a dynamic model of the WPT system based on a double-side LCC. Firstly, in the multivariable framework, the dynamic characteristics of double-side LCC resonant compensation topology are analyzed by the mutual inductance model. The approximate small-signal model of double-side LCC resonant converter is derived by generalized state-space averaging (GSSA). Additionally, a double-side LCC compensation topology based on double closed-loop average current mode control approach is proposed. By contrasting the behavior of the WPT system under various operating conditions, the efficacy of the suggested dynamic model is illustrated. Finally, a wireless power transmission system experiment platform with a resonant frequency of 85 kHz and an output power of 3 kW was built. Through the experiments, it is determined that the model has a certain ability to predict the dynamic behavior of the wireless charging system. So, it can be utilized as a useful instrument for the transient's analysis and the controller development optimization.© 2017 Elsevier Inc. All rights reserved.

Adaptive network traffic control with approximate dynamic programming based on a non-homogeneous Poisson demand model

ABSTRACT In this study, we develop a stochastic dynamic traffic-flow model subject to practical restrictions under the non-homogeneous Poisson vehicle arrival process. Using the cell transmission strategy, we establish traffic dynamics between two intersections. We also discuss simulating the random demand of source links from an estimated intensity function. Additionally, we propose an algorithm to optimize time interval division for aggregated data, aiming to enhance estimation performance. We explore applying our traffic flow model to the adaptive traffic network management problem, which is formulated as a Markov decision process. Leveraging approximate dynamic programming with recursive least squares-temporal difference learning, we achieve adaptive optimal policies. To validate our approach, we conduct a series of numerical experiments with random demands. The results of non-homogeneous Poisson demand conducted using random numbers and a real-word dataset indicate high efficiency with the piecewise constant, I-SMOOTH, and MNO-PQRS estimators. Compared to the Webster and Max-pressure control systems, our proposed approximate dynamic programming-based model exhibits superior stability and applicability.

Resonant Excitation of Planetary Eccentricity due to a Dispersing Eccentric Protoplanetary Disk: A New Mechanism of Generating Large Planetary Eccentricities

We present a new mechanism of generating large planetary eccentricities. This mechanism applies to planets within the inner cavities of their companion protoplanetary disks. A massive disk with an inner truncation may become eccentric due to nonadiabatic effects associated with gas cooling and can retain its eccentricity in long-lived coherently precessing eccentric modes; as the disk disperses, the inner planet will encounter a secular resonance with the eccentric disk when the planet and the disk have the same apsidal precession rates; the eccentricity of the planet is then excited to a large value as the system goes through the resonance. In this work, we solve the eccentric modes of a model disk for a wide range of masses. We then adopt an approximate secular dynamics model to calculate the long-term evolution of the “planet + dispersing disk” system. The planet attains a large eccentricity (between 0.1 and 0.6) in our calculations even though the disk eccentricity is quite small (≲0.05). This eccentricity excitation can be understood in terms of the mode conversion (“avoided crossing” between two eigenstates) phenomenon associated with the evolution of the “planet + disk” eccentricity eigenstates.

Design method for overwind arrestors

ABSTRACT The relentless drive for safer winding systems has seen more serious consideration given to arresting systems in recent years. Design criteria have been debated. Arrestors are roughly selected based on average retardation rates and energy absorption capacity. Standards Australia sets criteria for design of arrestors that go beyond average retardation rates and energy absorption but provide little design guidance. Although sophisticated dynamic simulation methods have illuminated the true dynamic behavior of arresting systems, they are not available to most designers. Based on approximate dynamic models of conveyance arresting, this paper addresses the opportunity to equip the designer with computational tools that go beyond mere energy considerations but stop short of full dynamic simulation. Methods are presented to estimate the conveyance displacement, velocity, and acceleration in a headframe or shaft bottom arrestor. Equations for the approximate calculation of head rope forces during headframe arrest are included. A model of crash beam impact results in an approach to assessing whether head ropes fail if this occurs.

Tackling Modeling and Kinematic Inconsistencies by Fixed Point Iteration-Based Adaptive Control

The Fixed Point Iteration-based Adaptive Control design methodology is an alternative to the Lyapunov function-based technology. It contains higher-order feedback terms than the standard resolved acceleration rate control. This design approach strictly separates the kinematic and dynamic issues. At first, a purely kinematic prescription is formulated for driving the components of the tracking error to zero. Then an available approximate dynamic model is used to calculate the approximated necessary control forces. Before exerting on the controlled system, these forces are adaptively deformed in order to precisely obtain the prescribed kinematic behavior. The necessary deformation is iteratively found by the use of a contractive map that results in a sequence that converges to the unique fixed point of this map. In the case of underactuated systems, when the relative order of the control task also increases, the highest-order time-derivative depends on the lower-order ones according to the dynamic model of the system. This makes it impossible to realize the arbitrarily constructed kinematic design. In the paper, a resolution to this discrepancy is proposed. The method is demonstrated using two non-linear paradigms, a three-degree-of-freedom robot arm, and a two-degree-of-freedom system, i.e., two coupled non-linear springs. The operation of the method was investigated via simulations made by the use of Julia language and simple sequential programs. It was found that the suggested solution could be considered as a new variant of the fixed point iteration-based model reference adaptive control that is applicable for underactuated systems even if the relative order of the task is increased.

Preliminary Design of a Receding Horizon Controller Supported by Adaptive Feedback

Receding horizon controllers are special approximations of optimal controllers in which the continuous time variable is discretized over a horizon of optimization. The cost function is defined as the sum of contributions calculated in the grid points and it is minimized under the constraint that expresses the dynamic model of the controlled system. The control force calculated only for one step of the horizon is exerted, and the next horizon is redesigned from the measured initial state to avoid the accumulation of the effects of modeling errors. In the suggested solution, the dynamic model is directly used without any gradient reduction by using a transition between the gradient descent and the Newton–Raphson methods to achieve possibly fast operation. The optimization is carried out for an "overestimated" dynamic model, and instead of using the optimized force components the optimized trajectory is adaptively tracked by an available approximate dynamic model of the controlled system. For speeding up the operation of the system, various cost functions have been considered in the past. The operation of the method is exemplified by simulations made for new cost functions and the dynamic control of a 4-degrees-of-freedom SCARA robot using the simple sequential Julia language code realizing Euler integration.

Nonlinear resonances in fast electronic circuits mimicking photonic oscillators

Nonlinear photonic oscillators are being investigated for decades but they still keep delivering disruptive technologies and innovative products based on their rich and complex dynamic features. Today, with the advent of ultrafast electronics, these revolutionary devices can be mimicked by solely using circuit elements to formulate a “photonics-without-photons” path. This study considers a fundamental unit cell of two coupled oscillators and identifies its resonant working regimes for arbitrary injected input amplitude and phase. An approximate dynamic model is developed to detect swiftly and reliably multistable modes that are vital in the design of integrated electronic systems with a variety of signal processing or information storage applications.

Tracking the state of pacemakers modeled by the van der Pol equation

It is known that in many applications of physics, biology and other sciences as an approximate dynamic model of complex nonlinear oscillatory processes a model of one or more interconnected van der Pol oscillators or some of its modifications is used \cite{ShD01}. For this reason, nonlinear oscillators are studied as a method of modeling, analysis or even control in various fields, such as electronics \cite{ShD02}, control, robotics \cite{ShD03, ShD04}, biomedical research \cite{ShD05}, geology \cite{ShD06} and others. Naturally, in such modeling there are problems in determining the state and parameters of the models based on the results of measuring the output signals in real time. One of these problems, namely: the problem of determining the state of pacemaker models, which are obtained as certain modifications of the van der Pol oscillator equation, is considered in this paper. In the scientific literature, publications on the modeling of cardiovascular activity using oscillatory systems are widely represented. In recent years, among them there are works that are related to the solution of inverse problems for such models. In particular, in \cite{ShD07} using differential-geometric methods of control theory, a general scheme for constructing asymptotically accurate estimates of the state of a two-dimensional dynamical system is proposed. The obtained results are used to effectively solve the problem of observing two models of pacemakers. In our case in this observation problem we used the method of invariant relations \cite{ShD08}, which was developed in analytical mechanics to find partial solutions (dependencies between variables) in the problems of dynamics of a rigid body with a fixed point. Modification of this method to the problems of control theory, observation, identification allowed to synthesize between known and unknown values of the original system additional connections that arise during the motion of its extended model \cite{ShD09, ShD10, ShD11}. The corresponding technique is to expand the original system by introducing additional controlled differential equations and immersing the original system in a system of greater dimension, which due to its sufficiently free structure is more suitable for constructing an observer or identifier. Controls in an extended system are used to synthesize on its trajectories pre-proposed relations that define the unknown components of the mathematical model (phase vector, parameters) as functions of known quantities. The obtained theoretical results are illustrated by numerical simulations of the corresponding nonlinear observers in Section 5.

Generalized Cell Mapping Method with Deep Learning for Global Analysis and Response Prediction of Dynamical Systems

A novel method that combines generalized cell mapping and deep learning is developed to analyze the global properties and predict the responses of dynamical systems. The proposed method only requires some prior knowledge of the system governing equations and obtains dynamical properties of the system from observed data. By combining the theoretical demonstration and empirical inference results, appropriate network structure and training hyperparameters are computed. Then a robust and efficient neural network approximation with the estimated mapping parameters is obtained. By using the approximate dynamical system model, we construct the one-step transition probability matrix and introduce the digraph analysis method to analyze the global properties. System responses at any time can be obtained with the trained model on the basis of the property of Markov chain. Several examples with periodic or chaotic attractors are presented to validate the proposed method. The influence of the number of hidden layers and the size of training data on calculated results is discussed, and an admissible architecture of the neural network is found. Numerical results indicate that the proposed method is quite effective for both global analysis and response prediction.

An application of symplectic integration for general relativistic planetary orbitography subject to non-gravitational forces

Spacecraft propagation tools describe the motion of near-Earth objects and interplanetary probes using Newton’s theory of gravity supplemented with the approximate general relativistic n-body Einstein–Infeld–Hoffmann equations of motion. With respect to the general theory of relativity and the long-standing recommendations of the International Astronomical Union for astrometry, celestial mechanics and metrology, we believe modern orbitography software is now reaching its limits in terms of complexity. In this paper, we present the first results of a prototype software titled General Relativistic Accelerometer-based Propagation Environment (GRAPE). We describe the motion of interplanetary probes and spacecraft using extended general relativistic equations of motion which account for non-gravitational forces using end-user supplied accelerometer data or approximate dynamical models. We exploit the unique general relativistic quadratic invariant associated with the orthogonality between four-velocity and acceleration and simulate the perturbed orbits for Molniya, Parker Solar Probe and Mercury Planetary Orbiter-like test particles subject to a radiation-like four-force. The accuracy of the numerical procedure is maintained using a 5-stage, 10^mathrm{th}-order structure-preserving Gauss collocation symplectic integration scheme. GRAPE preserves the norm of the tangent vector to the test particle worldline at the order of 10^{-32}.

Steady-state real-time optimization using transient measurements in the absence of a dynamic mechanistic model: A framework of HRTO integrated with Adaptive Self-Optimizing IHMPC

In processes with slow dynamics or subjected to frequent disturbances, the detection of a steady-state operation might be rare, which hinders the application of the classic RTO. To overcome this issue, the Hybrid RTO (HRTO) is a proposition where a dynamic observer substitutes the Steady-State Detection (SSD) and the static parameter estimation steps. Recent progress has been made in HRTO frameworks. Still, all of them start from the assumption that a reliable mechanistic dynamic model is available, which is not true in many applications. In fact, the development of a dynamic process model is not considered in most typical RTO design projects. Therefore, the present work proposes an HRTO framework aiming, mainly, to overcome this first assumption. We present a complete control framework where the basic assumption is that a reliable mechanistic dynamic model is not available, but a static process model is at hand. The HRTO is made possible by using an approximate dynamic model that takes advantage of the static process model and identified linear dynamics from the plant in a Hammerstein structure. Three models are proposed based on the Hammerstein structure. These models are used in the dynamic observer, a proposed variation of an Extended Kalman Filter (EKF), and as the controller’s internal model. The economic objectives are introduced into the control layer by the self-optimizing variables in an adaptive infinite-horizon MPC formulation. The framework presents full model compatibility between the observer, controller, and optimizer layers. A validation case study is developed in the Williams–Otto reactor with two proposed EKF tunings. The open-loop results provide evidence that the proposed Hammerstein structure is adequate as an approximate dynamic model, preserving the observability characteristics of the static model. The closed-loop results show that our framework outperforms the classic RTO structure in economic return, especially in the transient regions. Moreover, the proposed approach has a very natural way of handling active constraint changes. This effect is shown in the results at the moment that a constraint becomes active. The economic performance of the RTO is impaired compared to our proposed HRTO scheme. Finally, the average computational cost of each iteration of our framework is twice as fast as the classic RTO framework, which suggests the potential applicability of the proposed methodology on an industrial scale.

Virtual tracking control of underwater vehicles based on error injection and adaptive gain

An improved virtual tracking control scheme is proposed based on error injection and adaptive gain for underwater vehicles in the presence of a large initial tracking error and external disturbances. To relieve the effect caused by a large initial tracking error, the developed control scheme is achieved based on two closed-loop systems. Specifically, a virtual closed-loop system is constructed based on an approximate dynamic model of an underwater vehicle, while an actual closed-loop system is built with a real underwater vehicle. Firstly, in order to improve the tracking precision of the virtual tracking control scheme, an auxiliary variable produced by a first-order filter is injected into a virtual tracking error in the virtual closed-loop system. And then, the virtual trajectory provided by the virtual closed-loop system is followed by the actual closed-loop system. In the actual closed-loop system, a modified sliding mode surface is designed to achieve the finite-time stability, while the control gains can be on-line adjusted based on the tracking performance. Finally, the effectiveness and feasibility of the proposed control scheme are demonstrated by case studies on an underwater vehicle subject to different external disturbances.

A model predictive approach for online mobile manipulation of non-holonomic objects using learned dynamics

Assistive robots designed for physical interaction with objects will play an important role in assisting with mobility and fall prevention in healthcare facilities. Autonomous mobile manipulation presents a hurdle prior to safely using robots in real-life applications. In this article, we introduce a mobile manipulation framework based on model predictive control using learned dynamics models of objects. We focus on the specific problem of manipulating legged objects such as those commonly found in healthcare environments and personal dwellings (e.g., walkers, tables, chairs). We describe a probabilistic method for autonomous learning of an approximate dynamics model for these objects. In this method, we learn dynamic parameters using a small dataset consisting of force and motion data from interactions between the robot and object. Moreover, we account for multiple manipulation strategies by formulating manipulation planning as a mixed-integer convex optimization. The proposed framework considers the hybrid control system composed of (i) choosing which leg to grasp and (ii) control of continuous applied forces for manipulation. We formalize our algorithm based on model predictive control to compensate for modeling errors and find an optimal path to manipulate the object from one configuration to another. We present results for several objects with various wheel configurations. Simulation and physical experiments show that the obtained dynamics models are sufficiently accurate for safe and collision-free manipulation. When combined with the proposed manipulation planning algorithm, the robot successfully moves the object to the desired pose while avoiding any collision.

Quantifying Drivers of Forecasted Returns Using Approximate Dynamic Factor Models for Mixed-Frequency Panel Data

This article considers the estimation of Approximate Dynamic Factor Models with homoscedastic, cross-sectionally correlated errors for incomplete panel data. In contrast to existing estimation approaches, the presented estimation method comprises two expectation-maximization algorithms and uses conditional factor moments in closed form. To determine the unknown factor dimension and autoregressive order, we propose a two-step information-based model selection criterion. The performance of our estimation procedure and the model selection criterion is investigated within a Monte Carlo study. Finally, we apply the Approximate Dynamic Factor Model to real-economy vintage data to support investment decisions and risk management. For this purpose, an autoregressive model with the estimated factor span of the mixed-frequency data as exogenous variables maps the behavior of weekly S&P500 log-returns. We detect the main drivers of the index development and define two dynamic trading strategies resulting from prediction intervals for the subsequent returns.

An adaptive controller for human lower extremity exoskeleton robot

Exoskeleton robot-assisted physical therapy has recently been studied extensively due to its proven effectiveness in providing different forms of physical therapy at any stage of physical recovery. The efficacy of robot-assisted physical therapy depends on the maneuverability of the robot during the rehabilitation application. Robot dynamics is inherently nonlinear. Often, robot control algorithms are developed based on an approximate robot dynamic model which leads to system instability and tracking errors. Accurately determining a rehabilitation robot's payload (human limb masses and inertial properties) is frequently impractical. An adaptive control scheme can handle modeling errors very efficiently. In this paper, a 7 degrees of freedom (DOF) human lower extremity dynamic model was developed using the Newton Euler’s method. To simulate joint friction, a realistic friction model is included. A direct adaptive controller is designed so that the robot can follow the prescribed trajectory with high speed and accuracy. A total of 31 model parameters were considered for adaption. To ensure system stability, the controller's adaptive gains are determined based on the Lyapunov stability approach. Simulation results show excellent tracking performance of the developed controller in the presence of joint friction.

Dynamic solution of high pressure tubing

In the real environment, the pressure of high-pressure oil pipe is not always stable due to the process of oil in and out. We created a simulation experiment: to set the time for each opening of the one-way valve to change the pressure in the high-pressure tubing, ensuring that the pressure remains relatively stable under the initial pressure condition 100Mpa. By using the simulated conditions, we obtained the relationship between elastic modulus E and pressure P with high fitting degree, and deduced the relationship between pressure P and density temperature. Since the tubing size V is constant, we established the approximate dynamic balance model of fuel mass in high pressure tubing according to the mV mass. Since the opening time of the one-way valve is unknown, the simplified operation method is used to find the approximate solution and then the dichotomy method is used to find the results in this range. Our contribution is that we proposed a method to control the pressure steadily and rapidly in simulation. For each search result, the iterative method is used to obtain the mean pressure of the injection pipe after the pressure is stable, and the objective function is established to make the average pressure reach 150Mpa. Finally, we present the exact solution with MATLAB simulation.

A replication of “A quasi-maximum likelihood approach for large, approximate dynamic factor models” (Review of Economics and Statistics, 2012)

Abstract The authors replicate and extend the Monte Carlo experiment presented in Doz, Giannone and Reichlin (A Quasi-Maximum Likelihood Approach For Large, Approximate Dynamic Factor Models, Review of Economics and Statistics, 2012) on alternative (time-domain based) methods for extracting dynamic factors from large datasets; they employ open source software and consider a larger number of replications and a wider set of scenarios. Their narrow sense replication exercise fully confirms the results in the original article. As for their extended replication experiment, the authors examine the relative performance of competing estimators under a wider array of cases, including richer dynamics, and find that maximum likelihood (ML) is often the dominant method; moreover, the persistence characteristics of the observable series play a crucial role and correct specification of the underlying dynamics is of paramount importance.

Наближені динамічні моделі нестаціонарних вимірювальних перетворювачів

Наближені динамічні моделі нестаціонарних вимірювальних перетворювачів

Finite-Horizon Discounted Optimal Control: Stability and Performance

Motivated by (approximate) dynamic programming and model predictive control problems, we analyse the stability of deterministic nonlinear discrete-time systems whose inputs minimize a discounted finite-horizon cost. We assume that the system satisfies stabilizability and detectability properties with respect to the stage cost. Then, a Lyapunov function for the closed-loop system is constructed and a uniform semiglobal stability property is ensured, where the adjustable parameters are both the discount factor and the horizon length, which corresponds to the number of iterations for dynamic programming algorithms like value iteration. Stronger stability properties such as global exponential stability are also provided by strengthening the initial assumptions. We give bounds on the discount factor and the horizon length under which stability holds and we provide conditions under which these are less conservative than the bounds of the literature for discounted infinite-horizon cost and undiscounted finite-horizon costs, respectively. In addition, we provide new relationships between the optimal value functions of the discounted, undiscounted, infinite-horizon and finite-horizon costs respectively, which are very different from those available in the approximate dynamic programming literature. These relationships rely on assumptions that are more likely to be satisfied in a control context. Finally, we investigate stability when only a near-optimal sequence of inputs for the discounted finite-horizon cost is available, covering approximate value iteration as a particular case.

Understanding Consumer Dynamic Decision Making Under Competing Loyalty Programs

The authors develop an incentive-aligned experimental paradigm to study how consumer purchase dynamics are affected by the interplay between competing firms’ loyalty programs and their pricing and promotional strategies. In this experiment, participants made sequential choices between two competing airlines in a stylized frequent traveler task for which an optimal dynamic decision policy can be numerically computed. The authors find that, on average, participants are able to partially realize the long-term benefits from loyalty programs, though most are sensitive to price. They also find that participants’ preferences and levels of bounded rationality depend on the nature of the competitive environment, the particular state of each decision scenario, and the type of optimal action. Accordingly, the authors use an approximate dynamic programming model to incorporate boundedly rational decision making. The model classifies participants into five segments that exhibit variation in their performance and decision strategies. Importantly, they find that participants are able to adapt their decision strategies to the environment they face, and thus the overall market outcome and the performance of each firm are influenced by both the competitive environment and the assumption on the extent of consumer optimality.