Piecewise optimal distributed Controls for 2D Boussinesq equations

In this article, we study the dynamics of a piecewise (in time) distributed optimal control problem for the Boussinesq equations which model velocity tracking over time coupled to thermal dynamics. We also study the dynamics of semidiscrete approximation of this problem. We prove that the rates of velocity tracking coupled to thermal dynamics are exponential and that the difference between the solution of the semi‐discrete piecewise optimal control problem and the desired states in L² and H¹ norms decay to zero exponentially as n→∞. Copyright © 2000 John Wiley & Sons, Ltd.     

Dynamics for Controlled 2D Generalized MHD Systems with Distributed Controls

We study the dynamics of a piecewise (in time) distributed optimal control problem for Generalized MHD equations which model velocity tracking coupled to magnetic field over time. The long-time behavior of solutions for an optimal distributed control problem associated with the Generalized MHD equations is studied. First, a quasi-optimal solution for the Generalized MHD equations is constructed; this quasi-optimal solution possesses the decay (in time) properties. Then, some preliminary estimates for the long-time behavior of all solutions of Generalized MHD equations are derived. Next, the existence of a solution of optimal control problemis proved also optimality system is derived. Finally, the long-time decay properties for the optimal solutions is established.     

速度追踪问题中鞍点系统的新分裂迭代

 有限元离散一类速度追踪问题后得到具有鞍点结构的线性系统,针对该鞍点系统,本文提出了一种新的分裂迭代技术.证明了新的分裂迭代方法的无条件收敛性,详细分析了新的分裂预条件子对应的预处理矩阵的谱性质.数值结果验证了对于大范围的网格参数和正则参数,新的分裂预条件子在求解有限元离散速度追踪问题得到的鞍点系统时的可行性和有效性.     

Dynamic modelling and design of various robust sliding mode controls for the wind turbine with estimation of wind speed

The main propose of this paper is extracting the maximum efficiency from variable speed wind turbine, which is modelled as an electromechanical system with two masses dynamics. The maximum efficiency can be obtained by tracking the optimal rotor speed, which is controlled by the generator torque as the input. One of the most important information that is required for designing of the control system is the measurement of the effective wind velocity. In this paper, a new ANFIS-based method for estimating the effective wind velocity is developed. The aerodynamic torque has a direct relationship with the power coefficient. So in this paper, power coefficient of WindPACT 1.5 MW turbine as a function of tip speed ratio (TSR) and blade pitch angle is considered. Then, three control methods based on high order sliding mode controllers are examined. The rotor speed and the wind velocity are the only variables required in the design of second and third order sliding mode controllers. FAST (Fatigue, Aerodynamics, Structures and Turbulence) is valid software that offers a fairly complete model of the wind turbine. Results of this paper are validated using FAST. Performance of the designed controllers is compared in terms of the generator torque and desired rotor speed tracking. Finally, the doubly fed induction generator (DFIG) is controlled such that the objectives of reactive power minimization and tracking the desired generator torque are achieved. Two main hindrances in designing the control systems are the uncertainties and the lack of sufficient information on measurements. Therefore robust performance of designed controllers against the model uncertainties is investigated.     

3D simulations and experiments of flow in a folded microchannel

We investigate the three–dimensional pressure–driven flow field in a folded microchannel. Experiments and numerical simulations are performed. A method termed “partial particle tracking”, resulting in partial velocity profiles, indicates that secondary flows exist. The comparison of numerical and experimental partial velocity fields shows good agreement. The existence of secondary flow results from centrifugal forces due to the curved channel geometry. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Funnel Control for Linear DAEs

We study funnel control for linear differential-algebraic multi-input multi-output systems which are not necessarily regular. We show that the funnel controller (that is a static nonlinear output error feedback) achieves - for a special class of right-invertible systems with asymptotically stable zero dynamics - tracking of a reference signal by the output signal within a pre-specified performance funnel. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A numerical study of the dynamics of elastic articulated systems in a fluid

We propose a method and an algorithm for computing the dynamics of elastic structures of articulated form in a fluid flow taking account of the weakening in certain structural elements. In describing the motion we use two sets of radius-vectors, which are approximated in the computations by parametric local splines of first degree. The possibilities of the proposed method are illustrated using the example of the study of the dynamics of transition processes in an articulated anchor-buoy structure, which arise when there is an abrupt change in the direction of the fluid flow velocity. We determine the kinematic and force characteristics of the structure under various changes in the direction of the flow velocity. We determine the structural elements in which the weakening occurs. Three figures. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 128–134.     

Dynamically evolving Gaussian spatial fields

We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields. By applying an extension of the standard moving average construction we obtain models which are stationary in time. The resulting surface changes with time but is dynamically inactive since its velocities, when sampled across the field, have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models. The models are extensions of the earlier discretized autoregressive models which account for a local velocity of traveling surface. We demonstrate that for such a surface its dynamics is a combination of dynamics introduced by the flow and the dynamics resulting from the covariance structure of the underlying stochastic field. We extend this approach to fields that are only locally stationary and have their parameters varying over a larger spatio-temporal horizon.     

A Particle Filtering Approach for Tracking an Unknown Number of Objects with Dynamic Relations

In recent years there has been a growing interest on particle filters for solving tracking problems, thanks to their applicability to problems with continuous, non-linear and non-Gaussian state spaces, which makes them more suited than hidden Markov models, Kalman filters and their derivations, in many real world tasks. Applications include video surveillance, sensor fusion, tracking positions and behaviors of moving objects, situation assessment in civil and bellic scenarios, econometric and clinical data series analysis. In many environments it is possible to recognize classes of similar entities, like pedestrians or vehicles in a video surveillance system, or commodities in econometric. In this paper, a relational particle filter for tracking an unknown number of objects is presented which exploits possible interactions between objects to improve the quality of filtering. We will see that taking into account relations between objects will ease the tracking of objects in presence of occlusions and discontinuities in object dynamics. Experimental results on a benchmark data set are presented.     

Funnel control for electrical circuits

We study the zero dynamics and funnel control for linear passive electrical circuits. We show that asymptotic stability of the zero dynamics can be characterized by criteria on the circuit topology. Thereafter we consider the output regulation problem for electrical circuits by funnel control. We show that for circuits with asymptotically stable zero dynamics, the funnel controller achieves tracking of a class of reference signals within a pre-specified funnel. This result can be relaxed to the case of non-autonomous zero dynamics by requiring the reference trajectory to evolve within a certain subspace. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

STUDY OF CRYSTAL GROWTH AND SOLUTE PRECIPITATION THROUGH FRONT TRACKING METHOD

Crystal growth and solute precipitation is a Stefan problem. It is a free boundary problem for a parabolic partial differential equation with a time-dependent phase interface. The velocity of the moving interface between solute and crystal is a local function. The dendritic structure of the crystal interface, which develops dynamically, requires high resolution of the interface geometry. These facts make the Lagrangian front tracking method well suited for the problem. In this paper, we introduce an upgraded version of the front tracking code and its associated algorithms for the numerical study of crystal formation. We compare our results with the smoothed particle hydrodynamics method （SPH） in terms of the crystal fractal dimension with its dependence on the Damkohler number and density ratio.     

The Use of Real-World Computer Models for Computer-Aided Design of Tracking Control Schemes for Induction Motors

The design of tracking controllers for induction motors is usually developed by neglecting the presence of power-supply devices, such as inverters, and measurement apparatuses, e.g., encoders. However, these components represent unmodeled dynamics that are present during the real operating conditions of the induction motor. Since the development of a numerical simulation study represents a low-cost, safe, and fast test to validate the design of tracking control schemes, the need arises to build a computer model of the overall system (i.e., motor, power supply, measurement devices, and tracking controller) as realistic as possible. In this context, the paper describes a computer model for simulation of an induction motor under a tracking control scheme including many real-world effects; namely, encoder's quantization, current sensors' noise, stator current dynamics, presence of a current-controlled voltage-source inverter within a stator current regulator loop, flux observer dynamics, saturation of the control signal, and discrete-time implementation of the control algorithm. The developed computer model is finally used in a case study and the simulation results obtained for an induction motor driving a single-link robotic arm under an H8 tracking control scheme are reported.     

Adaptive Robust Tracking for Flexible Spacecraft in Presence of Disturbances

The paper deals with trajectory tracking for a flexible spacecraft, subject to a gravity-gradient disturbance, under parameter uncertainties. The controls are gas jets and reaction wheels, and the measured variables describe the attitude and angular velocity of the rigid part. The flexible dynamics is treated as an additional disturbance acting on a rigid structure. First, an adaptive control is designed with only the gravity-gradient disturbance acting on the spacecraft; second, it is proved to be effective also in the presence of disturbance due to the flexibility, provided that appropriate robustness conditions on the controller gains are satisfied. These conditions use partial knowledge of the parameters describing the elastic dynamics. Simulations show the good performance of such control scheme and demonstrate its applicability even in the presence of input saturation.     

Irreversibility and the role of an instrument in the functional formulation of classical mechanics

We analyze the role of an instrument in the recently proposed functional formulation of classical mechanics, whose basic equation is the Liouville equation. Its solution has the delocalization (spreading) property, which is interpreted as irreversibility on the microlevel. We show that the reversible and recurrent dynamics for a particle can be observed by tracking the particle dynamics using instruments, but repeated measurements inevitably lead to a heat release and an increase in the entropy of the instrument. The irreversible behavior is thus transported from the system under study to the instrument, which is also a physical system.     

Flocking Dynamics of the Inertial Spin Model with a Multiplicative Communication Weight

In this paper, we study a flocking dynamics of the deterministic inertial spin (IS) model. The IS model was introduced for the collective dynamics of active particles with an internal angular momentum, or spin. When the generalized moment of inertia becomes negligible compared to spin dissipation (overdamped limit) and mutual communication weight is a function of a relative distance between interacting particles, the deterministic inertial spin model formally reduces to the Cucker–Smale (CS) model with constant speed constraint whose emergent dynamics has been extensively studied in the previous literature. We present several sufficient frameworks leading to the asymptotic mono-cluster flocking, in which spins and relative velocities tend to zero asymptotically. We also provide several numerical simulations for the decoupled and coupled inertial spin models to see the effect of the C–S velocity flocking and compare them with our analytical results.

     

Ballistic motion of a tracer particle coupled to a Bose gas

We study the motion of a heavy tracer particle weakly coupled to a dense interacting Bose gas exhibiting Bose–Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations. We derive the effective dynamics of the tracer particle, which is described by a non-linear integro-differential equation with memory, and prove that if the initial speed of the tracer particle is below the speed of sound in the Bose gas the motion of the particle approaches an inertial motion at constant velocity at large times.     

Data-driven optimal tracking control of switched linear systems

This paper addresses the optimal tracking control for switched linear systems with unknown dynamics. We convert the problem into an optimal control problem of the augmented switched systems. In view of the augmented systems, we propose a data-driven switched linear quadratic regular algorithm for obtaining the optimal switching signal under unknown system dynamics. It is proved that the optimal switching signal will not cause Zeno behavior and can make the system stable. Besides, with the proposed algorithm, we just need to identify an autonomous system instead of the original systems, which has fewer parameters to be determined. A numerical example is given to illustrate the validity of the main results.     

Tracking within a time interval on the basis of data supplied by finite observers

We solve the tracking control problem, in which one should bring a trajectory of a system of linear ordinary differential equations into a neighborhood of a trajectory of another system within a given time interval. After getting into this neighborhood, one should keep the trajectory of the first subsystem in it for a time interval of given duration. For the control synthesis, we use incomplete and imprecise information on the online deviation of one trajectory from the other, which is obtained in real time from linear equations of observation. We consider distinct structures of observers, which substantially affect the solution of control problems for such systems. The equations of dynamics and admissible measurements contain uncertainty for which one knows only some hard pointwise constraints. To solve the main problem, we use an approach that can be reduced to the construction of auxiliary information sets and weakly invariant sets with a subsequent “aiming” of one set at a tube. We suggest an efficient method for an approximate solution on the basis of ellipsoidal calculus techniques. The results of the algorithm operation are illustrated by an example of the solution of a tracking control problem for two fourth-order subsystems.     

Uniform global asymptotic stability of adaptive cascaded nonlinear systems with unknown high-frequency gains

We study adaptive tracking problems for nonlinear systems with unknown control gains. We construct controllers that yield uniform global asymptotic stability for the error dynamics, and hence tracking and parameter estimation for the original systems. Our result is based on a new explicit, global, strict Lyapunov function construction. We illustrate our work using a brushless DC motor turning a mechanical load. We quantify the effects of time-varying uncertainties on the motor electric parameters.