This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale observations on the flow field. A relaxation-based approach is proposed for accomplishing this, which makes use of a nonlinear property of the equations of motions to asymptotically enslave small scales to large scales. In particular, an algorithm is introduced that systematically produces approximations of the flow field on the unobserved scales in order to generate an approximation to the unknown force; the process is then repeated to generate an improved approximation of the unobserved scales, and so on. A mathematical proof of convergence of this algorithm is established in the context of the two-dimensional Navier–Stokes equations with periodic boundary conditions under the assumption that the force belongs to the observational subspace of phase space; at each stage in the algorithm, it is shown that the model error, represented as the difference between the approximating and true force, asymptotically decreases to zero in a geometric fashion provided that sufficiently many scales are observed and certain parameters of the algorithm are appropriately tuned.

The development of high-intensity ultrafast laser facilities provides the possibility to create novel physical phenomena and matter states. The timing fluctuation of the laser pulses is crucial for pump–probe experiments, which is one of the vital means to observe the ultrafast dynamics driven by intense laser pulses. In this paper, we demonstrate the timing fluctuation characterization and control of the front end of a 100-PW laser that is composed of a high-contrast optical parametric amplifier (seed) and a 200-TW optical parametric chirped pulse amplifier (preamplifier). By combining the timing jitter measurement with a feedback system, the laser seed and preamplifier are synchronized to the reference with timing fluctuations of 1.82 and 4.48 fs, respectively. The timing system will be a key prerequisite for the stable operation of 100-PW laser facilities and provide the basis for potential pump–probe experiments performed on the laser.

Speech production requires the combined efforts of feedforward and feedback control, but it remains unclear whether the relative weighting of feedforward and feedback control is organized differently between the first language (L1) and the second language (L2). In the present study, a group of Chinese–English bilinguals named pictures in their L1 and L2, while being exposed to multitalker noise. Experiment 1 compared feedforward control between L1 and L2 speech production by examining intensity increases in response to a masking noise (90 dB SPL). Experiment 2 compared feedback control between L1 and L2 speech production by examining intensity increases in response to a weak (30 dB SPL) or strong noise (60 dB SPL). We also examined a potential relationship between L2 fluency and the relative weighting of feedforward and feedback systems. The results indicated that L2 speech production relies less on feedforward control relative to L1, exhibiting attenuated Lombard effects to the masking noise. In contrast, L2 speech production relies more on feedback control than L1, producing larger Lombard effects to the weak and strong noise. The relative weighting of feedforward and feedback control is dynamically changed as second language learning progresses.

We study the problem of pseudostate and static output feedback stabilization for singular fractional-order linear systems with fractional order $\unicode[STIX]{x1D6FC}$ when $0<\unicode[STIX]{x1D6FC}<1$. All the results are given by linear matrix inequalities. First, a new sufficient and necessary condition for the admissibility of singular fractional-order systems is presented. Then based on the admissible result, not only are sufficient conditions for designing pseudostate and static output feedback controllers obtained, but also sufficient and necessary conditions are presented by using different methods that guarantee the admissibility of the closed-loop systems. Finally, the effectiveness of the proposed approach is demonstrated by numerical simulations and a real-world example.

In medical interventional procedures such as brachytherapy, biopsy and radio-frequency ablation, precise tracking through the preplanned desired trajectory is very essential. This important requirement is critical due to two major reasons: anatomical obstacle avoidance and accurate targeting for avoiding undesired radioactive dose exposure or damage to neighboring tissue and critical organs. Therefore, a precise control of the needling device in the unstructured environment in the presence of external disturbance is required to achieve accurate target reaching in clinical applications. In this paper, a shape memory alloy actuated active flexible needle controlled by an adaptive sliding mode controller is presented. The trajectory tracking performance of the needle is tested while having its actual movement in an artificial tissue phantom by giving various input reference trajectories such as multi-step and sinusoidal. Performance of the adaptive sliding mode controller is compared with that of the proportional, integral and derivative controller and is proved to be the effective method in the presence of the external disturbances.

There is a large gap between reality and grasp models that are currently available because of the static analysis that characterizes these approaches. This work attempts to fill this need by proposing a control law that, starting from an initial contact state which does not necessarily correspond to an equilibrium, achieves dynamically a stable grasp and a relative finger orientation in the case of pinching an object with arbitrary shape via rolling soft fingertips. Controlling relative finger orientation may improve grasping force manipulability and allow the appropriate shaping of the composite object consisted of the distal links and the object, for facilitating subsequent tasks. The proposed controller utilizes only finger proprioceptive measurements and is not based on the system model. Simulation and experimental results demonstrate the performance of the proposed controller with objects of different shapes.

We discuss a control problem involving a stochastic Burgers equation with a random diffusion coefficient. Numerical schemes are developed, involving the finite element method for the spatial discretisation and the sparse grid stochastic collocation method in the random parameter space. We also use these schemes to compute closed-loop suboptimal state feedback control. Several numerical experiments are performed, to demonstrate the efficiency and plausibility of our approximation methods for the stochastic Burgers equation and the related control problem.

A reduced-order model for distributed feedback control of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is discussed. To retain more information in our model, we first calculate the functional gain in the full-order case, and then invoke the proper orthogonal decomposition (POD) method to design a low-order controller and thereby reduce the order of the model. Numerical experiments demonstrate that a solution of the reduced-order model performs well in comparison with a solution for the full-order description.

We discuss the zero-controllability and the zero-stabilizability for the nonnegative solutions to some Fisher-like models with nonlocal terms describing the dynamics of biological populations with diffusion, logistic term and migration. A necessary and sufficient condition for the nonnegative zero-stabilizabiity for a linear integro-partial differential equation is obtained in terms of the sign of the principal eigenvalue to a certain non-selfadjoint operator. For a related semilinear problem a necessary condition and a sufficient condition for the local nonnegative zero-stabilizability are also derived in terms of the magnitude of the above mentioned principal eigenvalue. The rate of stabilization corresponding to a simple feedback stabilizing control is dictated by the principal eigenvalue. A large principal eigenvalue leads to a fast stabilization to zero. A necessary condition and a sufficient condition for the stabilization to zero of the predator population in a predator-prey system is also investigated. Finally, a method to approximate the above mentioned principal eigenvalues is indicated.

Flow around a cavity is characterized by a self-sustained mechanism in which the shear layer impinges on the downstream edge of the cavity resulting in a feedback mechanism. Direct Numerical Simulations of the flow at low Reynolds number has been carried out to get pressure and velocity fluctuations, for the case of un-actuated and multi frequency actuation. A Reduced Order Model for the isentropic compressible equations based on the method of Proper Orthogonal Decomposition has been constructed. The model has been extended to include the effect of control. The Reduced Order dynamical system shows a divergence in time integration. A method of calibration based on the minimization of a linear functional of error, to the sensitivity of the modes, is proposed. The calibrated low order model is used to design a feedback control of cavity flows based on an observer design. For the experimental implementation of the controller, a state estimate based on the observed pressure measurements is obtained through a linear stochastic estimation. Finally the obtained control is introduced into the Direct Numerical Simulation to obtain a decrease in spectra of the cavity acoustic mode.

We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent. In this paper, the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the interrogator. The problem is formulated in two different ways; one is based on the evolution of the probability density function of the intensity of reflected signal and leads to a controlled forward Kolmogorov or Fokker-Planck equation. The other formulation is based on the evolution of expected value of the intensity of reflected signal and leads to controlled backward Kolmogorov equations. In addition, a number of numerical results are presented to illustrate the usefulness of the proposed approach in exploring problems of control in a general dynamic game setting.

The paper introduces a novel general feedback control framework, which allows applying the motion controllers originally dedicated for the unicycle model to the motion task realization for the car-like kinematics. The concept is formulated for two practically meaningful motorizations: with a front-wheel driven and with a rear-wheel driven. All the three possible steering angle domains for car-like robots—limited and unlimited ones—are treated. Description of the method is complemented by the formal stability analysis of the closed-loop error dynamics. The effectiveness of the method and its limitations have been illustrated by numerous simulations conducted for the three main control tasks, namely, for trajectory tracking, path following, and set-point regulation.

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a one-dimensional wave equation system for which the boundary observation suffers from an arbitrary long time delay. We use the observer and predictor to solve the problem: The state is estimated in the time span where the observation is available; and the state is predicted in the time interval where the observation is not available. It is shown that the estimator/predictor based state feedback law stabilizes the delay system asymptotically or exponentially, respectively, relying on the initial data being non-smooth or smooth. Numerical simulations are presented to illustrate the effect of the stabilizing controller.

A global feedback control of a system that exhibits a subcritical monotonic instabilityat a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zeromode is investigated using a Ginzburg-Landau equation coupled to an equation for the zeromode. The method based on a variational principle is applied for the derivation of alow-dimensional evolution model. In the framework of this model the investigation of thesystem’s dynamics and the linear and nonlinear stability analysis are carried out. Theobtained results are compared with the results of direct numerical simulations of theoriginal problem.


In this paper, the stability of a Timoshenko beam with time delaysin the boundary input is studied. The system is fixed at the leftend, and at the other end there are feedback controllers, in which time delays exist. We prove that this closed loop system iswell-posed. By the complete spectral analysis, we show that there isa sequence of eigenvectors and generalized eigenvectors of thesystem operator that forms a Riesz basis for the state Hilbert space. Hence the system satisfies the spectrum determined growth condition. Then we conclude the exponential stability of the system under certain conditions. Finally, we give some simulations to support our results.


In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of the two-dimensional Burgers equation. We end this paper with a few numerical simulations, comparing the performance of the nonlinear law with the linear one.

The application of the joint force sensory feedback in both the gross and fine motion control of manipulation robots is considered in the paper. One of the objectives of the paper is to give a historical overview how the idea of the joint force sensory feedback has appeared and developed in the past two decades. The control schemes, which include joint torque sensory feedback, are surveyed in the paper. The main advantages of this approach are discussed: the joint torque feedback offers an elegant way to compensate for the effects of the robot dynamics without real time computation of the robot dynamics, the control schemes are robust in respect of parameter variations. Various problems regarding design and implementation of joint torque sensor are also considered. Special emphasis is given to the application of this approach in hybrid position/force control schemes.

This paper presents a linearization by static feedbacks in the robotic field, i.e. by feedback depending on the whole state space. A phenomenological approach is considered, which by using the derivation with respect to time, leads to the major results of the method. Simulation results are presented, and some aspects of the correction of the effect of the characteristic numbers are also discussed.

In this work we deal with the design of the robust feedback control ofwastewater treatmentsystem, namely the activated sludge process. This problem is formulated by anonlinearordinary differential system. On one hand, we develop a robust analysis when thespecific growthfunction of the bacterium μ is not well known. On the other hand, when alsothe substrate concentrationin the feed stream s in is unknown, we provide an observer of system andpropose a designof robust feedback control in term of recycle rate, in order to keep thepollutant concentration lowerthan an allowed maximum level s d .

This paper presents a two-level control strategy for bipedal walking mechanism that accounts for implicit control of push-off on the between-step control level and tracking of imposed holonomic constraints on kinematic variables via feedback control on within-step control level. The proposed control strategy was tested in a biologically inspired model with minimal set of segments that allows evolution of human-like push-off and power absorption. We investigated controller's stability characteristics by using Poincaré return map analysis in eight simulation cases and further evaluated the performance of the biped walking model in terms of how variations in torso position and gait velocity relate to push-off and power absorption. The results show that the proposed control strategy, with the same set of controller's gains, enables stable walking in a variety of chosen gait parameters and can accommodate to various trunk inclinations and gait velocities in a similar way as seen in humans.