Yongsheng Ou

Design and simulation of extremum-seeking open-loop optimal control of current profile in the DIII-D tokamak

In a magnetic fusion reactor, the achievement of a certain type of plasma current profiles, which are compatible with magnetohydrodynamic stability at high plasma pressure, is key to enable high fusion gain and non-inductive sustainment of the plasma current for steady-state operation. The approach taken toward establishing such plasma current profiles at the DIII-D tokamak is to create the desired profile during the plasma current ramp-up and early flattop phases. The evolution in time of the current profile is related to the evolution of the poloidal flux, which is modeled in normalized cylindrical coordinates using a partial differential equation usually referred to as the magnetic diffusion equation. The control problem is formulated as an open-loop, finite-time, optimal control problem for a nonlinear distributed parameter system, and is approached using extremum seeking. Simulation results, which demonstrate the accuracy of the considered model and the efficiency of the proposed controller, are presented.

Human gesture recognition through a Kinect sensor

Gesture recognition can be applied to many research areas, such as vision-based interface, communication and human robot interaction (HRI). This paper implements a non-intrusive, real-time gesture recognition system using a depth sensor. Related features are obtained from the human skeleton model generated by the Kinect sensor. Hidden Markov Models (HMMs) are used to model the dynamics of the gestures. We conducted offline experiments to check the accuracy and robustness of the system. Online experiments were also performed to verify the real-time requirement. Final results indicate that the average recognition accuracy is around 85% for the subject who provides the training data and 73% for the other subject who does not. The system was also used to interact with a mobile robot through gestures. This application indicates that it is robust to work in real-time.

A detection system for human abnormal behavior

This paper introduces a real-time video surveillance system which detects human abnormal behaviors. We present two approaches to such a problem. The first one employs principal component analysis for feature selection and support vector machine for classification of human behaviors. The proposed feature selection method is based on the border information of four consecutive blobs. The second approach computes optical flow to obtain the velocity of each pixel for determining whether a human behavior is normal or not. Both algorithms are successfully implemented in crowded environments for detecting the human abnormal behaviors, such as (1) running people in a crowded environment, (2) bending down movement while most are walking or standing, (3) a person carrying a long bar and (4) a person waving hand in the crowd. Experimental results demonstrate the two methods proposed are robust and efficient in detecting human abnormal behaviors.

Optimal Tracking Control of Current Profile in Tokamaks

Setting up a suitable current spatial profile in tokamak plasmas has been demonstrated to be a key condition for one possible advanced scenario with improved confinement and possible steady-state operation. Experiments at the DIII-D tokamak focus on creating the desired current profile during the plasma current ramp-up and early flattop phases with the aim of maintaining this target profile during the subsequent phases of the discharge. The evolution in time of the current profile is related to the evolution of the poloidal magnetic flux, which is modeled in normalized cylindrical coordinates using a parabolic partial differential equation usually referred to as the magnetic diffusion equation. We propose a framework to solve a finite-time, optimal tracking control problem for the current profile evolution via diffusivity, interior, and boundary actuation during the ramp-up and early flattop phases of the discharge. The proposed approach is based on reduced order modeling via proper orthogonal decomposition and successive optimal control computation for a bilinear system. Simulation results illustrate the performance of the proposed controller.

Dynamic Modeling of Driver Control Strategy of Lane-Change Behavior and Trajectory Planning for Collision Prediction

This paper introduces a dynamic model of the driver control strategy of lane-change behavior and applies it to trajectory planning in driver-assistance systems. The proposed model reflects the driver control strategies of adjusting longitudinal and latitudinal acceleration during the lane-change process and can represent different driving styles (such as slow and careful, as well as sudden and aggressive) by using different model parameters. We also analyze the features of the dynamic model and present the methods for computing the maximum latitudinal position and arrival time. Furthermore, we put forward an extended dynamic model to represent evasive lane-change behavior. Compared with the fifth-order polynomial lane-change model, the dynamic models fit actual lane-change trajectories better and can generate more accurate lane-change trajectories. We apply the dynamic models in emulating different lane-change strategies and planning lane-change trajectories for collision prediction. In the simulation, we use the models to compute the percentage of safe trajectories in different scenarios. The simulation shows that the maximum latitudinal position and arrival time of the generated lane-change trajectories can be good indicators of safe lane-change trajectories. In the field test, the dynamic models can generate the feasible lane-change trajectories and efficiently obtain the percentage of safe trajectories by computing the minimum gap and time to collision. The proposed dynamic model and module can be combined with the human-machine interface to help the driver easily identify safe lane-change trajectories and area.

An energy model approach to people counting for abnormal crowd behavior detection

Abnormal crowd behavior detection plays an important role in surveillance applications. We propose a camera parameter independent and perspective distortion invariant approach to detect two types of abnormal crowd behavior. The two typical abnormal activities are people gathering and running. Since people counting is necessary for detecting the abnormal crowd behavior, we present an potential energy-based model to estimate the number of people in public scenes. Building histograms on the X- and Y-axes, respectively, we can obtain probability distribution of the foreground object and then define crowd entropy. We define the Crowd Distribution Index by combining the people counting results with crowd entropy to represent the spatial distribution of crowd. We set a threshold on Crowd Distribution Index to detect people gathering. To detect people running, the kinetic energy is determined by computation of optical flow and Crowd Distribution Index. With a threshold, kinetic energy can be used to detect people running. To test the performance of our algorithm, videos of different scenes and different crowd densities are used in the experiments. Without camera calibration and training data, our method can robustly detect abnormal behaviors with low computation load.

Ramp-Up-Phase Current-Profile Control of Tokamak Plasmas via Nonlinear Programming

The achievement of suitable toroidal-current-density profiles in tokamak plasmas plays an important role in enabling high fusion gain and noninductive sustainment of the plasma current for steady-state operation with improved magnetohydrodynamic stability. The evolution in time of the current profile is related to the evolution of the poloidal magnetic flux, which is modeled in normalized cylindrical coordinates using a partial differential equation (PDE) usually referred to as the magnetic flux diffusion equation. The dynamics of the plasma current density profile can be modified by the total plasma current and the power of the noninductive current drive. These two actuators, which are constrained not only in value and rate but also in their initial and final values, are used to drive the current profile as close as possible to a desired target profile at a specific final time. To solve this constrained finite-time open-loop PDE optimal control problem, model reduction based on proper orthogonal decomposition is combined with sequential quadratic programming in an iterative fashion. The use of a low-dimensional dynamical model dramatically reduces the computational effort and, therefore, the time required to solve the optimization problem, which is critical for a potential implementation of a real-time receding-horizon control strategy.

Extremum-Seeking Finite-Time Optimal Control of Plasma Current Profile at the DIII-D Tokamak

In a magnetic fusion reactor, the achievement of a certain type of plasma current profiles, which are compatible with magnetohydrodynamic (MHD) stability at high plasma pressure, is key to enable high fusion gain and noninductive sustainment of the plasma current for steady-state operation. The approach taken toward establishing such plasma current profiles at the DIII-D tokamak is to create the desired profile during the plasma current ramp-up and early flattop phases. The evolution in time of the current profile is related to the evolution of the poloidal flux, which is modeled in normalized cylindrical coordinates using a partial differential equation (PDE) usually referred to as the magnetic diffusion equation. The control problem is formulated as an open-loop, finite-time, optimal control problem for a nonlinear distributed parameter system, and is approached using extremum seeking. Simulation results, which demonstrate the accuracy of the considered model and the efficiency of the proposed controller, are presented.

Plasma models for real-time control of advanced tokamak scenarios

Anintegratedplasmaprofilecontrolstrategy,ARTAEMIS,isbeingdevelopedforextrapolatingpresent-dayadvanced tokamak (AT) scenarios to steady-state operation. The approach is based on semi-empirical modelling and was initiallyexploredonJET(Moreauetal2008Nucl.Fusion48106001). Thispaperdealswiththegeneralapplicability of this strategy for simultaneous magnetic and kinetic control on various tokamaks. The determination of thedevicespecific, control-oriented models that are needed to compute optimal controller matrices for a given operation scenario is discussed. The methodology is generic and can be applied to any device, with different sets of heating and current drive actuators, controlled variables and profiles. The system identification algorithms take advantage of the large ratio between the magnetic and thermal diffusion time scales and have been recently applied to both JT-60U and DIII-D data. On JT-60U, an existing series of high bootstrap current (∼70%), 0.9MA non-inductive AT discharges was used. The actuators consisted of four groups of neutral beam injectors aimed at perpendicular injection (on-axis and off-axis), and co-current tangential injection (also on-axis and off-axis). On DIII-D, dedicated system identification experiments were carried out in the loop voltage (Vext) control mode (as opposed to current control) to avoid feedback in the response data from the primary circuit. The reference plasma state was that of a 0.9MA AT scenario which had been optimized to combine non-inductive current fractions near unity with 3.5 <β N < 3.9, bootstrap current fractions larger than 65% and H98(y,2) = 1.5. Actuators other than Vext were co-current,counter-currentandbalancedneutralbeaminjection,andelectroncyclotroncurrentdrive. Powerandloop voltage modulations resulted in dynamic variations of the plasma current between 0.7 and 1.2MA. It is concluded that the response of essential plasma parameter profiles to specific actuators of a given device can be satisfactorily identified from a small set of experiments. This provides, for control purposes, a readily available alternative to first-principles plasma modelling. (Some figures in this article are in colour only in the electronic version)

Brief paper: Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction

We present a framework to solve a finite-time optimal control problem for parabolic partial differential equations (PDEs) with diffusivity-interior actuators, which is motivated by the control of the current density profile in tokamak plasmas. The proposed approach is based on reduced order modeling (ROM) and successive optimal control computation. First we either simulate the parabolic PDE system or carry out experiments to generate data ensembles, from which we then extract the most energetic modes to obtain a reduced order model based on the proper orthogonal decomposition (POD) method and Galerkin projection. The obtained reduced order model corresponds to a bilinear control system. Based on quasi-linearization of the optimality conditions derived from Pontryagins maximum principle, and stated as a two boundary value problem, we propose an iterative scheme for suboptimal closed-loop control. We take advantage of linear synthesis methods in each iteration step to construct a sequence of controllers. The convergence of the controller sequence is proved in appropriate functional spaces. When compared with previous iterative schemes for optimal control of bilinear systems, the proposed scheme avoids repeated numerical computation of the Riccati equation and therefore reduces significantly the number of ODEs that must be solved at each iteration step. A numerical simulation study shows the effectiveness of this approach.