Minimum Tracking Error Research Articles

A Cognitive Nonlinear Trajectory Tracking Controller Design for Wheeled Mobile Robot based on Hybrid Bees-PSO Algorithm

The aim of the work for this paper is a comparative study of different types of on-line cognitive algorithms for the proposed nonlinear controller of the trajectory tracking for dynamic wheeled mobile robot that has a capability to track a continuous desired path. Three optimization algorithms are used (Bees, PSO and proposed hybrid Bees-PSO) in order to find and tune the values of the control gains of the neural controller as simple on-line with fast tuning techniques. The best torques control actions of the right wheel and left wheel for the cart mobile robot are generated on-line from the proposed controller. Simulation results (Matlab Package) show that the proposed nonlinear neural controller with hybrid Bees-PSO cognitive algorithm is more accurate in terms of fast on-line finding and tuning parameters of the controller; obtaining smoothness control action as well as minimizing tracking error of the wheeled mobile robot than PSO or Bees optimization algorithms.

Constrained optimal iterative learning control with mixed-norm cost functions

Iterative learning Control (ILC) is a widely used design technique for determining feedforward control inputs to systems that perform the same task repeatedly. This feedforward control design problem can be posed as an optimization problem in the Norm Optimal ILC (NO-ILC) framework. Although NO-ILC problems are usually formulated without constraints, they may be extended to enforce constraints by posing an analogous constrained optimization problem, termed Constrained Optimal ILC (CO-ILC). Typical NO-ILC and CO-ILC algorithms use 2-norm type cost functions (i.e., minimizing tracking error and control effort 2-norms), which are smooth and have analytical gradient expressions for design of the update law. However, in many applications, the max (∞) norm of tracking error is critical, which is a nonsmooth function and thus gradient-based ILC methods cannot be directly used. In this manuscript, we design a CO-ILC algorithm to explore the performance of using non-smooth type cost functions and compare them with the case using 2-norm cost function with actuator (or more generally state) box constraints. Specifically, CO-ILC algorithms for linear system with linear constraints are derived using (1) an ∞-norm cost function, (2) a mixed (2−∞)-norm cost function and (3) a sequential (2−∞)-norm cost function; the performance results of these are then compared with the traditional CO-ILC using 2-norm cost function on a precision motion control stage experimentally. We also provide proofs for robust monotone convergence of the proposed CO-ILC algorithms for a class of uncertainty models.

A Cognitive Nonlinear Fractional Order PID Neural Controller Design for Wheeled Mobile Robot based on Bacterial Foraging Optimization Algorithm

The aim of this paper is to design a proposed non-linear fractional order proportional-integral-derivative neural (NFOPIDN) controller by modifying and improving the performance of fractional order PID (FOPID) controller through employing the theory of neural network with cognitive optimization techniques for the differential - drive wheeled mobile robot (WMR) multi-input multi-output (MIMO) system in order to follow a pre-defined trajectory. In this paper a cognitive bacterial foraging optimization algorithm (BFOA) has been utilized to find and tune the parameters of the proposed (NFOPIDN) controller and then find the optimal torque control signals for the differential - drive WMR. The simulation results show that the proposed controller can give excellent performance in terms of compared with other works (minimized tracking error for Ranunculoid-curve trajectory, smoothness of torque control signals obtained without saturation state and no sharp spikes action as well as minimum number of memory units needed for the structure of the proposed NFOPIDN controller).

Stereovision-based target tracking system for USV operations

A stereovision based methodology to estimate the position, speed and heading of a moving marine vehicle from a pursuing unmanned surface vehicle (USV) is considered, in support of enabling a USV to follow a target vehicle in motion. The methodology involves stereovision ranging, object detection and tracking, and minimization of tracking error due to image quantization limitations and pixel miscorrespondences in the stereo pixel-matching process. The method consists of combining a simple stereovision-matching algorithm, together with a predictive-corrective approach based on an extended Kalman filter (EKF), and use of suitable choices of probabilistic models representing the motion of the target vehicle and the stereovision measurements. Simple matching algorithms perform faster at the expense of potential errors in depth measurement. The approach considered aims to minimize the tracking errors related to such errors in stereovision measurements, thereby improving the accuracy of the state estimation of the vehicle. Results from simulations and a real-time implementation reveal the effectiveness of the system to compute accurate estimates of the state of the target vehicle over non-compliant trajectories subjected to a variety of motion conditions.

What’s in the news? The ambiguity of the information content of index reconstitutions in Germany

We analyze stock price behavior around reconstitutions of the German DAX index family from 1990 to 2013. The strong price run-up of added stocks in the 2 months preceding the announcement date remains robust until 2 months after the effective date (ED), and is fully reversed 5 months later. Conversely, stock prices of deleted firms are under pressure until 10 months after the ED. Unlike most previous studies, we find that outright entries and exits have temporary price effects, as do additions to and deletions from better-known indices; however, promotions and demotions related to lesser-known indices command permanent stock price responses. Rather surprisingly, deleted stocks consistently earn higher abnormal returns than added stocks in the 5-year post-event period. Specifically, the return differential levels out at 77.3%. We establish that this differential in permanent stock prices is attributable to differences in operating performance and media coverage. In practice, index reconstitutions do not appear to give unambiguous signals about the long-run investment appeal of affected firms. However, index fund managers not constrained by tracking error minimization would be better off holding deleted stocks for 5 years after the ED.

Data-Driven Networked Optimal Iterative Learning Control for Discrete Linear Time-Varying Systems with One-Operation Bernoulli-Type Communication Delays

This paper develops a type of data-driven networked optimal iterative learning control strategy for a class of discrete linear time-varying systems with one-operation Bernoulli-type communication delays. In terms of the stochastic Bernoulli-type one-operation communication delayed inputs and outputs, the previous-iteration synchronous compensations are adopted. By means of deriving gradients of two types of objective functions that express the optimal approximation of the system matrix and the minimal tracking error, the strategy approximates the system matrix and upgrades the control inputs in an interact mode as the iteration evolves. By taking advantage of matrix theory and statistical technique, it is derived that the approximation discrepancy of the system matrix is bounded and the mathematical expectation of the tracking error vanishes as the iteration goes on. Numerical simulations manifest the validity and effectiveness.

Algorithms for <i>l</i><SUB align="right">1-norm minimisation of index tracking error and their performance

Algorithms for <i>l</i><SUB align="right">1-norm minimisation of index tracking error and their performance

Motion Control of An Autonomous Mobile Robot using Modified Particle Swarm Optimization Based Fractional Order PID Controller

This paper presents a comparison between two nonlinear PID controllers, the first is the Neural based controller and the second is the nonlinear fractional order PID controller (FOPID) for a trajectory tracking control of a non-holonomic two wheeled mobile robots (2-WMR). A modified particle swarm optimization (MPSO) has been proposed in this work to tune the parameters of the nonlinear FOPID controller to design the controller so that the 2-WMR follows exactly a predefined continuous track. The kinematic model of a differential drive 2-WMR has been derived to simulate the behavior of the 2-WMR and it is used in the design and simulations of the proposed FOPID controller. From simulation and results, it can be seen that the efficiency of the proposed nonlinear FOPID controller outperforms the nonlinear integer order PID controller; this is proved by the minimized tracking error and the speed control signals obtained.

Dual-loop H∞ controller design for a grid-connected single-phase photovoltaic system

A nonlinear dual-loop H∞ controller is presented in this paper synthesized with linear matrix inequality (LMI) method with primary objectives of generating switching signals for inverters for maximum power point tracking and improving dynamic response of a single-phase grid-connected photovoltaic (PV) system. A state-space model of the PV system is developed with parametric uncertainty in terms of linear fractional transformation. A dual control loop is implemented into the control structure: one is outer dc-link voltage control loop and the other is inner grid current control loop. Weighting functions are first selected and tuned to achieve minimum tracking error and robust performance. Next, control laws are obtained by synthesizing the controller. To facilitate practical implementation, model order of the controller is reduced by Henkel-norm method. The performance of the proposed controller is demonstrated on a test system through simulation results under different parametric, atmospheric and load conditions as well as system contingencies. From the simulation results, it is evident that the controller provides superior performance under various operating conditions.

Incremental Clustering-Based Facial Feature Tracking Using Bayesian ART

Person-independent, emotion specific facial feature tracking have been of interest in the machine vision society for decades. Among various methods, the constrained local model (CLM) has shown significant results in person-independent feature tracking. In 63this paper, we propose an automatic, efficient, and robust method for emotion specific facial feature detection and tracking from image sequences. Considering a 17-point feature model on the frontal face region, the proposed tracking framework incorporates CLM with two incremental clustering algorithms to increase robustness and minimize tracking error during feature tracking. The Patch Clustering algorithm is applied to build an appearance model of face frames by organizing previously encountered similar patches into clusters while the shape Clustering algorithm is applied to build a structure model of face shapes by organizing previously encountered similar shapes into clusters followed by Bayesian adaptive resonance theory (ART). Both models are used to explore the similar features/shapes in the successive images. The clusters in each model are built and updated incrementally and online, controlled by amount of facial muscle movement. The overall performance of the proposed incremental clustering-based facial feature tracking (ICFFT) is evaluated using the FGnet database and the extended Cohn-Kanade (CK+) database. ICFFT demonstrates better results than baseline-method CLM and provides robust tracking as well as improved localization accuracy of emotion specific facial features tracking.

Efficient sensory cortical coding optimizes pursuit eye movements.

In the natural world, the statistics of sensory stimuli fluctuate across a wide range. In theory, the brain could maximize information recovery if sensory neurons adaptively rescale their sensitivity to the current range of inputs. Such adaptive coding has been observed in a variety of systems, but the premise that adaptation optimizes behaviour has not been tested. Here we show that adaptation in cortical sensory neurons maximizes information about visual motion in pursuit eye movements guided by that cortical activity. We find that gain adaptation drives a rapid (<100 ms) recovery of information after shifts in motion variance, because the neurons and behaviour rescale their sensitivity to motion fluctuations. Both neurons and pursuit rapidly adopt a response gain that maximizes motion information and minimizes tracking errors. Thus, efficient sensory coding is not simply an ideal standard but a description of real sensory computation that manifests in improved behavioural performance.

Tracking Control of Linear Time-Invariant Nonminimum Phase Systems Using Filtered Basis Functions

An approach for minimizing tracking errors in linear time-invariant (LTI) single-input single-output (SISO) discrete-time systems with nonminimum phase (NMP) zeros using filtered basis functions (FBF) is studied. In the FBF method, the control input to the system is expressed as a linear combination of basis functions. The basis functions are forward filtered using the dynamics of the NMP system, and their coefficients are selected to minimize the error in tracking a given desired trajectory. Unlike comparable methods in the literature, the FBF method is shown to be effective in tracking any desired trajectory, irrespective of the location of NMP zeros in the z-plane. The stability of the method and boundedness of the control input and system output are discussed. The control designer is free to choose any suitable set of basis functions that satisfy the criteria discussed in this paper. However, two rudimentary basis functions, one in time domain and the other in frequency domain, are specifically highlighted. The effectiveness of the FBF method is illustrated and analyzed in comparison with the truncated series (TS) approximation method.

An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems

In this paper, an optimal adaptive robust PID controller based on fuzzy rules and sliding modes is introduced to present a general scheme to control MIMO uncertain chaotic nonlinear systems. In this control scheme, the gains of the PID controller are updated by using an adaptive mechanism, fuzzy rules, the gradient search method, and the chain rule of differentiation in order to minimize the sliding surfaces of sliding mode control. More precisely, sliding mode control is used as a supervisory controller to provide sufficient control inputs and guarantee the stability of the control approach. To ascertain the parameters of the proposed controller and avoid trial and error, the multi-objective genetic algorithm is employed to augment the performance of proposed controller. The chaotic system of a Duffing-Holmes oscillator and an industrial robotic manipulator are the case studies to evaluate the performance of the proposed control approach. The obtained results of this study regarding both systems are compared with the outcomes of two notable studies in the literature. The results and analysis prove the efficiency of the proposed controller with regard to MIMO uncertain systems having challenging external disturbances in terms of stability, minimum tracking error and optimal control inputs.

Periodic learning disturbance observer based precision motion control in PMLSM motion systems considering long-term instability problem

This paper presents a novel periodic learning disturbance observer(PLDOB) based controller that considers a long-term instability problem to achieve high precision position control in permanent magnet linear synchronous motor (PMLSM) motion systems under repetitive motion conditions. In the proposed scheme, an initial condition for PLDOB, which is the learning law in the proposed controller, is designed by a linear disturbance observer (DOB) due to an advantage that the learning law is designed directly from a point of a view of the disturbance, unlike ILC and RC. The use of the initial condition in the proposed scheme improves the learning speed to minimize tracking errors and guarantees the stability of the overall system at fast learning speed. In the proposed controller, no mathematical models are required to compensate for the dominant disturbances such as friction forces, force ripples, and model parametric errors in the PMLSM motion system, and the lumped disturbance is attenuated by PLDOB. The weaknesses induced by the use of Q-filter of DOB, such as the phase lag and limited frequency range for the estimated disturbance, are compensated, and it improves the transient performance and tracking performance. Also, theoretical analysis for the long-term instability problem is performed

Particle tracking microrheology of protein solutions

Video-based particle tracking microrheology that requires ∼2 μl per sample is used to measure the viscosity of protein solutions of monoclonal antibodies. Direct imaging provides an immediate assessment of probe stability and the validity of the microrheology measurement. Precise measurements are made by choosing a displacement lag time that is a balance between minimizing tracking error while maximizing the number of sampled particle displacements. The excess kurtosis α2 of the probe displacement probability distribution and its test statistic Zα2 are used to set the optimal lag time. The viscosity is calculated by fitting a Gaussian distribution to the sampled displacements. Microrheology viscosities for two monoclonal antibody solutions are in good agreement with bulk rheology. Using a similar comparison of the microrheology of sucrose solutions with a correlation relating viscosity and concentration, an analysis of covariance (p = 0.941) demonstrates the high accuracy of small volume microrheology measurements. Based on the relative error between measured and tabulated viscosities, the uncertainty of viscosities derived from particle tracking is less than 2% of the true value.

An Adaptive INS-Aided PLL Tracking Method for GNSS Receivers in Harsh Environments.

As the weak link in global navigation satellite system (GNSS) signal processing, the phase-locked loop (PLL) is easily influenced with frequent cycle slips and loss of lock as a result of higher vehicle dynamics and lower signal-to-noise ratios. With inertial navigation system (INS) aid, PLLs’ tracking performance can be improved. However, for harsh environments with high dynamics and signal attenuation, the traditional INS-aided PLL with fixed loop parameters has some limitations to improve the tracking adaptability. In this paper, an adaptive INS-aided PLL capable of adjusting its noise bandwidth and coherent integration time has been proposed. Through theoretical analysis, the relation between INS-aided PLL phase tracking error and carrier to noise density ratio (C/N0), vehicle dynamics, aiding information update time, noise bandwidth, and coherent integration time has been built. The relation formulae are used to choose the optimal integration time and bandwidth for a given application under the minimum tracking error criterion. Software and hardware simulation results verify the correctness of the theoretical analysis, and demonstrate that the adaptive tracking method can effectively improve the PLL tracking ability and integrated GNSS/INS navigation performance. For harsh environments, the tracking sensitivity is increased by 3 to 5 dB, velocity errors are decreased by 36% to 50% and position errors are decreased by 6% to 24% when compared with other INS-aided PLL methods.

A trajectory optimization method for improved tracking of motion commands using CNC machines that experience unwanted vibration

This paper presents a trajectory optimization method for minimizing tracking errors in CNC machines that experience unwanted vibration. The motion command sent to the machine is parameterized using B-splines whose basis functions are filtered using a model of the machine's dynamics. The control points associated with the filtered basis functions are then selected to minimize tracking errors subject to the kinematic limits of the machine. The proposed method is shown to be very systematic and easy to use, and it does not sacrifice tracking speed. Experiments are used to demonstrate its superior performance compared to an existing method.

Robust PID Controller for a Pneumatic Actuator

In this paper the position control pneumatic actuator using a robust PID controller is presented. The parameters of the PID controller are computed using a Hurwitz invariability technique enriched with a Simulated Annealing Algorithm. The nonlinear model involves uncertain parameters due to linearization of the servo valve, variations of the initial volume of the cylinder and variation of the external load. The problem is proven to be solvable and the controller parameters are chosen to provide a suboptimal solution for tracking error minimization. Simulation results are presented for the nonlinear model.

ALPHA-BETA SEPARATION PORTFOLIO STRATEGIES FOR ISLAMIC FINANCE

The purpose of this paper is to develop a mathematical alpha-beta separation model that can be used to create a core-satellite portfolio management strategy that complies with the principles of Islamic finance. Methodology. Core-satellite portfolio construction methodology is used to implement the alpha-beta separation approach, where the core part of the portfolio is managed using the tracking error minimization strategy, and the satellite part of the portfolio is managed using the mean-variance optimization strategy. Results of the portfolio dynamics clearly show that a significant amount of value was created by alpha-beta separation. The typical alpha ranges from 4% to 5.7%. The most aggressive portfolio strategies that allow short positions in the satellite portfolio work best with frequent rebalancing and benefit from the active bets. Smoothing technique that was introduced to decrease the portfolio turnover and stabilize its composition works better when active bets are less efficient, particularly with less frequent rebalancing. The best risk-return combinations are achieved with modest (3% to 10%) allocation of the total portfolio to the satellite, and the remaining part (90% to 97%) being managed in order to minimize the tracking error. Practical implications. The alpha-beta separation framework suggested in this paper can be used to enhance the portfolio management techniques for the hedge funds that operate under tight restrictions, particularly under the Islamic finance principles. The mathematical models developed in this paper allow practical implementation of the alphabeta separation concept. Originality/value. While the idea of alpha-beta separation existed in hedge fund management before, there was no comprehensive mathematical model under it, so its implementation was based on the ad hoc approach. This paper introduces such a mathematical model and demonstrates how portfolio managers can create value for their clients using it.

Precise Positioning Control Using Online Modification of Reference Trajectory

SUMMARYA control method for improving tracking performance with respect to a reference trajectory has been developed. The proposed control system has an inner/outer control structure. The inner control system is the existing control system based on a conventional PID controller, which is designed in advance and is independent of the outer control system. In order to improve tracking performance, the outer control system is designed based on optimal preview control theory and is added to the outside of the inner control system. A polynomial trajectory is used as the reference trajectory and is fed to the outer control system. The reference trajectory is modified online to minimize tracking error. The modified reference trajectory is derived as a control input signal from the outer control system and is fed to the inner control system. The effectiveness of the proposed control method is confirmed using numerical simulations in a benchmark problem for hard disk drives (HDDs).