Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

This paper is concerned with the problem of H_∞ output tracking control for networked control systems (NCSs) with network‐induced delay and packet disordering. Different from the results in existing literature, the controller design in this paper is both delay‐ and packet‐disordering‐dependent. Based on the different cases of consecutive predictions, the networked output tracking system is modeled into a switched system. Moreover, by the corresponding switching‐based Lyapunov functional approach, a linear matrix inequality (LMI)‐based procedure is proposed for designing state‐feedback controllers, which guarantees that the output of the closed‐loop NCSs tracks the output of a given reference model well in the H_∞ sense. In addition, the proposed method can be applied variously due to all kinds of prediction numbers of the consecutive disordering packet have been considered, and the designed controller is based on the prediction case in the last transmission interval, which brings about less conservatism. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching‐based method and the delay‐ and packet‐disordering‐dependent H_∞ output tracking controller design.     

An improved sum‐of‐squares based approach to fuzzy tracking control design of nonlinear systems

In this paper, using a more general Lyapunov function, less conservative sum‐of‐squares (SOS) stability conditions for polynomial‐fuzzy‐model‐based tracking control systems are derived. In tracking control problems the objective is to drive the system states of a nonlinear plant to follow the system states of a given reference model. A state feedback polynomial fuzzy controller is employed to achieve this goal. The tracking control design is formulated as an SOS optimization problem. Here, unlike previous SOS‐based tracking control approaches, a full‐state‐dependent Lyapunov matrix is used, which reduces the conservatism of the stability criteria. Furthermore, the SOS conditions are derived to guarantee the system stability subject to a given H_∞ performance. The proposed method is applied to the pitch‐axis autopilot design problem of a high‐agile tail‐controlled pursuit and another numerical example to demonstrate the effectiveness and benefits of the proposed method.     

Observer‐based H ∞ output tracking control for networked control systems

This paper is concerned with observer‐based H _∞ output tracking control for networked control systems. An observer‐based controller is implemented through a communication network to drive the output of a controlled plant to track the output of a reference model. The inputs of the controlled plant and the observer‐based tracking controller are updated in an asynchronous way because of the effects of network‐induced delays and packet dropouts in the controller‐to‐actuator channel. Taking the asynchronous characteristic into consideration, the resulting closed‐loop system is modeled as a system with two interval time‐varying delays. A Lyapunov–Krasovskii functional, which makes use of information about the lower and upper bounds of the interval time‐varying delays, is constructed to derive a delay‐dependent criterion such that the closed‐loop system has a desired H _∞ tracking performance. Notice that a separation principle cannot be used to design an observer gain and a control gain due to the asynchronous inputs of the plant and the controller. Instead, a novel design algorithm is proposed by applying a particle swarm optimization technique with the feasibility of the stability criterion to search for the minimum H _∞ tracking performance and the corresponding gains. The effectiveness of the proposed method is illustrated by an example. Copyright © 2013 John Wiley & Sons, Ltd.     

A further result of the nonlinear mixed H2/H∞ tracking control problem for robotic systems

The design objective of a mixed H₂/H_∞ control is to find the H₂ optimal tracking control law under a prescribed disturbance attenuation level. With the help of the technique of completing the squares, a further result of the mixed H₂/H_∞ optimal tracking control problem is presented, by combining it with standard LQ optimal control technique. In this paper, only a nonlinear time‐varying Riccati equation is required to solve the problem in the design procedure—instead of two coupled nonlinear time‐varying Riccati equations, or two coupled linear algebraic Riccati‐Iike equations—with some assumptions made regarding the weighting matrices in the existing results. A closed‐form controller for the mixed H₂/H_∞ robotic tracking problem is simply constructed with a matrix inequality check. Moreover, it shows that the existing results are the special cases of these results. Finally, detailed comparison is performed by numerical simulation of a two‐link robotic manipulator. © 2002 John Wiley & Sons, Inc.     

H∞ output tracking control for uncertain networked control systems via a switched system approach

In this paper, the problem of H_∞ output tracking control for networked control systems with random time delays and system uncertainties is investigated. Effective sampling instant that is tightly related with transmission delay from sensor to actuator is proposed to ensure that the random variable time delay is always shorter than one effective sampling period. By using both active time‐varying sampling period strategy and hybrid node‐driven mechanism, the switching instant is coincided with the effective sampling instant. An augmented time‐varying networked tracking system model is provided by including the output tracking error as an additional state. However, random transmission delay causes indeterminate sampling period, which induces infinite subsystems. Gridding approach is introduced to transform the continuous time axis into discrete‐time sequences, which guarantees the finite number of switching rules. By employing multiple Lyapunov–Krasovskii functions, linear matrix inequality (LMI)‐based output tracking H_∞ performance analysis is presented, and robust switching H_∞ model reference tracking controller for networked control systems with communication constraints and system uncertainties is designed to guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. Finally, simulation results illustrate the correctness and effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

H∞ tracking control for linear discrete‐time systems via reinforcement learning

In this paper, the H_∞ tracking control of linear discrete‐time systems is studied via reinforcement learning. By defining an improved value function, the tracking game algebraic Riccati equation with a discount factor is obtained, which is solved by iteration learning algorithms. In particular, Q‐learning based on value iteration is presented for H_∞ tracking control, which does not require the system model information and the initial allowable control policy. In addition, to improve the practicability of algorithm, the convergence analysis of proposed algorithm with a discount factor is given. Finally, the feasibility of proposed algorithms is verified by simulation examples.     

Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

In this study, a robust nonlinear L_∞‐gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L_∞ ‐gain optimal tracking control cannot be solved directly, the nonlinear L_∞ ‐gain optimal tracking problem is transformed into a nonlinear L_∞ ‐gain tracking problem by given a prescribed disturbance attenuation level for the L_∞ ‐gain tracking performance. To guarantee that the L_∞ ‐gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L_∞ ‐gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L_∞ ‐gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

ADAPTIVE FUZZY‐BASED MIXED H2/H∞ TRACKING CONTROL DESIGN IN UNCERTAIN ROBOTIC SYSTEMS

In this study, an adaptive fuzzy‐based mixed H₂/H_∞ tracking control design is developed in robotic systems under unknown or uncertain plant parameters and external disturbances. The mixed H₂/H_∞ control design has the advantage of both H₂ optimal control performance and H_∞ robust control performance and the fuzzy adaptive control scheme is used to compensate for the plant uncertainties. By virtue of the skew‐symmetric property in the robotic systems and adequate choice of state variable transformation, sufficient conditions are developed for the adaptive fuzzy‐based mixed H₂/H_∞ tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled differential equations. The proposed methods are simple and the coupled algebraic equations can be solved analytically. Simulation results indicate that the desired performance of the proposed adaptive fuzzy‐based mixed H₂/H_∞ tracking control schemes for the uncertain robotic systems can be achieved.     

Medical image fusion algorithm based on L0 gradient minimization for CT and MRI

In this paper, a novel medical image fusion method based on L₀ Gradient Minimization for CT and MRI is proposed. Compared with traditional algorithms, the proposed method performs well in preserving bones structures from CT and sustaining the soft tissue detail from MRI. It’s worth mentioning that both the proposed low- and high-frequency fusion rules have the capability of generating appropriate weight maps according to the characteristics of CT and MRI images. The fusion algorithm using L₀ Gradient Minimization mainly comprises of four steps: First, source images are decomposed into multi-scale representations via L₀ Gradient Minimization. Second, we propose a low-frequency fusion rule based on local energy and Gaussian filters, which can generate the fused base layer in accord with the basic principle of human beings’ visual system. Third, high-frequency sub-bands are fused by utilizing saliency detection rule based on texture extraction, which generates the satisfying maps according to the degree of significance. Finally, we get the fused result according to the image reconstruction. The proposed algorithm is compared with nine advanced fusion methods and shows superior performance in whether subjective or objective evaluations.

     

Eso‐Based Adaptive Robust Control of Dual Motor Driving Servo System

Based on extended state observer (ESO), we propose an adaptive robust control (ARC) for a dual motor driving servo system, in which there exist nonlinearities affecting control performance. To apply ESO and estimate the lumped uncertainty online, backlash and friction are analyzed and the nonlinear model of the plant is derived. We achieve several control objectives. First, the bias torque is considered in order to eliminate the effect of backlash. Second, the speed feedback is used to maintain the speed synchronization of motors. Then, to achieve feedforward control, finite‐time ESO is designed to estimate the unknown nonlinearities online. Furthermore, the ESO‐based adaptive robust controller is designed to guarantee L_∞ of tracking error by an initialization method, maintaining the transient performance of tracking behavior. Finally, extensive experimental results on a practical test rig validate the effectiveness of our proposed method.     

Optimal‐switched extended H∞ filter for nonlinear systems with stochastic uncertainties

The extended H_∞ filter (EH_∞F) is a conservative solution with infinite‐horizon robustness for the state estimation problem regarding nonlinear systems with stochastic uncertainties, which leads to excessive costs in terms of filtering optimality and reduces the estimation precision, particularly when uncertainties related to external disturbances and noise appear intermittently. In order to restore the filtering optimality lost due to the conservativeness of the EH_∞F design, we developed an optimal‐switched (OS) filtering mechanism based on the standard EH_∞F to obtain an optimal‐switched extended H_∞ filter (OS‐EH_∞F). The OS mechanism has an error‐tolerant switched (ETS) structure, which switches the filtering mode between optimal and H_∞ robust by setting a switching threshold with redundancy to uncertainties, and a robustness‐optimality cost function (ROCF) is introduced to determine the threshold and optimize the ETS structure online. The ROCF is the weighted sum of the quantified filtering robustness and optimality. When a weight is given, the proposed OS‐EH_∞F can obtain the optimal state estimates while maintaining the filtering robustness at an invariant ratio. A simulation example of space target tracking has demonstrated the superior estimation performance of the OS‐EH_∞F compared with some other typical filters, thereby verifying the effectiveness of using the weight to evaluate the estimation result of the filters.     

Monocular human motion tracking with discriminative sparse representation

In this work, we address the problem of monocular tracking the human motion based on the discriminative sparse representation. The proposed method jointly trains the dictionary and the discriminative linear classifier to separate the human being from the background. We show that using the online dictionary learning, the tracking algorithm can adapt the variation of human appearance and background environment. We compared the proposed method with four state-of-the-art tracking algorithms on eight benchmark video clips (Faceocc, Sylv, David, Singer, Girl, Ballet, OneLeaveShopReenter2cor, and ThreePastShop2cor). Qualitative and quantitative experimental validation results are discussed at length. The proposed algorithm for human tracking achieves superior tracking results, and a Matlab run time on a standard desktop machine of four frames per second.     

Stochastic approximation with nondecaying gain: Error bound and data‐driven gain‐tuning

Our problem of interest is to minimize a sequence of scalar‐valued loss functions f_k(·) or to locate the root(s) of a sequence of vector‐valued functions g _k(·) corresponding to time with respect to a parameter . The available information for the minimization/root‐finding is the noise‐corrupted observation(s) of either f_k(·) or g _k(·) evaluated at a few of certain design points only. Taking both the dynamics and randomness into consideration, we use stochastic approximation (SA) algorithms to solve the time‐varying problem, but with a nondecaying gain (stepsize). The tracking performance of the nondecaying gain SA algorithm is guaranteed by a computable bound for the root‐mean‐squared error and mean‐absolute‐deviation. The only assumption imposed on the drifts is that the average distance between two consecutive underlying true parameters is bounded from above—this assumption allows the varying target to change abruptly. The error term arising from using the noisy evaluation of f_k(·) or g _k(·) in constructing the search direction is assumed to have bounded second‐moment—this allows for biased estimator to be used in the SA algorithms. Given the lenient assumptions on the drift and error term, the error bounds apply to a broad class of time‐varying scenarios and are useful for finite‐sample analysis. Since the tracking capability characterizes the average performance across all possible sample paths, it may not provide much guidance on the gain‐tuning strategies useful for one single run. Hence, we propose a data‐dependent gain‐tuning strategy based on estimating the Hessian information and the noise level. The adaptive rule is advantageous as it enables the step size to vary with information gathered during the progress of the estimation procedure.     

H ∞ output tracking control for discrete‐time switched systems via output feedback

This paper studies the problem of H _∞ output tracking control for a class of discrete‐time switched systems. Neither the measurability of the system state nor the solvability of the output tracking control problem for each individual subsystem is required. We design controllers for subsystems and a switching law to solve the H _∞ output tracking problem for the switched system. The designed controllers use only the measured output feedback, and the switching law is based on the measured output tracking error. In addition, the quadratic function corresponding to each subsystem is not required to be positive definite. A numerical example is provided to demonstrate the feasibility and validity of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponential l2−l∞ output tracking control for discrete‐time switched system with time‐varying delay

The problem of exponential l₂?l_∞ output tracking control is considered in this paper for discrete‐time switched systems with time‐varying delay. The exponential l₂?l_∞ performance index is first introduced to study this problem for discrete‐time switched systems. By resorting to the average dwell time approach and Lyapunov–Krasovskii functional technology, some new delay‐dependent criteria guaranteeing exponential stability are developed. In addition, the corresponding solvability conditions using cone complement linearization method for the desired exponential l₂?l_∞ output tracking controller is established. A numerical example is provided to demonstrate the effectiveness of the obtained results. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust observer–controller compensator design using the loop shaping design procedure and the algebraic method

This paper investigates robust observer‐controller compensator design using Vidyasagar's structure (VS). VS has a unit matrix parameter H similar to the Q parameter for the Youla–Kucera parameterization. VS can be designed based on the left coprimeness of the central controller in the H_∞‐loop shaping design procedure (H_∞‐LSDP) and therefore can preserve the intrinsic properties of the H_∞‐LSDP. This paper introduces algebraic methods to simplify the design of H in the VS controller by solving specific algebraic equations. In particular, the algebraic design of H can achieve two things. First, a dynamic H adjusts the tracking performance and yields the integral action. Second, a dynamic H rejects the input and output sinusoidal disturbances with known frequencies. These attributes are indications of the flexibility of the proposed method since the output‐feedback controller design of the H_∞‐LSDP cannot easily deal with such conditions. This paper discusses the achieved loop and the closed‐loop behavior of the system with VS, and also gives two numerical examples. The first example shows that the proposed method results in a better design in many aspects than the resulting from H_∞‐LSDP. The second example shows the application of the proposed method to rejecting input and output step disturbances, and input and output multiple sinusoidal disturbances, for which the H_∞‐LSDP can hardly be used. Copyright © 2009 John Wiley & Sons, Ltd.     

Guaranteed performance in semi global trajectory tracking for matched disturbance nonlinear systems

In this article, we present a semi global trajectory tracking approach that guarantees a priori computable L ₂ and L _∞ performance bounds for matched disturbance control affine systems. The proposed controller is derived by combining a standard inverse control technique with an extended nonlinear robust state feedback. The latter is based on a control Lyapunov function used for stabilising one operating point inside the considered state space. A difference gradient formulation of this Lyapunov function is then applied to prove stabilisation along any trajectory in the considered state space. Results for L ₂ and L _∞ bounded disturbances will be presented and further extended to the case of actuator uncertainties and disturbance offsets. The theoretical contributions are verified applying them to a numerical example.     

Robust H∞ fuzzy observer‐based tracking control design for a class of nonlinear stochastic Markovian jump systems

This paper investigates the stochastic H_∞ tracking control problem for a class of nonlinear stochastic Markovian jump systems. The attention is focused on the design of a fuzzy observer‐based fuzzy controller such that an H_∞ model reference tracking performance is guaranteed for admissible disturbances. A sufficient condition is established to guarantee the existence of the desired robust controller, which is given in terms of a set of coupled matrix inequalities. Moreover, a novel decoupled method is proposed to transform the sufficient condition into some linear matrix inequality (LMI) form such that observer gains and control gains can be simultaneously obtained by solving a set of LMIs. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

Event-triggered Networked H∞ Output Tracking Control Based on Dynamic Compensation Controller

In this paper, the event-triggered H_∞ output tracking problem is investigated for networked control systems. In order to reduce the output tracking error as well as to improve network resource utilization, we propose an idea of dynamic compensation controller with the discrete-time event-triggered mechanism, that is, the integral term of tracking error and the state of the reference system are introduced to form states of the augmented system. We first examine the dynamic compensation idea by the H_∞ output tracking control problem for linear time-invariant (LTI) systems. Then, we model the closed-loop event-triggered networked control system as a time-delay augmented linear system. By constructing a Lyapunov-Krasovskii functional with the delay fractioning technique, the stability conditions with lower conservatism are derived in the form of the linear matrix inequalities (LMIs). Furthermore, a method is proposed to design the H_∞ dynamic compensation controllers and the discrete-time event-triggered mechanisms. Finally, the satellite tracking control problem is used as an example to show that the dynamical compensation idea is effective in reducing the tracking error and that the proposed method in this paper can achieve better performance than that in the existing literature.