In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertaintie...In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.展开更多
Security and stability control system(SSCS)in power systems involves collecting information and sending the decision from/to control stations at different layers;the tree structure of the SSCS requires more levels.Fai...Security and stability control system(SSCS)in power systems involves collecting information and sending the decision from/to control stations at different layers;the tree structure of the SSCS requires more levels.Failure of a station or channel can cause all the execution stations(EXs)to be out of control.The randomness of the controllable capacity of the EXs increases the difficulty of the reliability evaluation of the SSCS.In this study,the loop designed SSCS and reliability analysis are examined for the interconnected systems.The uncertainty analysis of the controllable capacity based on the evidence theory for the SSCS is proposed.The bidirectional and loop channels are introduced to reduce the layers and stations of the existing SSCS with tree configuration.The reliability evaluation and sensitivity analysis are proposed to quantify the controllability and vulnerable components for the SSCS in different configurations.By aiming at the randomness of the controllable capacity of the EXs,the uncertainty analysis of the controllable capacity of the SSCS based on the evidence theory is proposed to quantify the probability of the SSCS for balancing the active power deficiency of the grid.展开更多
To achieve fast, smooth and accurate set point tracking in servo positioning systems, a parameterized design of nonlinear feedback controllers is presented, based on a so-called composite nonlinear feedback (CNF) co...To achieve fast, smooth and accurate set point tracking in servo positioning systems, a parameterized design of nonlinear feedback controllers is presented, based on a so-called composite nonlinear feedback (CNF) control technique. The controller designed here consists of a linear feedback part and a nonlinear part. The linear part is responsible for stability and fast response of the closed-loop system. The nonlinear part serves to increase the damping ratio of closed-loop poles as the controlled output approaches the target reference. The CNF control brings together the good points of both the small and the large damping ratio cases, by continuously scheduling the damping ratio of the dominant closed-loop poles and thus has the capability for superior transient performance, i.e. a fast output response with low overshoot. In the presence of constant disturbances, an integral action is included so as to remove the static bias. An explicitly parameterized controller is derived for servo positioning systems characterized by second-order model. Practical application in a micro hard disk drive servo system is then presented, together with some discussion of the rationale and characteristics of such design. Simulation and experimental results demonstrate the effectiveness of this control design methodology.展开更多
A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input vari...A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group (EMORG) is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.展开更多
In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, ...In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, without zeros, and with measurable state. The controller guarantees that the control system is Type 1 and has the desired constant gain and poles or that the control system tracks, with a specified maximum error and with a specified maximum time constant, a generic reference with bounded derivative (variation in the discrete-time case), also in the presence of a generic disturbance with bounded derivative (variation). In addition, it is considered the case in which the reference is known a priori. The utility and the efficiency of the proposed methods are illustrated with attractive and significant examples of motion control and temperature control. This book is useful for the design of control systems, especially for manufacturing systems, that are versatile, fast, precise and robust.展开更多
The general structure of expert system for controlling sintering process has been proposed. It includes knowledge base, inference engine, data acquisition system, learning system, knowledge base management system, exp...The general structure of expert system for controlling sintering process has been proposed. It includes knowledge base, inference engine, data acquisition system, learning system, knowledge base management system, explanation system and so on. The control functions consist of sintering chemical composition control centered on basicity and sintering process state control centered on permeability. The adaptive prediction of sintering chemical composition, the control strategy centered on basicity, the control strategy centered on permeability, the judgement of permeability and the prediction of burn through point were studied. The software of system, which includes about 1 000 expert rules, was successfully applied in off line control of sintering process in a sintering plant.展开更多
Expert systems aimed at the general design of projectiles can implement a series of intelligent designs, such as the design of HE shell, the scheme expounded and proved, the emulation analysis and calculation, etc. Ai...Expert systems aimed at the general design of projectiles can implement a series of intelligent designs, such as the design of HE shell, the scheme expounded and proved, the emulation analysis and calculation, etc. Aiming at the product design feature, the expert system adopts the object-oriented knowledge representation and all kinds of inference control engines to describe and reason the relevant knowledge regarding the product through the microcomputer. It embodies the foundation of emulation analysis and simulated manufacturing of the shell. It makes use of the method that knowledge expression is combined with condition of inference to carry out the overall design and emulation and reference. The paper gives the ways through which the functions can be achieved, gives the modularization of reference and the design methods of systematization, puts forward the method of knowledge expression and working interface, and supplies a platform for similar products of the shell category that can be quickly designed.展开更多
There has been an increasing interest in integrating decision support systems (DSS) and expert systems (ES) to provide decision makers a more accessible, productive and domain-independent information and computing env...There has been an increasing interest in integrating decision support systems (DSS) and expert systems (ES) to provide decision makers a more accessible, productive and domain-independent information and computing environment. This paper is aimed at designing a multiple expert systems integrated decision support system (MESIDSS) to enhance decision makers' ability in more complex cases. The basic framework, management system of multiple ESs, and functions of MESIDSS are presented. The applications of MESIDSS in large-scale decision making processes are discussed from the following aspects of problem decomposing, dynamic combination of multiple ESs, link of multiple bases and decision coordinating. Finally, a summary and some ideas for the future are presented.展开更多
This paper deals with control system design and implementation problems encountered in multiple robot systems. The methodology developed is depicted by a set of coordination mechanisms using hierarchical net structure...This paper deals with control system design and implementation problems encountered in multiple robot systems. The methodology developed is depicted by a set of coordination mechanisms using hierarchical net structures and their accompanying rules. With the net models, the hierarchical and distributed control system is designed for an assembly task. Synchronization commands allow coordination of the movements of the robots. The net models make concurrency of the movements of the robots transparent to users. The net based machine controller executes robot motion control through the communication with the external robot controller using the command/response concept. Sensory signals indicating the change of state of robots are used to trigger or initiate tasks. Simultaneous movement of the robots is obtained by creating different background threads running in parallel under Windows OS. The multilevel hierarchical control system can be consistently constructed using net models.展开更多
This paper investigates the H∞ controller design method for a class of singular networked control systems (SNCS) based on the singular plant. In view of the network-induced delay less than or equal to a sampling peri...This paper investigates the H∞ controller design method for a class of singular networked control systems (SNCS) based on the singular plant. In view of the network-induced delay less than or equal to a sampling period, finite external disturbance, clock-driven sensors, event-driven controller and actuators as well as impulse behavior and structural instability of singular plants, the H∞ controller design method of SNCS with state feed- back way and dynamic output feedback way is investigated respectively by means of the linear matrix inequality method. The existence condition of H∞ control law, the solving approaches of H∞ controller parameters and disturbance attenuation degree are presented. Finally, a simulation example is given to illustrate the effectiveness and feasibility of the presented method.展开更多
The frequency response design method for PDFSV (Pseudo Derivative Feedback Subvariable) control of electrohydraulic servo system is introduced. Theoretical analysis and computer simulation show that PDFSV con...The frequency response design method for PDFSV (Pseudo Derivative Feedback Subvariable) control of electrohydraulic servo system is introduced. Theoretical analysis and computer simulation show that PDFSV control is a high robust system, and a very good performance can be obtained when this theory is employed in electrohydraulic servo system.展开更多
A difficult but important problem in optimal control theory is the design of an optimal feedback control, i.e., the design of an optimal control as function of the phase (state) coordinates [1,2]. This problem can be ...A difficult but important problem in optimal control theory is the design of an optimal feedback control, i.e., the design of an optimal control as function of the phase (state) coordinates [1,2]. This problem can be solved not often. We study here the autonomous nonlinear system of second order in general form. The constraints imposed on the control input can depend on the phase (state) coordinates of the system. The goal of the control is to maximize or minimize one phase coordinate of the considered system while other takes a prescribed in advance value. In the literature, optimal control problems for the systems of second order are most frequently associated with driving both phase coordinates to a prescribed in advance state. In this statement of the problem, the optimal control feedback can be designed only for special kind of systems. In our statement of the problem, an optimal control can be designed as function of the state coordinates for more general kind of the systems. The problem of maximization or minimization of the swing amplitude is considered explicitly as an example. Simulation results are presented.展开更多
On the basis of the relationship between the Hamiltonian of spin 1/2 quantum system under control and the energy level structure and transitions, a radio frequency pulse sequence is designed using intuitive and half c...On the basis of the relationship between the Hamiltonian of spin 1/2 quantum system under control and the energy level structure and transitions, a radio frequency pulse sequence is designed using intuitive and half counter-intuitive sequences of pulse to transfer the population of the 3-qubit system coherently. The effectiveness of the designed control sequence is verified through the system simulation experiment of the evolution of state. In principle, the design method of the control pulse sequence proposed can be generalized to use in the quantum systems of higher dimension.展开更多
Reinforcement learning(RL) has roots in dynamic programming and it is called adaptive/approximate dynamic programming(ADP) within the control community. This paper reviews recent developments in ADP along with RL and ...Reinforcement learning(RL) has roots in dynamic programming and it is called adaptive/approximate dynamic programming(ADP) within the control community. This paper reviews recent developments in ADP along with RL and its applications to various advanced control fields. First, the background of the development of ADP is described, emphasizing the significance of regulation and tracking control problems. Some effective offline and online algorithms for ADP/adaptive critic control are displayed, where the main results towards discrete-time systems and continuous-time systems are surveyed, respectively.Then, the research progress on adaptive critic control based on the event-triggered framework and under uncertain environment is discussed, respectively, where event-based design, robust stabilization, and game design are reviewed. Moreover, the extensions of ADP for addressing control problems under complex environment attract enormous attention. The ADP architecture is revisited under the perspective of data-driven and RL frameworks,showing how they promote ADP formulation significantly.Finally, several typical control applications with respect to RL and ADP are summarized, particularly in the fields of wastewater treatment processes and power systems, followed by some general prospects for future research. Overall, the comprehensive survey on ADP and RL for advanced control applications has d emonstrated its remarkable potential within the artificial intelligence era. In addition, it also plays a vital role in promoting environmental protection and industrial intelligence.展开更多
Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems (RFDDSs) by the method of inequali...Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems (RFDDSs) by the method of inequalities, in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian's original formulation, which was first proposed in connection with rational systems, is extended to the case of RFDDSs. In making the use of this formulation possible for RFDDSs, the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors. During the design process, the time responses are obtained by a known method for the numerical inversion of Laplace transforms. Two numerical examples are given, where fractional controllers are designed for a time-delay and a heat-conduction plants.展开更多
In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear funct...In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of "explosion of complexity" in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller (SMC). Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.展开更多
文摘In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.
基金supported by Science and Technology Project of SGCC“Research on Flat Architecture and Implementation Technology of Security and Stability Control System in Ultra Large Power Grid”(52170221000U).
文摘Security and stability control system(SSCS)in power systems involves collecting information and sending the decision from/to control stations at different layers;the tree structure of the SSCS requires more levels.Failure of a station or channel can cause all the execution stations(EXs)to be out of control.The randomness of the controllable capacity of the EXs increases the difficulty of the reliability evaluation of the SSCS.In this study,the loop designed SSCS and reliability analysis are examined for the interconnected systems.The uncertainty analysis of the controllable capacity based on the evidence theory for the SSCS is proposed.The bidirectional and loop channels are introduced to reduce the layers and stations of the existing SSCS with tree configuration.The reliability evaluation and sensitivity analysis are proposed to quantify the controllability and vulnerable components for the SSCS in different configurations.By aiming at the randomness of the controllable capacity of the EXs,the uncertainty analysis of the controllable capacity of the SSCS based on the evidence theory is proposed to quantify the probability of the SSCS for balancing the active power deficiency of the grid.
文摘To achieve fast, smooth and accurate set point tracking in servo positioning systems, a parameterized design of nonlinear feedback controllers is presented, based on a so-called composite nonlinear feedback (CNF) control technique. The controller designed here consists of a linear feedback part and a nonlinear part. The linear part is responsible for stability and fast response of the closed-loop system. The nonlinear part serves to increase the damping ratio of closed-loop poles as the controlled output approaches the target reference. The CNF control brings together the good points of both the small and the large damping ratio cases, by continuously scheduling the damping ratio of the dominant closed-loop poles and thus has the capability for superior transient performance, i.e. a fast output response with low overshoot. In the presence of constant disturbances, an integral action is included so as to remove the static bias. An explicitly parameterized controller is derived for servo positioning systems characterized by second-order model. Practical application in a micro hard disk drive servo system is then presented, together with some discussion of the rationale and characteristics of such design. Simulation and experimental results demonstrate the effectiveness of this control design methodology.
基金supported by the National Natural Science Foundation of China (No.70471087)China Postdoctoral Science Foundation Funded Project(No.20080430929)Liaoning Province Education Bureau Foundation (No.20060106)
文摘A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group (EMORG) is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.
基金Supported by National Nature Science Foundation of China (61074068, 60774009, 61034007), and the Research Fund for the Doc- toral Program of Chinese Higher Education (200804220028)
文摘In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, without zeros, and with measurable state. The controller guarantees that the control system is Type 1 and has the desired constant gain and poles or that the control system tracks, with a specified maximum error and with a specified maximum time constant, a generic reference with bounded derivative (variation in the discrete-time case), also in the presence of a generic disturbance with bounded derivative (variation). In addition, it is considered the case in which the reference is known a priori. The utility and the efficiency of the proposed methods are illustrated with attractive and significant examples of motion control and temperature control. This book is useful for the design of control systems, especially for manufacturing systems, that are versatile, fast, precise and robust.
文摘The general structure of expert system for controlling sintering process has been proposed. It includes knowledge base, inference engine, data acquisition system, learning system, knowledge base management system, explanation system and so on. The control functions consist of sintering chemical composition control centered on basicity and sintering process state control centered on permeability. The adaptive prediction of sintering chemical composition, the control strategy centered on basicity, the control strategy centered on permeability, the judgement of permeability and the prediction of burn through point were studied. The software of system, which includes about 1 000 expert rules, was successfully applied in off line control of sintering process in a sintering plant.
文摘Expert systems aimed at the general design of projectiles can implement a series of intelligent designs, such as the design of HE shell, the scheme expounded and proved, the emulation analysis and calculation, etc. Aiming at the product design feature, the expert system adopts the object-oriented knowledge representation and all kinds of inference control engines to describe and reason the relevant knowledge regarding the product through the microcomputer. It embodies the foundation of emulation analysis and simulated manufacturing of the shell. It makes use of the method that knowledge expression is combined with condition of inference to carry out the overall design and emulation and reference. The paper gives the ways through which the functions can be achieved, gives the modularization of reference and the design methods of systematization, puts forward the method of knowledge expression and working interface, and supplies a platform for similar products of the shell category that can be quickly designed.
基金Supported by National High Technology Research and Development Program of China (863 Program) (2006AA04Z183), National Natural Science Foundation of China (60621001, 60534010, 60572070, 60774048, 60728307), Program for Changjiang Scholars and Innovative Research Groups of China (60728307, 4031002)
文摘There has been an increasing interest in integrating decision support systems (DSS) and expert systems (ES) to provide decision makers a more accessible, productive and domain-independent information and computing environment. This paper is aimed at designing a multiple expert systems integrated decision support system (MESIDSS) to enhance decision makers' ability in more complex cases. The basic framework, management system of multiple ESs, and functions of MESIDSS are presented. The applications of MESIDSS in large-scale decision making processes are discussed from the following aspects of problem decomposing, dynamic combination of multiple ESs, link of multiple bases and decision coordinating. Finally, a summary and some ideas for the future are presented.
文摘This paper deals with control system design and implementation problems encountered in multiple robot systems. The methodology developed is depicted by a set of coordination mechanisms using hierarchical net structures and their accompanying rules. With the net models, the hierarchical and distributed control system is designed for an assembly task. Synchronization commands allow coordination of the movements of the robots. The net models make concurrency of the movements of the robots transparent to users. The net based machine controller executes robot motion control through the communication with the external robot controller using the command/response concept. Sensory signals indicating the change of state of robots are used to trigger or initiate tasks. Simultaneous movement of the robots is obtained by creating different background threads running in parallel under Windows OS. The multilevel hierarchical control system can be consistently constructed using net models.
文摘This paper investigates the H∞ controller design method for a class of singular networked control systems (SNCS) based on the singular plant. In view of the network-induced delay less than or equal to a sampling period, finite external disturbance, clock-driven sensors, event-driven controller and actuators as well as impulse behavior and structural instability of singular plants, the H∞ controller design method of SNCS with state feed- back way and dynamic output feedback way is investigated respectively by means of the linear matrix inequality method. The existence condition of H∞ control law, the solving approaches of H∞ controller parameters and disturbance attenuation degree are presented. Finally, a simulation example is given to illustrate the effectiveness and feasibility of the presented method.
文摘The frequency response design method for PDFSV (Pseudo Derivative Feedback Subvariable) control of electrohydraulic servo system is introduced. Theoretical analysis and computer simulation show that PDFSV control is a high robust system, and a very good performance can be obtained when this theory is employed in electrohydraulic servo system.
文摘A difficult but important problem in optimal control theory is the design of an optimal feedback control, i.e., the design of an optimal control as function of the phase (state) coordinates [1,2]. This problem can be solved not often. We study here the autonomous nonlinear system of second order in general form. The constraints imposed on the control input can depend on the phase (state) coordinates of the system. The goal of the control is to maximize or minimize one phase coordinate of the considered system while other takes a prescribed in advance value. In the literature, optimal control problems for the systems of second order are most frequently associated with driving both phase coordinates to a prescribed in advance state. In this statement of the problem, the optimal control feedback can be designed only for special kind of systems. In our statement of the problem, an optimal control can be designed as function of the state coordinates for more general kind of the systems. The problem of maximization or minimization of the swing amplitude is considered explicitly as an example. Simulation results are presented.
基金supported by the National Natural Science Foundation of China (60774098)the National Key Basic Research Program (2006922004)
文摘On the basis of the relationship between the Hamiltonian of spin 1/2 quantum system under control and the energy level structure and transitions, a radio frequency pulse sequence is designed using intuitive and half counter-intuitive sequences of pulse to transfer the population of the 3-qubit system coherently. The effectiveness of the designed control sequence is verified through the system simulation experiment of the evolution of state. In principle, the design method of the control pulse sequence proposed can be generalized to use in the quantum systems of higher dimension.
基金supported in part by the National Natural Science Foundation of China(62222301, 62073085, 62073158, 61890930-5, 62021003)the National Key Research and Development Program of China (2021ZD0112302, 2021ZD0112301, 2018YFC1900800-5)Beijing Natural Science Foundation (JQ19013)。
文摘Reinforcement learning(RL) has roots in dynamic programming and it is called adaptive/approximate dynamic programming(ADP) within the control community. This paper reviews recent developments in ADP along with RL and its applications to various advanced control fields. First, the background of the development of ADP is described, emphasizing the significance of regulation and tracking control problems. Some effective offline and online algorithms for ADP/adaptive critic control are displayed, where the main results towards discrete-time systems and continuous-time systems are surveyed, respectively.Then, the research progress on adaptive critic control based on the event-triggered framework and under uncertain environment is discussed, respectively, where event-based design, robust stabilization, and game design are reviewed. Moreover, the extensions of ADP for addressing control problems under complex environment attract enormous attention. The ADP architecture is revisited under the perspective of data-driven and RL frameworks,showing how they promote ADP formulation significantly.Finally, several typical control applications with respect to RL and ADP are summarized, particularly in the fields of wastewater treatment processes and power systems, followed by some general prospects for future research. Overall, the comprehensive survey on ADP and RL for advanced control applications has d emonstrated its remarkable potential within the artificial intelligence era. In addition, it also plays a vital role in promoting environmental protection and industrial intelligence.
基金supported by the AUN/SEED-Net collaborative research program.
文摘Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems (RFDDSs) by the method of inequalities, in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian's original formulation, which was first proposed in connection with rational systems, is extended to the case of RFDDSs. In making the use of this formulation possible for RFDDSs, the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors. During the design process, the time responses are obtained by a known method for the numerical inversion of Laplace transforms. Two numerical examples are given, where fractional controllers are designed for a time-delay and a heat-conduction plants.
基金supported by National Natural Science Foundation of China (No. 60525303 and 60704009)Key Research Program of Hebei Education Department (No. ZD200908)
文摘In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of "explosion of complexity" in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller (SMC). Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.