A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial d...A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial differential equations （PDEs） with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy.展开更多
Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The nece...Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The necessary and sufficient conditions concerning the exponential stability of thefirst order singular distributed parameter systems are given.展开更多
The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the ...The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.展开更多
The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional ...The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.展开更多
The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwel...The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient con- ditions are derived in terms of linear operator inequalities frame- work for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these lin- ear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system＇s parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.展开更多
The modelling of one kind of nonlinear parabolic distributed parameter control system with moving boundary, which had extensive applications was presented, Two methods were used to investigate the basic characteristic...The modelling of one kind of nonlinear parabolic distributed parameter control system with moving boundary, which had extensive applications was presented, Two methods were used to investigate the basic characteristics of the system: I) transforming the system it? the variable domain into that in the fixed domain; 2) transforming the distributed parameter system into the lumped parameter system. It is found that there are two critical values for the control variable : the larger one determines whether or not the boundary would move, while the smaller one determines whether or not the boundary, would atop automatically. For one-dimensional system of planar, cylindrical and spherical cases the definite solution problem can be expressed as a unified form. By means of the computer simulation the open-loop control system and close-cycle feedback control system have been investigated. Numerical results agree well with theoretical results. The computer simulation shows that the system is well posed, stable, measurable and controllable.展开更多
Feedback stabilization for a class of second order singular distributed parameter system with multi- inputs is discussed via functional analysis and operator theory in Hilbert space, the solutions of the problem and t...Feedback stabilization for a class of second order singular distributed parameter system with multi- inputs is discussed via functional analysis and operator theory in Hilbert space, the solutions of the problem and the constructive expressions of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the stability of the singular distributed parameter system.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61174021 and 61473136)
文摘A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial differential equations （PDEs） with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy.
基金This research is supported by the National Natural Science Foundation of China under Grant No.60674018.
文摘Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The necessary and sufficient conditions concerning the exponential stability of thefirst order singular distributed parameter systems are given.
基金The National Natural Science Foundation of China(No.61273119,61104068,61374038)the Natural Science Foundation of Jiangsu Province(No.BK2011253)
文摘The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.
基金This work was partially supported by the National Natural Science Foundation of China(No.60504008).
文摘The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.
基金supported by the National Natural Science Foundation of China(6127311961374038+2 种基金6147307961473083)the Natural Science Foundation of Shanxi Province(2012011002-2)
文摘The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient con- ditions are derived in terms of linear operator inequalities frame- work for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these lin- ear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system＇s parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.
文摘The modelling of one kind of nonlinear parabolic distributed parameter control system with moving boundary, which had extensive applications was presented, Two methods were used to investigate the basic characteristics of the system: I) transforming the system it? the variable domain into that in the fixed domain; 2) transforming the distributed parameter system into the lumped parameter system. It is found that there are two critical values for the control variable : the larger one determines whether or not the boundary would move, while the smaller one determines whether or not the boundary, would atop automatically. For one-dimensional system of planar, cylindrical and spherical cases the definite solution problem can be expressed as a unified form. By means of the computer simulation the open-loop control system and close-cycle feedback control system have been investigated. Numerical results agree well with theoretical results. The computer simulation shows that the system is well posed, stable, measurable and controllable.
基金Supported by the National Natural Science Foundation of China(No.60674018)the Natural Sciences Research Foundation of the Education Department of Jiangsu Province in China(No.08KJD510003)
文摘Feedback stabilization for a class of second order singular distributed parameter system with multi- inputs is discussed via functional analysis and operator theory in Hilbert space, the solutions of the problem and the constructive expressions of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the stability of the singular distributed parameter system.
