The global exponential stabilization is considered for a class of distributed parameter control systems with Markovian jumping parameters and time-varying delay. By employing a new Lyapunov-Krasovskii functional, a li...
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The global exponential stabilization is considered for a class of distributed parameter control systems with Markovian jumping parameters and time-varying delay. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish some easy-to-test criteria for global exponential stabilization in the mean square for the stochastic systems. A numerical example is exploited to show the usefulness of the derived LMI-based stabilization conditions.
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...
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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 distributedparametersystem into the lumped parametersystem. 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 controlsystem and close-cycle feedback controlsystem have been investigated. Numerical results agree well with theoretical results. The computer simulation shows that the system is well posed, stable, measurable and controllable.
The problem of controlling the temperature distribution in a solid cylinder whose length varies with time and with one end in contact with a constant temperature medium is considered. This problem is motivated from th...
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The problem of controlling the temperature distribution in a solid cylinder whose length varies with time and with one end in contact with a constant temperature medium is considered. This problem is motivated from that of controlling the temperature and thermal gradient inside a crystal pulled from a melt by the Czochralski method. Boundary feedback controls are derived by considering the time rate of change of a cost functional involving the deviations of both the solid temperature and its gradient from their desired values. The derived feedback controls consist of spatially distributed proportional-plus-rate and lag compensators and a non-linear feedback control involving the temperature gradient at the cylinder surface and the velocity of the spatial domain boundary. The resulting feedback-controlled system has the property that the cost functional along any motion decreases monotonically to zero with time. A numerical scheme for solving the partial differential equation of the feedback-controlled system is proposed. Typical numerical results on the dynamic behaviour of the feedback-controlled system obtained by means of the proposed scheme are presented.
This paper concerns a static multi-objective control problem of the distributedparametersystem, in which regionally decentralized plural decision-makers carry out control actions based on their own goals. The proble...
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This paper concerns a static multi-objective control problem of the distributedparametersystem, in which regionally decentralized plural decision-makers carry out control actions based on their own goals. The problem is formulated as minimization of vector functional to generate noninferior controls. Optimality conditions are derived. Moreover, we study a multi-objective decision problem to choose a preference optimal solution from among a set of non-inferior controls. We consider the following two cases; a) there exists a central decision-maker in the upper level (a central decision problem), and b) no central decision-maker exists and a collective decision is made (a collective decision problem). Two-level computational procedures using a constrained simplex method and an interior penalty method are presented for both cases. Gradient method is used for optimizing a system governed by partial differential equations.
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