Traditional control techniques are mainly concerned with mean and/or variance of the variable in stochastic systems. Recently, the controllers design is focussed also on shaping the probability density function(PDF),which is a new topic in stochastic control research, where the system has its input as a deterministic variable and its output as the PDF of the system output. The study of SDC systems includes mathematic modelling,the controller design and the closed systems analysis. In this thesis, the modelling, control and applications of the stochastic distribution systems (SDC) will be described. The main works and innovative contributions in this thesis are summarized as follows. 1. For the stochastic parameter system , its model is developed based on the B spline. Furthermore, the control strategy based on state feedback and output feedback are established by solving several linear matrix inequalities. 2.Using the linear B-spline approximation, a affine nonlinear state space model and PDF approximation equation can be obtained. Using a linear time-varying system iteration the optimal track control of nonlinear dynamic stochastic system has been obtained. Moreover, PDF tracking control is realized. 3. The modeling method of three dimension curve welding seam is presented based on macro-micro robot, which includes a simple teaching model and a real- time seam model. It has been shown that the model can be obtained by using cubic parameter B-spline least square method and polynomial least square method. The modeling performance is compared based on the two methods. 4. Based upon the macro-micro robot, the tracking control of three dimension seam and 'S' type of planar seam are studied, respectively. 5. The probability density function (PDF) control method has been developed to deal with the random tracking error for a class of robotic manipulator that are subjected to non-Gaussian noises, where noises follow non-Gaussian probability distribution. The iterative learning control (ILC) framework on the PDF control approach of manipulators system with non-Gaussian noises has been proposed and a recursive optimization solution batch-by-batch has been developed.In addition, the convergence condition of the tracking control algorithm has been analyzed.
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