Shape control on probability density function in stochastic systems

A novel strategy of probability density function (PDF) shape control is proposed in stochastic systems. The controller is designed whose parameters are optimally obtained through the improved particle swarm optimization algorithm. The parameters of the controller are viewed as the space position of a particle in particle swarm optimization algorithm and updated continually until the controller makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The controller is excellent in making the state PDF follow the expected PDF and has the very small error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.