The LQG Algorithm For Stochastic Control Systems And Its Convergence

In this paper,the approximation algorithm of the nonlinear stochastic optimal control system is considered.And the convergence of the series of approximate problems is also discussed.One hand,in the case of incomplete state information,the approximation algorithm of the nonlinear stochastic optimal control system with time delay is concerned.By using Taylor expansion,the stochastic optimal control system is discretized.Then the original problem is transformed into a linear quadratic Gaussian(LQG)problem with the controlling increment and the state increment.By using the Bellman's dynamic programming principle,the recursive formula of the affine feedback optimal control law and the optimal state trajectory of LQG problem is obtained.Using Kalman's filter method,the gain matrix is constructed and the optimal filter is designed.LQG algorithm scheme is given.On the other hand,in the case of complete state information,the convergence of a series of the approximation problems for a class of nonlinear stochastic optimal control systems is discussed.It is proved that the series of solutions corresponding to approximate problems converge to a real solution which satisfied the original problem.The validity of the conclusion is verified through an experiment.