Numerical solution for optimal regulation of stochastic hereditary systems with multiple discrete delays

An approximation scheme for the solution of the linear quadratic Gaussian control problem for general hereditary systems is developed. The proposed solution is achieved by the definition of two approximating subspaces: the first one to approximate the Riccati equation for the control and the second one to approximate the filtering equations. Such subspaces being finite dimensional the resulting filtering and feedback equations can be easily implemented. An example of application to an unstable delay system is also reported, showing high performance of this method