The recursive algorithm for Riccati matrix and the equivalent action

Linear quadratic optimal control and Kalman filtering problem can be described by Hamiltonian dual equations uniformly. Based on the T-parameter solution of Hamiltonian dual equations, the recursive formulas for Riccati matrix and the equivalent action were deduced. The backward and forward recursive algorithms were presented for the nodal variables of multiple segments system, and the recursive algorithms can be applied in linear quadratic optimal control and Kalman filtering problem.