with the symmetric positive definite cost-to-go matrix X evolving backwards in time from X_S = Q according to .
X_{t-1} = Q+\text{E}[A^TX_tA] - \text{E}[A^TX_tB][\text{E}(B^TX_tB+R)]^{-1}\text{E}(B^TX_tA), \, .