A computational method for interval mixed variable energy matrices in precise integration (Q5942749)

An integration scheme is proposed for the solution of the autonomous matrix Riccati differential equation \[ P'(t)= P(t) SP(t)- A^\top P(t)- P(t) A-Q \] arising in the linear-quadratic optimization problem on a finite time interval. The scheme is based on the state transfer matrix of the augmented system for the state and co-state vectors. Numerical examples show that the method proposed is faster and as accurate as the method based on Taylor series expansions.