We consider a splitting-based approximation of the abstract differential Riccati equation in the setting of Hilbert–Schmidt operators. The Riccati equation arises in many different areas and is important within the field of optimal control. In this paper we conduct a temporal error analysis and prove that the splitting method converges with the same order as the implicit Euler scheme, under the...

In this paper, a computational algorithm for solving sign-indefinite general multiparameter algebraic Riccati equation (SIGMARE) that arises in the H∞ filtering problem is investigated. After establishing the asymptotic structure of the solution of the SIGMARE, in order to solve the SIGMARE, Newton’s method and two fixed point algorithms are combined. As a result, the new iterative algorithm ac...

We consider a recently published method for solving algebraic Riccati equations. We present a new perspective on this method in terms of the underlying linear-quadratic optimal control problem: we prove that the matrix obtained by this method expresses the optimal cost for a projected optimal control problem. The projection is determined by the so-called shift parameters of the method. Our repr...

In this paper, we proposed an unconditionally stable NonStandard Finite Difference (NSFD) scheme to solve nonlinear Riccati differential equation. The accuracy and efficiency of the proposed scheme is verified by comparing the results with other numerical techniques such as Euler and RK-4 and semi analytical technique DTM. The obtained results show that the performance of NSFD scheme is more ac...

We consider the numerical solution of the continuous algebraic Riccati equation AX +XA−XFX +G = 0, with F = F , G = G of low rank and A large and sparse. We develop an algorithm for the low rank approximation of X by means of an invariant subspace iteration on a function of the associated Hamiltonian matrix. We show that the sought after approximation can be obtained by a low rank update, in th...

We will consider He’s variational iteration method for solving fractional Riccati differential equation. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converges to the exact solution of the problem. The present method performs extremely well in terms of efficiency ...