Discrete Riccati equation for systems with singular transition matrix

Solutions of the Riccati equation for H Discrete Time Systems

Let H and Y be separable Hilbert spaces, and U finite dimensional. Let A ∈ L(H), B ∈ L(U,H), C ∈ L(H,Y ), D ∈ L(U, Y ), and suppose that the open loop transfer function D(z) := D+zC(I−zA)B ∈ H(D;L(U, Y )), where D is the open unit disk. We consider a subset of self adjoint solutions P of the discrete time algebraic operator Riccati equation (DARE)    APA− P + CJC = K PΛPKP , ΛP = D JD +BPB...

Order Reduction of Discrete–time Algebraic Riccati Equations with Singular Closed Loop Matrix

We study the general discrete-time algebraic Riccati equation and deal with the case where the closed loop matrix corresponding to an arbitrary solution is singular. In this case the extended symplectic pencil associated with the DARE has 0 as a characteristic root and the corresponding spectral deflating subspace gives rise to a subspace where all solutions of the DARE coincide. This allows fo...

Solution of matrix Riccati differential equation for nonlinear singular system using neural networks

In this paper, the solution of the matrix Riccati differential equation(MRDE) for nonlinear singular system is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the MRDE obtained from well known traditional Runge Kutta(RK)method and nontraditional neural network method. Accuracy of the neural solution to the problem...

Perturbation analysis of the discrete Riccati equation

The sensitivity of the discrete-time matrix Riccati equation relative to perturbations in its coefficients is studied. Both local and non-local perturbation bounds are obtained. In particular the conditioning of the equation is determined.

The discrete Riccati equation of optimal control