Optimal Control and Filtering of Weakly Coupled Linear Continuous-Time Stochastic Systems by the Eigenvector Approach

N. Prljaca (Bosnia and Herzegovina), Z. Gajic (USA), and Z. Sehic (Bosnia and Herzegovina)


Optimal control and filtering, Weakly coupled systems, Block diagonalization, Decoupling


In this paper the regulator and filter algebraic Riccati equations, corresponding to the steady state optimal control and filtering of weakly coupled linear continuous-time stochastic systems are solved in terms of reduced-order sub problems by using the eigenvector approach. In addition, the optimal global Kalman filter is decomposed into local optimal filters both driven by the system measurements and the system optimal control inputs. The eigenvector method outperforms iterative methods (fixed point iterations, Newton method) of solutions to reduced-order sub problems in case of higher level of coupling between subsystems. In such cases the iterative methods could fail to produce solutions of the corresponding algebraic Riccati equations.

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