Hamiltonian Method for Steady State Optimal Control and Filtering
Zoran Gajić, Myo–Taeg Lim, Dobrila Škatarić, Wu‐Chung Su, Vojislav Kecman · 2014
This chapter shows how the algebraic Riccati equations of weakly coupled control continuous-and discrete-time systems composed of two subsystems can be completely and exactly decomposed into two reduced-order algebraic Riccati equations corresponding to local subsystems. The decomposed algebraic Riccati equations are nonsymmetric. The chapter shows how the considered procedures can be extended to weakly coupled continuous-time stochastic systems composed of subsystems. The algebraic regulator and filter Riccati equations of weakly coupled discrete-time stochastic linear control systems are completely and exactly decomposed into reduced-order continuous time algebraic Riccati equations corresponding to subsystems. The chapter uses the separation principle to solve the linear-quadratic Gaussian control problem of weakly coupled discrete stochastic systems. It solves the filtering problem of linear discrete-time weakly coupled systems using the problem formulation from Shen and Gajic.