in this dissertation the problem of the reduced-order nearopt iami stochastic control is solved for:​ 1) linear weakly coupled continuous systems (Chapter 3 ) , 2) linear weakly coupled discrete systems (Chapter 5) and 3) linear singularly perturbed discrete systems (Chapter 7).

The result of Chapter 3 is obtained via the use of a decoupling transformation developed in Chapter 2. The transformation completely and exactly decouples the linear weakly coupled continuous and discrete systems into reducedorder subsystems under nonrestrictive conditions. Applied to the global Kalman filter the transformation produces two reduced-order local filters and reduces on-line computational requirements.

In Chapters 4 and 6 the recursive reduced-order algorithms based on bilinear transformations are developed for the solutions of the discrete weakly coupled and singularly perturbed algebraic Riccati equations. These algorithms reduce off-line computations. The algorithms are used in Chapters 5 and 7 where corresponding discrete linearquadratic Gaussian control problems are studied.

Results of Chapters 2, 4 and 6 are employed in order to solve problems formulated in Chapter 3, 5 and 7. The nearoptimal reduced-order stochastic controllers are obtained by approximating coefficients of the optimal control law (regulator and filter gains, filter coefficients) by O(ε_N), where ε is a small perturbation parameter and N is the order of approximation. It is shown that corresponding approximations are near-optimal in the sense that the absolute errors for the performance criteria are O(ε_N) for both continuous and discrete weakly coupled systems, and O(ε_N+1) for singularly perturbed systems (represented in the fast time scale). The approximate trajectories are O(ε_2N) close to the optimal ones for both continuous and discrete weakly coupled systems, and corresponding trajectory errors are Oε_2N+1) for slow variables and 0(ε_2N) for fast variables of singularly perturbed systems.

The proposed methods reduce both off-line and on-line computational requirements and allow parallel processing of information. Thus, the methods are very useful for practical implementation since they introduce full parallelism in the design procedures.