Optimal LQG Synthesis for Simpliu001ced Models - Non-Separable Control and Estimation Design

摘要

The optimal linear-quadratirn-Gaussian synthesis design approarnh andrnthe assorniated separation prinrniple are investigated for thernase wherernthe algorithm design model is a simpliu001ced version of the underlying sys-rntem model. Performanrne of the simpliu001ced algorithms in the full-staternsystem environment is formulated in terms of an augmented state vern-rntorrnonsisting of the system state verntor and the simpliu001ced algorithmrnstate verntor. Assuming linearrnontrol and estimation laws, arnalrnulusrnof variations/Hamiltonian approarnh is used to determine the nernessaryrnonditions for the optimalrnontroller and estimator gains for the simpli-rnu001ced algorithms. Results show that the optimal solution is not separable,rni.e., the optimalrnontroller and estimator gains arernoupled andrnannotrnbernomputed independently. A numerirnal example of an inu001cnite horizonrnontrol and estimation problemrnlearly shows the advantages of using thernnon-separablernoupled solutions.