Optimal reduced-order LQG synthesis: Nonseparable control and estimation design

The optimal linear-quadratic-Gaussian synthesis design approach and the associated separation principle are investigated for the case where the observer design model is a reduced model of the underlying system model. Performance of the resulting reduced-order controller in the full-state system environment is formulated in terms of an augmented state vector consisting of the system state vector and the reduced model state vector. Considering explicitly separated linear control and estimation laws, a calculus of variations/Hamiltonian approach is used to determine the necessary conditions for the optimal controller and observer gains for the simplified algorithms. Results show that the optimal gains are not separable, ie, the optimal controller and observer gains are coupled and cannot be computed independently. Numerical examples of an infinite-horizon and finite-horizon control and estimation large-scale multiagent system problem clearly show the advantages of using the nonseparable coupled solutions.