Stabilizing Regulators for Nonlinear Continuous Systems of Large Dimension Using the Asymptotics of the Matrix Algebraic Riccati Equations Solutions

In this paper an approach for the construction of composite stabilizing regulators for singular perturbed optimal control problems and optimal control problems for weakly coupled nonlinear systems based on the decomposition of initial problems into subproblems of smaller dimensions is proposed. Here, the SDRE technique with a quadratic quality criterion is applied for continuous pseudo-linear control systems, where the right-hand sides are formally linear in state and control, with state dependent coefficients.