Higher-order optimal control design via singular perturbation

Control design is generally based on an approximate model of a real-life system. In this paper, a complex dynamical system is depicted using not one but several models of the same system. Based on interest for robust implementation of reduced-order controllers in higher-order models, we study the regulator problem for a dynamical system expressed as a framework of several models where the reduction between them is made by singular perturbation theory. This multiresolutional representation portrays the model and cost at different levels of complexity, allowing to study analytical solutions for the minimization problem at each level to determine cases in which the cost can be minimized without necessarily requiring an exact optimal control. As result, we show that sometimes a small improvement in the reduced-order optimal control may improve the minimum cost value for the high-order model in a significant way. A singularly perturbed quadratic regulator accounting for actuator dynamics expressed as the discontinuous nonlinearity sign in its structure is shown as example to illustrate these properties.