SINGULAR PERTURBATION METHOD IN THE THEORY OF OPTIMAL CONTROL,
Abstract
A detailed description of physical phenomena usually requires a mathematical model of high-order. The existing optimal control synthesis procedures generally become impractical for dynamic systems of high-order. One is therefore forced to construct a simplified low-order model in order to make existing numerical procedures applicable. In constructing a low-order model it is a common practice to neglect some small time-constants, masses, inductances, capacitances and similar 'parasitic' parameters. Typically control is synthesized for such a low-order model and then its applicability is checked on a more realistic high-order model. Unfortunately, more frequently than not the result of such a low-order design is unsatisfactory. In this report, a method called 'Optimally Sensitive Design' is developed. This method allows an improvement of the result of a low-order design by using low-order models only. It accepts the low-order design at the beginning of the design procedure and then improves the obtained result by adding an 'optimally sensitive' term to the low order-optimal control. This term is the first variation of the high-order-optimal control due to the change in system order. For the computation of the 'optimally sensitive' control, the 'Singular Perturbation' theory is used. Several examples worked out illustrates the practical applicability and computional simplicity of the optimally sensitive design method. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1968
- Accession Number
- AD0675321
Entities
People
- Peddapullaiah Sannuti
Organizations
- University of Illinois Urbana–Champaign