Research Summaries

Back Further Development of the Patchy Method for Solving the Partial Difference and Differential Equations of Nonlinear Control

Fiscal Year 2013
Division Graduate School of Engineering & Applied Science
Department Applied Mathematics
Investigator(s) Krener, Arthur J.
Sponsor Air Force Office of Scientific Research (Air Force)
Summary There are great needs for effective algorithms to control highly nonlinear plants such as modem aircraft and spacecraft. Fortunately there has been great progress in nonlinear control theory over the last three decades and many of the needed algorithms have been developed. However their implementation has lagged behind. The principle reason for this is computational. There are few effective computational methods available to solve the nonlinear partial differential equations that are required by the nonlinear theory. This is in contrast to linear control where the theory has been complimented by excellent numerical methods such as those in the MATLAB Control Toolbox. The goal of this research project is to continue to develop the numerical tools needed to solve Hamilton Jacobi Bellman partial differential equations and others that arise in nonlinear control theory. We have made substantial progress to date using patchy methods to solve Hamilton Jacobi Bellman partial differential equations, the dynamic programming equations and the Francis Byrnes Isidori equation for regulation of nonlinear plants. These equations admit power series solutions in a neighborhood of an operating point and linear algorithms can compute the lowest terms of these series. This yields a solution on some patch of the state space containing the operating point. We have extended the solution on other patches encircling the original patch.
Keywords
Publications Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal
Data Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal