Robust Control of Constrained Linear Parameter Varying Systems and Applications

Pennsylvania State Univ University Park, University Park PA

Investigators

Abstract

0115946 Sznaier Robust control of linear time invariant systems has undergone extensive developments in the past two decades, leading to powerful formalisms such as H8, u-synthesis/analysis and, more recently, l1optimal control, that have been successfully applied to challenging practical problems. In contrast, tools for handling linear parameter varying plants have just emerged and are still far from complete. An open issue, central to many practical problems, is the non-conservative handling of constraints, both on the outputs and in the control action. The proposed research is aimed at addressing this issue by incorporating into the LPV frame-work the capability to deal exactly with a broad class of performance specifications and model uncertainty. Specifically, the objectives of the proposed research are: O Development of an analytical framework for synthesizing robust LPV systems subject to hard constraints. This framework should exhibit the following properties: (a) Handle control and output constraints in a non-conservative fashion; (b) Identify the intrinsic limits of performance of the system as well as the limiting factors; and (c) Result in computationally tractable procedures leading to practically implementable controllers. O Application of the resulting theory to several problems spanning a broad spectrum of applications such as active vision and oil prospection. The proposed research will combine elements from functional analysis, viability theory and dynamical systems theory, following an approach successfully used by the co-PIs to handle constraints in the case of LTI systems. Preliminary results indicate that this approach leads to a framework with the desired features. The PI expects that this research effort will result in an expanded robust control framework for LPV systems, capable of addressing realistic problems necessitating neither potentially conservative approximations nor multiple trial and error type iterations. Moreover, in addition to advancing the state of the art in control theory, he expects that by removing some of the limitations of currently available LPV tools, it will foster progress in related areas. An example is computer vision, an area where recent technological advances have rendered a number of practical applications feasible, provided that certain related control issues can be resolved. These applications range from intelligent highway systems to remote surgery and have the potential to broadly impact society. The proposed research will also have a direct bearing upon the quality of graduate and undergraduate education both at Penn State University (PSU) and the Universidad Autonoma Metropolitana (UAM). In addition to direct student involvement and incorporation of the results into the curriculum, it will allow students from the UAM to use state-of-the-art computer vision equipment available at PSU, while Penn State students will benefit from having access to proprietary data and experiments from the Mexican Petroleum Institute.