CAREER: Hybrid Control of Nonlinear Systems

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

The theory of automatic control has reached considerable maturity in the last few decades. Solutions to a large number of diverse and challenging problems have been obtained, and many important mathematical aspects of the theory are well understood. However, there remain several categories of problems for which the success of standard control tools has been limited. These include: 1. Control of systems that cannot be stabilized by continuous feedback. 2. Control of systems with sensor or actuator constraints. 3. Control of systems with large-scale modeling uncertainty. The research and educational development plan proposed here is aimed at designing hybrid control algorithms. In this framework, a continuous-time process is controlled by means of logic-based switching among a family of regulators. The closed-loop system is then called hybrid because it combines continuous and discrete dynamics. We study several situations in which such a control paradigm is natural and helps overcome various shortcomings of more traditional control methodologies. The primary focus of this research is on systematic development of tools for hybrid control design, applicable to general and useful classes of nonlinear dynamical systems. We propose to achieve this goal by recognizing common trends that unify different aspects of the problems under consideration, and by exploiting recent advances made by the proposer and collaborators in nonlinear disturbance attenuation and in stability analysis of switched systems. Hybrid control techniques are suitable for implementation in the context of many important applications that drive the modern technology, such as software-enabled control, control over networks, and vision-based control. These methods help bridge the gap between the mathematical control theory and engineering practice. For this reason, they also generate high student interest. Our research program will be integrated into the academic curriculum of the Electrical and Computer Engineering Department of the University of Illinois at Urbana-Champaign through course development, student mentoring, laboratory creation, and tutorial publications.