Grant: Discovery Grants Program - Individual

The research program proposed in this application aims at development of novel methods of modular control design for networks of nonlinear dynamical systems based on systematic use of generalized scattering transformations, and their application to practical engineering problems. The generalized scattering transformation, which was introduced in the previous works of the applicant, is an input-output transformation which allows for rendering the dynamic behavior of a nonlinear dissipative system with quadratic supply rate into a prescribed non-planar cone. This property of generalized scattering transformation makes it an effective design tool which can, in particular, be used for stabilization of interconnections of dynamical systems, including those with communication delays. The long-term objective of the proposed research program is comprehensive development of generalized scattering transformation based techniques which will make these techniques powerful and versatile tools applicable to a wide range of systems and control design problems. The specific short-term research objectives include development of methods for modular scattering-based design for complex networks of nonlinear dissipative systems with quadratic supply rates, development of methods for scattering-based control design for cyberphysical systems, including design in the presence of communication constraints (such as irregular communication delays, information losses, limited bandwidth), scattering-based control design for switched dissipative systems, extension of the scattering-based design methods to the case of conic systems with nonlinear sector bounds, design methods for contact stability problem in robotics with extension to multi-robot interaction, as well as generalized scattering-based design methods for bilateral and multi-lateral teleoperator systems. In terms of methodology, we will look into existing as well as new and emerging engineering problems where the control design either directly employs or based on the notions of conicity and/or dissipativity, and systematically explore additional degrees of freedom that can be brought by application of the generalized scattering transformations. The proposed research program will lead to development of new powerful methods for systematic modular design of complex networks of dissipative systems, which can be subsequently applied to many practical problems that involve physical interaction and/or information exchange between their components. The training received over the course of the proposed research program will provide a solid background for the trainees' future professional success and will give them competitive advantage in today's high-tech job market.