Grant: Discovery Grants Program - Individual

Many robotic, mechanical and electromechanical devices that are described by highly nonlinear dynamics are present in different applications of industry, locomotion, transportation and human assistance for their multiple advantages like dexterity, mobility and safety. To use these setups in efficient ways, one needs to ensure high levels of stability, accuracy and sensitivity through a wide range of applications. But, because of their nonlinearities and strong varying behavior, intrinsic difficulties in controlling these dynamics limit their use in precise applications. The present project is conducted to investigate new ways to improve the accuracy of the control of such devices. The proposed control approach considers exactly or approximately (with a higher degree of fidelity when compared to any local linearizing method) the entire dynamics (nonlinearities and uncertainties) of the process. The applicant uses the Kronecker matrix product (KMP), the power of matrices and vectors (PMV) algebra and the linear matrix inequality (LMI) framework. This latter is widely applied in control of linear systems theory, while the KMP tensor has been used to solve some problems of identification, optimal control and stability analysis of nonlinear systems. This research is an extension of some of these results to the stabilization, the robustness and the multi-objective control design for a large scale of nonlinear systems known as polynomial systems. It is on the border between the wide linear control theory and the formal nonlinear control design. The proposed techniques draw a new road map for nonlinear control theory and its application. Numerical simulations and real-time experiments are carried out on different electromechanical devices (an actual 1-DOF magnetic levitation system, an actual 2-DOF flight engine simulator system, and models of linear induction motors and pneumatic muscle actuators) to validate the proposed methods of control.