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This plenary talk gives an overview of our research in optimization and control of mechatronic systems. In the first part of the talk, a convex program known as semidefinite program (SDP) will be presented. An SDP is an optimization problem with a linear objective function, and constraints on the eigenvalues of a linear matrix-valued function of the optimization variables. Key practical features of the SDP will be reviewed using mathematical language common to most control and automation engineers. The value of utilizing semidefinite programming in several important engineering problems will be discussed. In particular, it will be shown how SDP has facilitated advancements in the following areas: the design of estimation and control algorithms with fixed point arithmetic, the design of control laws with multiple specifications, the analysis of vibrations in turbomachinery components, and the design of state estimation algorithms with probability constraints on the state trajectories. In the second part of this talk, a (virtually) model-free optimization algorithm for control known as extremum seeking control (ESC) will be described. The ESC is based on the gradient method of nonlinear programming. The effectiveness of ESC to identify and track operating points of maximum performance of complex nonlinear mechatronic systems will be illustrated using a thermoacoustic cooling process. This talk will conclude with a personal perspective of growth opportunities for higher education in mechatronics and automation, which was developed essentially during my recent tenure as Program Director for Control Systems at the National Science Foundation.
Date of Conference: 5-8 Aug. 2007