Data-driven trajectory-mapping based control: Theory & applications

Data-driven modeling and control methods have attracted increasing interest over the last decade. With the data-driven approach, the system dynamics model or the control input is generated from the data collected when the system is difficult/expensive to build, and the past sampling data can be obtained easily. However, limitations exist in current data-driven modeling and control methods. For example, the control performance can be sensitive to the data noise, or the effect of data noise is not sufficiently considered. Impractical assumptions about the system dynamics or strict requirements for data sampling also limit the application of current data-driven methods. Moreover, the effect of the non-minimal phase zeros has not yet been addressed in the existing controller design. Also, intensive computation efforts make it difficult to employ in an online manner. These challenges exist in a wide range of applications, including high-speed nano-manipulation, advanced manufacturing, robotics, and biological system modeling, to name a few. In this dissertation, first, an optimal data-driven difference-inversion-based iterative control method is proposed for high-speed precision tracking in the presence of dynamic changes and random disturbances. The convergence of the proposed method under the effect of random disturbance is analyzed. The optimal frequency- and iteration-dependent iteration gain that minimizes the residual tracking error and maximizes the convergence rate is also obtained. It is shown that the proposed optimal data-driven difference-inversion-based iterative control method improves both the robustness and the tracking performance over the previous methods. Secondly, to extend the optimal data-driven difference-inversion-based iterative control to multiple input multiple outputsystems, we propose a data-driven robust optimal iterative learning control technique to multiple input multiple output systems. The input-output data measured in previous iterations are utilized to approximate the system inverse and update the control input. It is shown that the convergence of the output tracking is guaranteed in the presence of cross-axis coupling dynamics and random output disturbance, and the iteration control gain can be optimized to minimize the residual tracking error and maximize the convergence rate. Finally, a data-driven control approach called the direct input synthesis control (DISC) technique is proposed to achieve precise output tracking of gls{NMP} multiple input multiple output linear time inviariant systems. The control input is synthesized directly using the past gls{I-O} dataset without modeling the system dynamics. An initialization, pre- and post-actuation are introduced to compensate for the boundary condition and the gls{NMP} zero effects. The robustness and performance of the approach are analyzed in the presence of random and bounded disturbance, and it is shown that the tracking error vanishes with the disturbance, and can be rendered arbitrarily small with a large enough initialization, pre- and post- actuation time. This proposed method is also extended to the optimization framework to accommodate the input energy and constraints. The explicit solution is analyzed, and the numerical solution is proposed. The proposed data-driven method is also used in the modeling of complex biological systems. A device and methodology to measure the dynamic characteristics of stomata have been developed. The developed methodology is based on a diffusion model proposed to quantify the transpiration rate and stomata conductance from the measured humidity data. A prototype of the developed device has been used to monitor the stomatal dynamics of a tobacco and a lettuce sample, respectively. The research work of this dissertation addresses the limits and further extends the data-driven modeling and control methods, the challengesinvolved in output tracking with system dynamics variation and random disturbances, stringent requirements on system and sampling data, tension computation for online applications, cross-axis coupling in high-speed multi-axis motion, and modeling of the biological systems.