We propose to estimate the region of attraction (ROA) for the stability of nonlinear systems from only system measurement data and without knowledge of the system model. The key to our result is the use of Koopman operator theory to approximate the nonlinear dynamics in linear coordinates. This approximation is typically more accurate than the traditional Jacobian-based linearization method. We then employ the Extended Dynamic Mode Decomposition (EDMD) method to estimate the linear approximation of the system through data. This is then used to construct a Lyapunov function that helps estimate the ROA. However, this estimate is typically very conservative. The trajectory reversing method is then used on the set of points that form this conservative estimate, to enlarge the ROA approximation. The output of EDMD is also utilized in the trajectory reversing method, keeping the entire analysis data-driven. Finally, an example is used to show the accuracy of this data-driven method, despite not knowing the system.

We design an output-feedback optimal tracking controller for a class of nonlinear systems that possess full relative degree. The design procedure follows the standard LQT method using an approximate linear model of the system obtained by following the Koopman operator theory. We further identify the observables used for the Koopman method relying on output measurements only, leading to minimal data collection costs. We achieved this latter objective by realizing that output derivatives can be a good choice as observables, and hence, using high-gain observer to provide estimates of these derivatives. Overall, the proposed approach allows for solving the problem of optimal control of the considered class of nonlinear systems without the need for a prior knowledge of the system model. That is, this problem is solved and the controller is driven solely based on output measurement. We demonstrate the efficacy of the closed-loop system in controlling a power system with an infinite bus.

As tomorrow's machines become more general and autonomous, building resiliency into these systems is of critical importance. High-gain observers aggressively respond to errors and guarantee semi-global stability. Supervisory shared control architectures demonstrate the utility of a human-on-the-loop approach to enhance controllers via configurable parameters. Here, we investigate how a cascade high-gain observer-based controller designed to achieve leader-follower tracking can be modified to allow for human intervention, with the specific objective of maintaining performance goals while minimizing control saturation and aggressiveness. We perform envelope-straining experiments that suggest an adjustment of the high-gain parameter before the saturation limits is a better strategy to minimize aggression and thus energy cost.