Reduced-order Adaptive Output Predictor for a Class of Uncertain Dynamical Systems: Application to EEG-Based Control of Working Memory

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Virginia Tech


This dissertation aims to develop a formal foundation to design an adaptive output feedback predictor for a class of unknown systems where parameters and order are unknown or high-dimensional. We present a reduced-order adaptive output-predictor scheme based on modal reduction and Lyapunov's method. Moreover, the credibility of the proposed reduced-order adaptive output-predictor scheme is validated by mathematical proof, and numerical and experimental studies, such as single pendulum, double pendulum, six-link pendulum, rope as a high-dimensional rope, and EEG data. Then the dissertation goal is to experimentally validate the proposed reduced-order model parameterization technique for tracking uncertain linear time-invariant (LTI) single-input, single-output (SISO) systems. The proposed theory focuses on parameterizing a high-dimensional, uncertain model and introduces a reduced-order adaptive output predictor capable of forecasting the system's output. This predictor utilizes auto-regressive filtered vectors, incorporating the input and output history. The adaptive output predictor is a simplified and known model, making it suitable for controlling high-dimensional, uncertain SISO systems without access to full-state measurements. Specifically, this work establishes the foundation for parameterizing uncertain models, creating a virtual structure that emulates the actual system, and offering a more manageable model for control when the objective is solely to regulate the system's output. The primary focus of this research is to assess the effectiveness and output-tracking capabilities of the proposed approach. These capabilities are extensively examined across diverse platforms and hardware configurations, relying solely on input and output data from the models without incorporating any additional information on the system dynamics. In the first experiment, the predictor's ability to track the angle of a single pendulum, including additional dynamics, is evaluated using only input-output data. The second experiment targets tracking the endpoint of a rope connected to a single pendulum, where the rope emulates a high-dimensional model. A vision system is designed and employed to acquire the rope endpoint position data. Before the rope experiment, a set of experiments is conducted on single pendulum hardware to ensure the accuracy of the vision system's data collection. Comparative analysis between data from object tracking via vision and data acquired through an encoder demonstrates negligible error. Finally, the input and the endpoint output data from the rope experiment are fed into the predictor to assess its capability to track the rope endpoint position without utilizing specific knowledge of the experimental hardware. Achieving negligible error in tracking implies that the predictor provides a simple and accurate representation of the rope dynamics. Consequently, designing a controller for this known model is equivalent to designing a controller for the actual rope system dynamics. The predictor, by closely emulating the behavior of the rope, becomes a reliable surrogate model for control design, simplifying the task of controller design for the complex and uncertain high-dimensional system. Finally, this study introduces a novel approach to enhance controller design for complex brain dynamics by employing a reduced-order adaptive output predictor proposed in [1], fine-tuned with chirp binaural beats. The proposed technique is promising for developing closed-loop controllers in non-invasive brain stimulation therapies, such as binaural beats stimulation, to improve working memory. The study focuses on parameterizing uncertain models and creates a predictor that utilizes auto-regressive filtered vectors to forecast mean phase lock values generated by binaural beats stimulation. The simplified and known model of the predictor proves effective in tracking brain responses, as demonstrated in experiments evaluating its ability to track mean phase locking values. The results indicate negligible tracking error, suggesting the predictor's reliability in representing brain dynamics and simplifying the task of controller design for the complex and uncertain high-dimensional system.



Unknown Systems, Adaptive Output Predictor, Modal Reduction, Binaural Beats, Connectivity, EEG Signals