High-gain Output Feedback Control Design for a Class of Uncertain Nonlinear Systems Using Gaussian Processes *

This paper considers the tracking control problem of a class of uncertain nonlinear systems with partial noisy measurements. To cope with the uncertainties including the unknown nonlinear dynamics and unmeasured state variables, simultaneous estimation of all the hidden states and unknown dynamics are required for the controller design. In this paper, a high-gain observer delivers a good property of disturbance rejection and provides state estimates which serves as the training data for learning the unknown dynamics. Because the measurements are corrupted by noise, this leads to estimation error in the state estimates. Since the Gaussian process (GP) has high flexibility to capture the complex unknown functions by using very few parameters and it inherently handles measurement noise, GP model is employed to learn the unknown dynamics from the state estimates. This provides critical information for the control design such that the unknown dynamics is compensated and a good tracking performance is delivered. In short, the high-gain observer provides state estimates for the GP model to learn the unknown dynamics from noisy measurements, which enables the development of the controller. Comparisons against ℒ
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adaptive control and high-gain output feedback controller without GP learning are carried out.