Thomas Vasileiou

Thomas Vasileiou

The present paper develops recursive algorithms to track shifts in the resonance frequency of linear systems in real time. To date, automatic resonance tracking has been limited to non-model-based approaches, which rely solely on the phase difference between a specific input and output of the system. Instead, we propose a transformation of the system into a complex-valued representation, which allows us to abstract the resonance shifts as an exogenous disturbance acting on the excitation frequency, perturbing the excitation frequency from the natural frequency of the plant. We then discuss the resonance tracking task in two parts: recursively identifying the frequency disturbance and incorporating an update of the excitation frequency in the algorithm. The complex representation of the system simplifies the design of resonance tracking algorithms due to the applicability of well-established techniques. We discuss the stability of the proposed scheme, even in cases that seriously challenge current phase-based approaches, such as nonmonotonic phase differences and multiple-input multiple-output systems. Numerical simulations further demonstrate the performance of the proposed resonance tracking scheme.

Dario Izzo, Dharmesh Tailor, Thomas Vasileiou

Recent work have shown how the optimal state-feedback, obtained as the solution to the Hamilton-Jacobi-Bellman equations, can be approximated for several nonlinear, deterministic systems by deep neural networks. When imitation (supervised) learning is used to train the neural network on optimal state-action pairs, for instance as derived by applying Pontryagin's theory of optimal processes, the resulting model is referred here as the guidance and control network. In this work, we analyze the stability of nonlinear and deterministic systems controlled by such networks. We then propose a method utilising differential algebraic techniques and high-order Taylor maps to gain information on the stability of the neurocontrolled state trajectories. We exemplify the proposed methods in the case of the two-dimensional dynamics of a quadcopter controlled to reach the origin and we study how different architectures of the guidance and control network affect the stability of the target equilibrium point and the stability margins to time delay. Moreover, we show how to study the robustness to initial conditions of a nominal trajectory, using a Taylor representation of the neurocontrolled neighbouring trajectories.