Robust hybrid estimation and rejection of multi‐frequency signals

Abstract

SUMMARYWe consider the problem of output regulation for LTI systems in the presence of unknown exosystems. The only a priori knowledge about the exosystem consists in the fact that it generates multi-frequency signals, while the number and the value of the frequencies are not known. The control scheme relies on two main components: an estimation algorithm, to reconstruct the signal generated by the exosystem, and a controller, to enforce the output regulation property to the closed-loop system. To tackle the first task, we propose a hybrid observer for the estimation of the (possibly piece-wise continuous) number and values of the frequencies contained in the exogenous signal. The hybrid observer is particularly appealing for numerical implementations and it is combined with a self-tuning algorithm of the free parameters (gains), thus improving its performance even in case of noisy measurements. Semi-global exponential convergence of the estimation error is provided. As far as the second task is concerned, a robust hybrid regulator is designed for practical rejection of the multi-frequency disturbance signal acting on the plant. The result is achieved by exploiting the frequencies estimated by the hybrid observer. The effectiveness of the proposed control scheme is shown by means of numerical simulations.

Robust Hybrid Output Regulation for Linear Systems With Periodic Jumps: The Non-Semiclassical Case

“…Suppose that conditions (9) hold for P 0 . Then there existsε > 0 such that any P ∈ F ε with ε ∈ (0,ε) satisfies (9).…”

“…The conditions(9) are formulated for a system of the form proposed in (8) for simplicity. Nonetheless, it can be easily shown that P 0 in (3) satisfies such conditions if and only if the plant transformed via (6), (7) satisfies(9).…”

Model‐based vs data‐driven adaptive control: An overview

“…Another important problem in adaptive control is the one dealing with unknown disturbance rejection, often referred to as “adaptive regulation.”) Indeed, in these works, the plant's model is known or identified, but the disturbance model is unknown or uncertain. In the direct adaptive methods, adaptive filters are used to tune the feedback controller (for example, via adaptive observers of the disturbance) to reject the unknown disturbance, without explicitly estimating its model.…”

An Adaptive-Observer-Based Robust Estimator of Multi-sinusoidal Signals

“…In particular, [26] presents a simplified global stability analysis by using contraction theory rather than traditional Lyapunov analysis; and, on the other hand, [28] proposes a hybrid observer to identify the n frequencies from a multi-frequency signal with saturated amplitudes. Recently, the effectiveness of the hybrid observer in the presence of poorly sampled signal is shown in [29].…”