On state-estimation in weakly-observable scenarios and implicitly regularized observers

Abstract

This work proposes a framework to design observers for systems that present low observability. It is shown that, in these scenarios, the estimation problem becomes illposed, which drastically limits the performance of standard observers, specially in the presence of noise. Consequently, this paper presents a method to design an observer that optimizes some potential function to be defined by the designer. This allows to implicitly regularize the estimation and recover a wellposed problem. The proposed technique is validated in a set of weakly-observable systems and the performance is compared with a common Kalman filter-like observer.

Canceling output disturbances in observer design through internal model filters

“…Future works will focus on relaxing this dissipativity condition and using Riemannian metrics (see, e.g., [39] and [1,Section 4]). Additionally, future works will explore the practical application of the proposal in multi-agent distributed problems [16] and masking protocols [17]…”

“…where the measured output is corrupted with an additive disturbance generated by the exosystem (6) with ω 1 = 0, ω 2 = 1 and ω 3 = 2π. Assume that the states of the system are estimated through a linear observer of the form (17) with the gain L = 0.994 0.093 0 0.704 0.094 1.534 . In the simulations we considered the following set of initial conditions: x(0) = (1, 1, 1), x(0) = 0 and w(0) = (1, 0.2, 0, 0.2, 0) and v is taken as a bounded realization of white noise of variance 0.01 in both outputs.…”

“…That is, the case where a (possibly nonlinear) observer is already given and the objective is to compensate a particular disturbance without modifying the observer structure or gain tuning. Such an extra constraint is motivated by possible applications that go beyond the mere scope of observers design, such as distributed multi-agent systems [16] or cyber-security problems [17], in which completely redesigning the given feedback controller could be critical or not allowed due to practical constraints.…”