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This paper proposes a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for autonomous nonlinear systems. The design of a KKL observer involves finding an injective map that transforms the system state into…
A method for detecting possible non-deterministic dynamics underlying a time series is introduced. Non-deterministic dynamics may arise due to the failure of the Lipschitz condition in the equations of motion. At a singular point, the phase…
Nonlinear friction has long been, and continues to be, one of the major challenges for precision motion control systems. A linear asymptotic observer of the motion state variables with nonlinear friction uses a dedicated state-space…
Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…
In statistical inference, a discrepancy between the parameter-to-observable map that generates the data and the parameter-to-observable map that is used for inference can lead to misspecified likelihoods and thus to incorrect estimates. In…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to…
State estimation for linear time-invariant systems with unknown inputs is a fundamental problem in various research domains. In this article, we establish conditions for the design of unknown input observers (UIOs) from a geometric approach…
This paper presents a first step towards tuning observers for general nonlinear systems. Relying on recent results around Kazantzis-Kravaris/Luenberger (KKL) observers, we propose an empirical criterion to guide the calibration of the…
We consider the problem of state and parameter estimation for a wide class of nonlinear oscillators. Observable variables are limited to a few components of state vector and an input signal. The problem of state and parameter reconstruction…
In this paper we develop numerical analysis for finite element discretization of semilinear elliptic equations with potentially non-Lipschitz nonlinearites. The nonlinearity is essecially assumed to be continuous and monotonically…
We provide two solutions to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only. Both of our solutions are global, employ the…
A systematic method for the design of linear residual generators for combined fault detection and estimation in nonlinear systems is developed. The proposed residual generator is a linear functional observer built for an extended system…
A fixed-order set-valued observer is presented for linear parameter-varying systems with bounded-norm noise and under completely unknown attack signals, which simultaneously finds bounded sets of states and unknown inputs that include the…
A method of expansion of solutions of singularly perturbed nonlinear systems in power series of small parameters is applied to the popular Lorenz model in synergetics.Simple asymptotic expressions for the solution to the model in…
We investigate a state estimation problem for the dynamical system described by uncertain linear operator equation in Hilbert space. The uncertainty is supposed to admit a set-membership description. We present explicit expressions for…
This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a…
This paper presents adaptive observers for online state and parameter estimation of a class of nonlinear systems motivated by biophysical models of neuronal circuits. We first present a linear-in-the-parameters design that solves a…
We study spectral stability estimates of elliptic operators in divergence form $-\textrm{div} [A(w) \nabla g(w)]$ with the Dirichlet boundary condition in non-Lipschitz domains $\widetilde{\Omega} \subset \mathbb C$. The suggested method is…
Data generated from dynamical systems with unknown dynamics enable the learning of state observers that are: robust to modeling error, computationally tractable to design, and capable of operating with guaranteed performance. In this paper,…