Multiple Unknown Input Research Articles

Blind Two-Dimensional Super-Resolution and Its Performance Guarantee

In this work, we study the problem of identifying the parameters of a linear system from its response to multiple unknown input waveforms. We assume that the system response, which is the only given information, is a scaled superposition of time-delayed and frequency-shifted versions of the unknown waveforms. Such kind of problem is severely ill-posed and does not yield a unique solution without introducing further constraints. To fully characterize the linear system, we assume that the unknown waveforms lie in a common known low-dimensional subspace that satisfies certain randomness and concentration properties. Then, we develop a blind two-dimensional (2D) super-resolution framework that applies to a large number of applications such as radar imaging, image restoration, and indoor source localization. In this framework, we show that under a minimum separation condition between the time-frequency shifts, all the unknowns that characterize the linear system can be recovered precisely and with very high probability provided that a lower bound on the total number of the observed samples is satisfied. The proposed framework is based on 2D atomic norm minimization problem which is shown to be reformulated and solved efficiently via semidefinite programming. Simulation results that confirm the theoretical findings of the paper are provided.

Structural and Strongly Structural Input and State Observability of Linear Network Systems

This paper studies linear network systems affected by multiple unknown inputs with the objective of reconstructing both the initial state and the unknown input with one time-step delay. We state conditions under which both the whole network state and the unknown input can be reconstructed from output measurements, over every window of length $N$ , with $N$ being the dimension of the system, for all system matrices that share a common zero/nonzero pattern (uniform $N$ -step strongly structural input and state observability) or at least for almost all system matrices that share a common zero/nonzero pattern (uniform $N$ -step structural input and state observability). Based on some specific assumptions on the structure of the interactions between the unknown input and the network states, we show that such a characterization depends only on strongly structural (respectively, structural) observability properties of a suitable subsystem.

Strong Structural Input and State Observability of LTV Network Systems with Multiple Unknown Inputs

This paper studies linear time-varying (LTV) network systems affected by multiple unknown inputs. The goal is to reconstruct both the initial state and the unknown input. The main result is a characterization of strong structural input and state observability, i.e., the conditions under which both the whole network state and the unknown input can be reconstructed for all system matrices that share a common zero/non-zero pattern. This characterization is in terms of strong structural observability of a suitably-defined linear time-invariant (LTI) subsystem.

Uncertainty Analysis in Lorentz Force Eddy Current Testing

The paper addresses the analysis of uncertainties in the framework of the nondestructive evaluation technique Lorentz force eddy current testing. A non-intrusive generalized polynomial chaos expansion is used in order to quantify the impact of multiple unknown input parameters. In this context, the statistics of the velocity and the conductivity of the specimen as well as the magnetic remanence and the lift-off distance of the permanent magnet are determined experimentally and modeled as $\beta $ -distributed and uniform distributed random variables. The results are compared with Monte Carlo simulations and showed errors <0.2%. Furthermore, the numerically predicted force profiles are validated with experiments. A sensitivity analysis by means of the Sobol decomposition revealed that the magnetic remanence and the lift-off distance contribute to more than 90% of the total variance of the resulting Lorentz force profile and should be considered first to improve reproducibility.

Adaptive control of MIMO mechanical systems with unknown actuator nonlinearities based on the Nussbaum gain approach

This paper investigates MIMO mechanical systems with unknown actuator nonlinearities. A novel Nussbaum analysis tool for MIMO systems is established such that unknown time-varying control coefficients are tackled. In contrast to existing literatures on continuous-time systems, the newly-developed Nussbaum tool focuses on extending the traditional Nussbaum result from one dimensional case to the multiple one. Specifically, not only the multiple unknown input coefficients are extended to the time-varying, but also the limitation of the prior knowledge of coefficients� upper and lower bounds is removed. Furthermore, an adaptive robust controller associated with the proposed tool is presented. The asymptotic tracking of MIMO mechanical systems is guaranteed with the help of the Lyapunov Theorem. Finally, a simulation example is provided to examine the validity of the proposed scheme.

Stabilization of Discrete-Time Linear Systems Subject to Input Saturation and Multiple Unknown Constant Delays

In this technical note, we study the semi-global stabilization of general linear discrete-time critically unstable systems subject to input saturation and multiple unknown input delays. Based on a simple frequency-domain stability criterion, we find upper bounds for delays that are inversely proportional to the argument of open-loop eigenvalues on the unit circle. For delays satisfying these upper bounds, linear low-gain state and finite dimensional dynamic measurement feedbacks are constructed to solve the semi-global stabilization problems.

Stabilization of linear system with input saturation and unknown constant delays

In this paper, we study the stabilization of linear critically unstable systems subject to input saturation and multiple unknown input delays. We find tight upper bounds for delays which are inversely proportional to the maximal magnitude of open-loop eigenvalues on the imaginary axis. For delays satisfying these upper bounds, linear low-gain state and finite dimensional dynamic measurement feedbacks are constructed to solve the semi-global stabilization problem. The effectiveness of the proposed design is illustrated by an example.

Discrete-Time Sliding-Mode State and Unknown Input Estimations for Nonlinear Systems

This paper addresses the problems of discrete-time state and unknown input/fault estimation for continuous-time nonlinear systems with multiple unknown inputs. Taylor series expansion and a nonlinear transformation are used to convert the nonlinear continuous-time system into a discrete-time model. The conditions for the observability of unknown inputs w.r.t. outputs are discussed. The novelty lies in the formulation of multiple sliding-mode estimator for the states that are directly influenced by unknown inputs, which cannot be decoupled by nonlinear transformation. This framework allows for the estimation of unknown inputs from the multiple sliding modes. The existence of discrete-time sliding mode is guaranteed, and the relation between the boundary layer thickness and the sliding-mode gain design that will eliminate chattering and the boundedness conditions is obtained. The proposed technique can be applied for fault detection and isolation. Simulation results with application to three-phase motor are given to demonstrate the effectiveness of the proposed method.

Observers for systems with unknown and inaccessible inputs†

Observer theory for constant-coefficient linear systems is extended to systems with unknown inaccessible inputs. Two types of observers for such systems are defined, and simplified criteria for their existence are developed. A theorem regarding the structure of these observers is given which allows the application of results for systems with single unknown inputs to systems with multiple unknown inputs.