To improve the predictive capacity of system models in the input–output sense, this paper presents a framework for model updating via learning of modeling uncertainties in locally and globally Lipschitz nonlinear systems. First, we introduce a method to extend an existing known model with an uncertainty model so that stability of the extended model is guaranteed in the sense of set invariance and input-to-state stability. To achieve this, we provide two tractable semi-definite programs. These programs allow obtaining optimal uncertainty model parameters for both locally and globally Lipschitz nonlinear models, given uncertainty and state trajectories. Subsequently, in order to extract this data from the available input–output trajectories, we introduce a filter that incorporates an approximated internal model of the uncertainty and asymptotically estimates uncertainty and state realizations. This filter is also synthesized using semi-definite programs with guaranteed robustness with respect to uncertainty model mismatches, disturbances, and noise. Numerical simulations for a large data-set of a roll plane model of a vehicle illustrate the effectiveness and practicality of the proposed methodology in improving model accuracy, while guaranteeing stability.

This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time) internal state–space representation (a finite chain of integrators) of the fault vector. Next, a nonlinear state observer is designed based on the known parts of the augmented dynamics. This nonlinear filter (observer) reconstructs the fault signal as well as the states of the augmented system. We provide sufficient conditions that guarantee stability of the estimation error dynamics: firstly, asymptotic stability (i.e., exact fault estimation) in the absence of perturbations induced by the fault model mismatch (mismatch between internal ultra-local model for the fault and the actual fault dynamics), uncertainty, external disturbances, and measurement noise and, secondly, Input-to-State Stability (ISS) of the estimation error dynamics is guaranteed in the presence of these perturbations. In addition, to support performance-based estimator design, we provide Linear Matrix Inequality (LMI) conditions for L₂-gain and L₂−L_∞ induced norm and cast the synthesis of the estimator gains as a semi-definite program where the effect of model mismatch and external disturbances on the fault estimation error is minimized in the sense of L₂-gain, for an acceptable L₂−L_∞ induced norm with respect to measurement noise. The latter result facilitates a design that explicitly addresses the performance trade-off between noise sensitivity and robustness against model mismatch and external disturbances. Finally, numerical results for a benchmark system illustrate the performance of the proposed methodologies.

We present a framework for learning of modeling uncertainties in Linear Time Invariant (LTI) systems to improve the predictive capacity of system models in the input-output sense. First, we propose a methodology to extend the LTI model with an uncertainty model. The proposed framework guarantees stability of the extended model. To achieve this, two semi-definite programs are provided that allow obtaining optimal uncertainty model parameters, given state and uncertainty data. Second, to obtain this data from available input-output trajectory data, we introduce a filter in which an internal model of the uncertainty is proposed. This filter is also designed via a semi-definite program with guaranteed robustness with respect to uncertainty model mismatches, disturbances, and noise. Numerical simulations are presented to illustrate the effectiveness and practicality of the proposed methodology in improving model accuracy, while guaranteeing model stability.

This paper addresses the problem of robust process and sensor fault reconstruction for nonlinear systems. The proposed method augments the system dynamics with an approximated internal linear model of the combined contribution of known nonlinearities and unknown faults - leading to an approximated linear model in the augmented state. We exploit the broad modeling power of ultra-local models to characterize this internal dynamics. We use a linear filter to reconstruct the augmented state (simultaneously estimating the state of the original system and the sum of nonlinearities and faults). Having this combined estimate, we can simply subtract the analytic expression of nonlinearities from that of the corresponding estimate to reconstruct the fault vector. Because the nonlinearity does not play a role in the filter dynamics (it is only used as a static nonlinear output to estimate the fault), we can avoid standard restrictive assumptions like globally (one-sided) Lipschitz nonlinearities and/or the need for Lipschitz constants to carry out the filter design. The filter synthesis is posed as a mixed H₂/H_∞ optimization problem where the effect of disturbances and model mismatches is minimized in the H_∞ sense, for an acceptable H₂ performance with respect to measurement noise.

In this paper, we present a methodology for actuator and sensor fault estimation in nonlinear systems. The method consists of augmenting the system dynamics with an approximated ultra-local model (a finite chain of integrators) for the fault vector and constructing a Nonlinear Unknown Input Observer (NUIO) for the augmented dynamics. Then, fault reconstruction is reformulated as a robust state estimation problem in the augmented state (true state plus fault-related state). We provide sufficient conditions that guarantee the existence of the observer and stability of the estimation error dynamics (asymptotic stability of the origin in the absence of faults and ISS guarantees in the faulty case). Then, we cast the synthesis of observer gains as a semidefinite program where we minimize the ℒ 2 -gain from the model mismatch induced by the approximated fault model to the fault estimation error. Finally, simulations are given to illustrate the performance of the proposed methodology.

For given system dynamics, control structure, and fault/attack detection procedure, we provide mathematical tools–in terms of Linear Matrix Inequalities (LMIs)–for characterizing and minimizing the set of states that sensor attacks can induce in the system while keeping the alarm rate of the fault detector sufficiently close to its false alarm rate in the attack-free case. This quantifies the attack's potential impact when it is constrained to stay hidden from the detector. Simulation results are presented to illustrate the performance of our tools.