Muhammad Umar B. Niazi

Muhammad Umar B. Niazi, John Cao, Xudong Sun et al.

Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output injection. The observer then estimates the system's state in the original coordinates by inverting the transformation map. However, finding a suitable injective transformation whose inverse can be derived remains a primary challenge for general nonlinear systems. We propose a novel approach that uses supervised physics-informed neural networks to approximate both the transformation and its inverse. Our method exhibits superior generalization capabilities to contemporary methods and demonstrates robustness to both neural network's approximation errors and system uncertainties.

John Cao, Muhammad Umar B. Niazi, Matthieu Barreau et al.

This paper presents a novel observer-based approach to detect and isolate faulty sensors in nonlinear systems. The proposed sensor fault detection and isolation (s-FDI) method applies to a general class of nonlinear systems. Our focus is on s-FDI for two types of faults: complete failure and sensor degradation. The key aspect of this approach lies in the utilization of a neural network-based Kazantzis-Kravaris/Luenberger (KKL) observer. The neural network is trained to learn the dynamics of the observer, enabling accurate output predictions of the system. Sensor faults are detected by comparing the actual output measurements with the predicted values. If the difference surpasses a theoretical threshold, a sensor fault is detected. To identify and isolate which sensor is faulty, we compare the numerical difference of each sensor meassurement with an empirically derived threshold. We derive both theoretical and empirical thresholds for detection and isolation, respectively. Notably, the proposed approach is robust to measurement noise and system uncertainties. Its effectiveness is demonstrated through numerical simulations of sensor faults in a network of Kuramoto oscillators.

Muhammad Umar B. Niazi, Arif Bülent Özgüler, Aykut Yıldız

Consensus formation in a social network is modeled by a dynamic game of a prescribed duration played by members of the network. Each member independently minimizes a cost function that represents his/her motive. An integral cost function penalizes a member's differences of opinion from the others as well as from his/her own initial opinion, weighted by influence and stubbornness parameters. Each member uses its rate of change of opinion as a control input. This defines a dynamic non-cooperative game that turns out to have a unique Nash equilibrium. Analytic explicit expressions are derived for the opinion trajectory of each member for two representative cases obtained by suitable assumptions on the graph topology of the network. These trajectories are then examined under different assumptions on the relative sizes of the influence and stubbornness parameters that appear in the cost functions.

Amr Alanwar, Muhammad Umar B. Niazi, Karl H. Johansson

This paper proposes a data-driven set-based estimation algorithm for a class of nonlinear systems with polynomial nonlinearities. Using the system's input-output data, the proposed method computes a set that guarantees the inclusion of the system's state in real-time. Although the system is assumed to be a polynomial type, the exact polynomial functions, and their coefficients are assumed to be unknown. To this end, the estimator relies on offline and online phases. The offline phase utilizes past input-output data to estimate a set of possible coefficients of the polynomial system. Then, using this estimated set of coefficients and the side information about the system, the online phase provides a set estimate of the state. Finally, the proposed methodology is evaluated through its application on SIR (Susceptible, Infected, Recovered) epidemic model.