Showing papers by "Hassan K. Khalil published in 2020"

Performance Recovery of Dynamic Feedback-Linearization Methods for Multivariable Nonlinear Systems

Abstract: We show, in this paper, how a classical method for feedback linearization of a multivariable invertible nonlinear system, via dynamic extension and state feedback, can be robustified. The synthesis of the controller is achieved by means of a recursive procedure that, at each stage, consists in the augmentation of the system state space, to the purpose of rendering feedback-linearization possible, and in the design of a high-gain extended observer, to the purpose of estimating the state of the plant as well as the perturbations due to model uncertainties. As a result, a closed-loop system is obtained that, for any bounded set of initial conditions and any bounded input, recovers the performance that would have been obtained by means of the classical technique of feedback linearization via dynamic state feedback.

Scalable Consensus in Networks of Multiagent Systems Using High-Gain Observers

Abstract: Consensus algorithms are popular in the field of multiagent systems due to their wide application in formation control, distributed estimation, sensor networks, etc. Generally, for certain classes of undirected graphs, with an increase in the network size, the second smallest eigenvalue of the graph Laplacian decreases toward zero, which leads to a slow convergence rate. We present a scalable consensus algorithm using proportional derivative (PD) control where the eigenvalues of the closed-loop Laplacian matrix are invariant with respect to the size of the network for general directed graphs. The PD controller is realized using a high-gain observer. We show that the trajectories of the closed-loop system when the high-gain observer is used can be brought arbitrarily close to the trajectories under the PD controller. Simulation results are presented to demonstrate the efficacy of the proposed algorithm.

Robust tracking of an unknown trajectory with a multi-rotor UAV: A high-gain observer approach

Abstract: We study a trajectory tracking problem for a multi-rotor in the presence of modeling error and external disturbances. The desired trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume that only position and orientation measurements for the multi-rotor and position measurements for the reference system can be accessed. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the feed-forward term required for trajectory tracking, the multi-rotor states, as well as modeling error and external disturbances. We design an output feedback controller for trajectory tracking that comprises a feedback linearizing controller and the EHGO. We rigorously analyze the proposed controller and establish its stability properties. Finally, we numerically illustrate our theoretical results using the example of a multi-rotor landing on a ground vehicle.

Practical Frequency Synchronization in Power Systems Using Extended High-Gain Observer Under Unknown Time-Varying Power Demand

Abstract: In this paper, we consider the frequency synchronization problem in a network of lossless, connected and network-reduced power system. Frequency synchronization is an important problem in power systems as frequency deviation can lead to degraded power quality, tripping of generators, etc. We present a load-estimator-based consensus algorithm that achieves practical frequency synchronization in the presence of unknown time-varying power demand. It is shown that the synchronization error can be made arbitrarily small by tuning a controller parameter. Finally, simulations are performed to show the efficacy of the proposed controller.

Robust tracking of an unknown trajectory with a multi-rotor UAV: A high-gain observer approach

Abstract: We study a trajectory tracking problem for a multi-rotor in the presence of modeling error and external disturbances. The desired trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume that only position and orientation measurements for the multi-rotor and position measurements for the reference system can be accessed. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the feed-forward term required for trajectory tracking, the multi-rotor states, as well as modeling error and external disturbances. We design an output feedback controller for trajectory tracking that comprises a feedback linearizing controller and the EHGO. We rigorously analyze the proposed controller and establish its stability properties. Finally, we numerically illustrate our theoretical results using the example of a multi-rotor landing on a ground vehicle.

Scalable Coherence in Large Scale Second-Order Networks Using High-Gain Observer

Abstract: We propose a scalable second-order consensus algorithm where by tuning the controller parameter, the convergence rate of the consensus protocol is almost invariant with respect to the size of the network. This is beneficial when the algebraic connectivity of the graph Laplacian decreases towards zero, with an increase in the network size, which leads to degraded closed-loop performance. We realize the controller using a high-gain observer and it is shown that for sufficiently small observer parameter, the convergence rate under output feedback approaches the one under state feedback. We also study the controller performance under stochastic disturbances by first defining a performance output and then calculating the ℋ 2 norm from the disturbance input to the performance output. We show that the ℋ 2 norm for the state feedback controller is scalable as the network size increases. Moreover, we also show that for sufficiently small observer parameter, the ℋ 2 norm under output feedback approaches the one under state feedback.

Nonlinear Model Predictive Control Using Output Feedback

Abstract: This paper presents an output feedback model predictive control for a class of nonlinear systems in a multirate scheme, where the control sampling period is larger than the estimation sampling period. With a small sampling period, the observer is designed to be faster than the dynamics of the closed-loop system under state feedback. Stabilization is achieved by a separation approach in which the control is designed first using state feedback and practical stabilization is achieved by output feedback.