Adaptive Backstepping Control for Fractional-Order Nonlinear Systems with External Disturbance and Uncertain Parameters Using Smooth Control

In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller is proposed with adaptive laws that are used to estimate the unknown system parameters and the bound of unknown disturbance. Instead of using discontinuous functions such as the $\mathrm{sign}$ function, an auxiliary function is employed to obtain a smooth control input that is still able to achieve perfect tracking in the presence of bounded disturbances. Indeed, global boundedness of all closed-loop signals and asymptotic perfect tracking of fractional-order system output to a given reference trajectory are proved by using fractional directed Lyapunov method. To verify the effectiveness of the proposed control method, simulation examples are presented.Comment: Accepted by the IEEE Transactions on Systems, Man and Cybernetics: Systems with Minor Revision

Solving specified-time distributed optimization problem via sampled-data-based algorithm

Despite significant advances on distributed continuous-time optimization of multi-agent networks, there is still lack of an efficient algorithm to achieve the goal of distributed optimization at a pre-specified time. Herein, we design a specified-time distributed optimization algorithm for connected agents with directed topologies to collectively minimize the sum of individual objective functions subject to an equality constraint. With the designed algorithm, the settling time of distributed optimization can be exactly predefined. The specified selection of such a settling time is independent of not only the initial conditions of agents, but also the algorithm parameters and the communication topologies. Furthermore, the proposed algorithm can realize specified-time optimization by exchanging information among neighbours only at discrete sampling instants and thus reduces the communication burden. In addition, the equality constraint is always satisfied during the whole process, which makes the proposed algorithm applicable to online solving distributed optimization problems such as economic dispatch. For the special case of undirected communication topologies, a reduced-order algorithm is also designed. Finally, the effectiveness of the theoretical analysis is justified by numerical simulations

Composite learning backstepping control with guaranteed exponential stability and robustness

Adaptive backstepping control provides a feasible solution to achieve asymptotic tracking for mismatched uncertain nonlinear systems. However, input-to-state stability depends on high-gain feedback generated by nonlinear damping terms, and closed-loop exponential stability with parameter convergence involves a stringent condition named persistent excitation (PE). This paper proposes a composite learning backstepping control (CLBC) strategy based on modular backstepping and high-order tuners to compensate for the transient process of parameter estimation and achieve closed-loop exponential stability without the nonlinear damping terms and the PE condition. A novel composite learning mechanism that maximizes the staged exciting strength is designed for parameter estimation, such that parameter convergence can be achieved under a condition of interval excitation (IE) or even partial IE that is strictly weaker than PE. An extra prediction error is employed in the adaptive law to ensure the transient performance without nonlinear damping terms. The exponential stability of the closed-loop system is proved rigorously under the partial IE or IE condition. Simulations have demonstrated the effectiveness and superiority of the proposed method in both parameter estimation and control compared to state-of-the-art methods

Intensity Mapping Functions For HDR Panorama Imaging: Weighted Histogram Averaging

It is challenging to stitch multiple images with different exposures due to possible color distortion and loss of details in the brightest and darkest regions of input images. In this paper, a novel intensity mapping algorithm is first proposed by introducing a new concept of weighted histogram averaging (WHA). The proposed WHA algorithm leverages the correspondence between the histogram bins of two images which are built up by using the non-decreasing property of the intensity mapping functions (IMFs). The WHA algorithm is then adopted to synthesize a set of differently exposed panorama images. The intermediate panorama images are finally fused via a state-of-the-art multi-scale exposure fusion (MEF) algorithm to produce the final panorama image. Extensive experiments indicate that the proposed WHA algorithm significantly surpasses the related state-of-the-art intensity mapping methods. The proposed high dynamic range (HDR) stitching algorithm also preserves details in the brightest and darkest regions of the input images well. The related materials will be publicly accessible at https://github.com/yilun-xu/WHA for reproducible research.Comment: 11 pages, 5 figure

Adaptive Backstepping Control of Uncertain Nonlinear Systems with Input and State Quantization

Author's accepted manuscript. © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Although it is common in network control systems that the sensor and control signals are transmitted via a common communication network, no result is available in investigating the stabilization problem for uncertain nonlinear systems with both input and state quantization. The issue is solved in this article, by presenting an adaptive backstepping based control algorithm for the systems with sector bounded input/state quantizers. In addition to overcome the difficulty to proceed recursive design of virtual controls with quantized states, the relation between the input signal and error state need be well established to handle the effects due to input quantization. It is shown that all closed-loop signals are ensured uniformly bounded and all states will converge to a compact set. Experimental results are provided to validate the effectiveness of the proposed control scheme.acceptedVersio

Resilient Multi-Dimensional Consensus in Adversarial Environment

This paper considers the multi-dimensional consensus in networked systems, where some of the agents might be misbehaving (or faulty). Despite the influence of these misbehaviors, the healthy agents aim to reach an agreement within the convex hull of their initial states. Towards this end, this paper develops a resilient consensus algorithm, where each healthy agent sorts its received values on one dimension, computes two "middle points" based on the sorted values, and moves its state toward these middle points. We further show that the computation of middle points can be efficiently achieved by linear programming. Compared with the existing works, this approach has lower computational complexity. Assuming that the number of malicious agents is upper bounded, sufficient conditions on the network topology are then presented to guarantee the achievement of resilient consensus. Some numerical examples are finally provided to verify the theoretical results.Comment: arXiv admin note: substantial text overlap with arXiv:1911.1083