Showing papers by "Jie Chen published in 2021"

Fixed-time stabilization of linear delay systems by smooth periodic delayed feedback

Abstract: This paper studies fixed-time stabilization (FxTS) of a general controllable linear system with an input delay τ. It is shown that such a problem is not solvable if the prescribed convergence time $T_{τ}$ is smaller than $2_{τ}$ . For $T_{τ} ≥ 3_{τ}$ , a solution based on linear periodic delayed feedback (PDF) without any distributed delay is established. For $T_{τ} > 2_{τ}$ , a solution based on linear predictor-based PDF containing a distributed delay is proposed. For both cases, the gains of the PDF can be chosen as continuous, continuously differentiable, and even smooth, in the sense of infinitely many times differentiable. If only an output signal is available for feedback, two classes of linear observers with periodic coefficients are designed so that their states converge to the current and future states of the system at a prescribed finite time, respectively. With the observed current and future states, FTS can also be achieved by using respectively the PDF and observer-based PDF. A linear periodic feedback (without delay) is also established to solve the FxTS problem of linear systems with both instantaneous and delayed controls, which cannot be stabilized by any constant instantaneous feedback in certain cases. Two numerical examples verify the effectiveness of the proposed approaches.

Delay Consensus Margin of First-Order Multiagent Systems With Undirected Graphs and PD Protocols

Abstract: In this article, we study robust consensus problems for continuous-time first-order multiagent systems (MASs) with time delays. We assume that the agents input is subject to an uncertain constant delay, which may arise due to interagent communication or additionally, also by self-delay in the agent dynamics. We consider dynamic feedback control protocol in the form of proportional and derivative (PD) control, and seek to determine the delay consensus margin (DCM) achievable by PD feedback protocols, whereas the DCM is a robustness measure that defines the maximal range of delay within which robust consensus can be achieved despite the uncertainty in the delay. With an undirected graph, we show that the DCM can be determined exactly by solving a unimodal concave optimization problem, which is one of univariate convex optimization and can be solved using convex optimization or gradient-based numerical methods. The results show how unstable agent dynamics and graph connectivity may limit the range of delay tolerable, so that consensus can or cannot be maintained in the presence of delay variations.

Delay Robustness of PID Control of Second-Order Systems: Pseudo-Concavity, Exact Delay Margin, and Performance Trade-Off

Abstract: In this paper we study delay robustness of PID controllers in stabilizing systems containing uncertain delays. We consider second-order systems and seek analytical characterization and exact computation of the PID delay margin, where by PID delay margin we mean the maximal range of delay values within which the system can be robustly stabilized by a PID controller. Our primary contribution is threefold. First, we show that under a nonrestrictive assumption, the delay margin achieved by PID control coincides with that by PD controllers. Second, we show that the PID delay margin can be computed efficiently by solving a pseudo-concave unimodal problem, that is, a univariate optimization problem that admits a unique maximum and hence is a convex optimization problem in one variable. As such, from a computational standpoint, the PID delay margin problem can be considered resolved. Finally, we demonstrate analytically the trade-off between achieving delay margin and tracking performance, showing that for several canonical performance criteria, integral control reduces the delay margin. These results not only ensure that the PID delay margin problem be readily solvable, b

Consensus of Continuous-Time Multiagent Systems via Delayed Output Feedback: Delay Versus Connectivity

Abstract: This article studies the consensus problem for continuous-time linear time-invariant multiagent systems, in which the agents exchange information through delayed communication channels in a fixed undirected topology. Our primary objective is to characterize explicitly the delay effect on consensus in the framework of distributed dynamic output feedback control and its implication on the graph network connectivity. For this purpose, we tackle and solve the consensus problem in the spirit of gain margin problem, using analytic interpolation techniques. We develop an explicit condition for consensus. The result provides a limit on network connectivity imposed by time delays as well as by the agent's unstable poles and nonminimum phase zeros.

Phase Inconsistency Error Compensation for Multichannel Spaceborne SAR Based on the Rotation-Invariant Property

Abstract: The azimuth multichannel technique has been widely used in synthetic aperture radar (SAR) systems for improving the resolution and expanding the illumination area. However, due to phase inconsistency (PI) of different channels, the image quality deteriorates significantly, including resolution loss and appearance of ghost targets. In this letter, by exploiting the rotation-invariant property of the steering vector of the multichannel SAR signal, a PI error compensation method is proposed based on the estimation of signal parameters by rotation invariance technique (ESPRIT). Experimental results are presented using both simulated and real data to demonstrate the performance of the proposed method.

Scalloping Suppression for ScanSAR Images Based on Modified Kalman Filter With Preprocessing

Abstract: Scanning synthetic aperture radar (ScanSAR) mode is widely used in Earth observation because of its capability of acquiring wide-swath images with moderate resolution. However, due to the operation mechanism of ScanSAR mode, the acquired images often suffer from the scalloping problem, resulting in significant deterioration of image quality. In this article, a novel scalloping suppression method is proposed for ScanSAR images based on the modified Kalman filter with preprocessing. First, an image model is built to analyze the effect caused by scalloping. Then, a modified Kalman filter is proposed to estimate the intensity of scalloping. However, if the scene is complicated or the scalloping effect is strong, the Kalman filter works with poor performance. Therefore, an innovative preprocessing operation is introduced, involving image segmentation and pixel value filling. Finally, the proposed method is verified by the GaoFen-3 (GF-3) and TerraSAR-X satellite images with different scenes. The results demonstrate that the proposed method can accommodate the complex scene well and achieve effective scalloping suppression.

An Algebraic Formula for Performance Bounds of a Weighted $\mathcal {H}_\infty$ Optimal Control Problem

Abstract: This article provides performance bounds for a particular $\mathcal {H}_\infty$ model-matching problem. We consider scalar linear time-invariant plants in a one-degree-of-freedom control loop. We obtained explicit expressions for the Gramians needed when Nehari's theorem is applied to this problem, leading to a simple algebraic equation for the optimal performance. This formula sheds light upon the effect that nonminimum-phase zeros have on the optimal performance and yields easily computable bounds and approximations.

The Impact of System Distortions and Noise on HV Backscatter and Its Relevance to Above-Ground Biomass Estimation from Spaceborne P-Band SAR Data

Abstract: This article analyses the effects of system distortions (crosstalk and channel imbalance), Faraday rotation and system noise on estimates of the cross-polarized backscattering coefficient, ${\boldsymbol{\sigma }}_{{{\bf hv}}}^0$ , by a spaceborne synthetic aperture radar. Modeling the unknown system errors and noise by a joint complex Gaussian distribution allows analytic first-order approximations to the mean and variance of the error in ${\boldsymbol{\sigma }}_{{{\bf hv}}}^0$ to be derived that do not depend on the SAR operating frequency. Simulation shows these approximations to be very accurate, given the statistical model and the expected magnitudes of system errors and noise for the P-band instrument to be carried by the European Space Agency BIOMASS mission. Simulation further shows that the ${\boldsymbol{\sigma }}_{{{\bf hv}}}^0$ errors are Gaussian distributed, so their exceedance probabilities can be calculated from just the analytic expressions for the mean and variance of the errors. Exceedance probabilities for above-ground biomass (AGB) can then be calculated under a power law relation between ${\boldsymbol{\sigma }}_{{{\bf hv}}}^0{{\rm{\sigma }}_{{\rm{hv}}}}$ and AGB that is consistent with P-band observations. This allows tradeoff curves between crosstalk and channel imbalance (shown to be segments of hyperbolas) to be calculated, along which the relative error in AGB is within a given percentage of its true value, from which limits on the permissible size of the errors can be determined if BIOMASS mission requirements are to be met.

Geometrical Characterization of Sensor Placement for Cone-Invariant and Multi-Agent Systems against Undetectable Zero-Dynamics Attacks.

Abstract: Undetectable attacks are an important class of malicious attacks threatening the security of cyber-physical systems, which can modify a system's state but leave the system output measurements unaffected, and hence cannot be detected from the output. This paper studies undetectable attacks on cone-invariant systems and multi-agent systems. We first provide a general characterization of zero-dynamics attacks, which characterizes fully undetectable attacks targeting the non-minimum phase zeros of a system. This geometrical characterization makes it possible to develop a defense strategy seeking to place a minimal number of sensors to detect and counter the zero-dynamics attacks on the system's actuators. The detect and defense scheme amounts to computing a set containing potentially vulnerable actuator locations and nodes, and a defense union for feasible placement of sensors based on the geometrical properties of the cones under consideration.