arXiv subjects

Zhi-Xue Zhao

Publications and source records attributed to Zhi-Xue Zhao.

4 recordsLinked to original sources

arXiv2025

Output regulation for a reaction-diffusion system with input delay and unknown frequency

This study solves the output regulation problem for a reaction-diffusion system confronting concurrent input delay and fully unidentified disturbances (encompassing both unknown frequencies and amplitudes) across all channels. The principal innovation emerges from a novel adaptive control architecture that synergizes the modal decomposition technique with a dual-observer mechanism, enabling real-time concurrent estimation of unmeasurable system states and disturbances through a state observer and an adaptive disturbance estimator. Unlike existing approaches limited to either delay compensation or partial disturbance rejection, our methodology overcomes the technical barrier of coordinating these two requirements through a rigorously constructed tracking-error-based controller, achieving exponential convergence of system output to reference signals. Numerical simulations are presented to validate the effectiveness of the proposed output feedback control strategy.

math.OC↗

arXiv2025

Output regulation for an unstable wave equation with output delay and one measurement only

This paper addresses the output regulation problem for a one-dimensional unstable wave equation subject to output delay and all-channel disturbances with unknown frequencies and amplitudes. First, this problem is transformed into a stabilization problem for an unstable wave equation with output delay and disturbances by employing regulator equations. Subsequently, a backstepping-based feedforward regulator is proposed to exponentially stabilize this system. To track the states of the unstable wave equation, the time interval is partitioned into two segments. The observers and predictors are designed at these distinct intervals, respectively. Therein, the observers comprise two components: a state observer proposed via dynamic compensators and an adaptive observer designed by the adaptive internal model method. Finally, a novel error-based feedback controller is derived using a single measurement, ensuring exponential convergence of the tracking error to zero. This work establishes the pioneering solution to the output regulation problem for distributed parameter systems (DPS) with output delay. Numerical simulations are provided to illustrate the results.

math.OC↗

arXiv2016

Simultaneous Identification of Coefficient and Initial State for One-Dimensional Heat Equation from Boundary Control and Measurement

In this paper, we consider simultaneous reconstruction of the diffusion coefficient and initial state for a one-dimensional heat equation through boundary control and measurement. The boundary measurement is known to make the system exactly observable, and both coefficient and initial state are shown to be identifiable by this measurement. By a Dirichlet series representation for observation, we can transform the problem into an inverse process of reconstruction of the spectrum and coefficients for Dirichlet series in terms of observation. This happens to be the reconstruction of spectral data for an exponential sequence with measurement error. This enables us to develop an algorithm based on the matrix pencil method in signal analysis. An error analysis is made for the proposed method. The numerical simulations are presented to verify the proposed algorithm.

math.AP↗

arXiv2016

Simultaneous Identification of Damping Coefficient and Initial Value in PDEs from boundary measurement

In this paper, the simultaneous identification of damping or anti-damping coefficient and initial value for some PDEs is considered. An identification algorithm is proposed based on the fact that the output of system happens to be decomposed into a product of an exponential function and a periodic function. The former contains information of the damping coefficient, while the latter does not. The convergence and error analysis are also developed. Three examples, namely an anti-stable wave equation with boundary anti-damping, the Schrödinger equation with internal anti-damping, and two connected strings with middle joint anti-damping, are investigated and demonstrated by numerical simulations to show the effectiveness of the proposed algorithm.

math.AP↗