arXiv subjects

Yongchun Bi

Publications and source records attributed to Yongchun Bi.

5 recordsLinked to original sources

arXiv2026

Input-to-State Stabilization of a Coupled ODE-PDE System with Time-Varying Coefficients via Composite Boundary Control

This paper proposes a novel composite boundary feedback control law that ensures input-to-state stability (ISS) for a coupled ODE-parabolic PDE system with time-varying coefficients in both subsystems. In controller design, we circumvent the need to directly solve coupled time-varying parabolic-hyperbolic kernel equations by employing an analytic pre-defined gain function and a time-varying Volterra kernel function to design the control law explicitly. In stability analysis, to address the simultaneous challenges of Dirichlet boundary disturbances and time-varying coefficients, we employ the square root of a time-varying positive definite matrix and a superlinear function to construct a nonquadratic Lyapunov function for the ODE and a generalized Lyapunov functional for the PDE, respectively, in the target system, thereby establishing the ISS in the $L^2$-norm of the closed-loop system. Numerical simulations are presented to illustrate the effectiveness of the proposed control scheme.

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arXiv2026

Robust synchronization for multi-agent systems governed by PDEs with observable and unobservable disturbances

This paper investigates robust synchronization for multi-agent systems (MASs) governed by parabolic partial differential equations in the presence of both observable and unobservable disturbances. Using only boundary output measurements, a disturbance observer is designed to estimate observable Dirichlet boundary disturbances while ensuring robustness of the observer error system with unobservable disturbances occurring in the domain. Using only the reference signal and local output information, distributed synchronization controllers are then constructed to enable all agents to track the reference trajectory. In particular, exponential tracking is achieved in the absence of unobservable disturbances, while robustness is preserved when additional unobservable disturbances occur during controller implementation. We further analyze the impact of unobservable Dirichlet-Robin boundary disturbances on synchronization performance by proving the boundedness of solutions to the synchronization error system. Moreover, to characterize the influence of all disturbances, input-to-state stability (ISS) is established for the closed-loop system. For the involved systems, the generalized Lyapunov method and the recursion technique are extensively employed in the stability analysis, and the lifting technique and semigroup theory are used to prove the well-posedness. Simulation results validate the proposed control scheme, demonstrating effective disturbance estimation and rejection, robust synchronization, and the ISS properties under various scenarios.

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arXiv2026

Input-to-state stabilization of an ODE cascaded with a parabolic equation involving Dirichlet-Robin boundary disturbances

This paper focuses on the input-to-state stabilization problem for an ordinary differential equation (ODE) cascaded by parabolic partial differential equation (PDE) in the presence of Dirichlet-Robin boundary disturbances, as well as in-domain disturbances. For the cascaded system with a Dirichlet pointwise interconnection, the ODE takes the value of a Robin boundary condition at the ODE-PDE interface as its direct input, and the PDE is driven by a Dirichlet boundary input at the opposite end. We first employ the backstepping method to design a boundary controller and to decouple the cascaded system. This decoupling facilitates independent stability analysis of the PDE and ODE systems sequentially. Then, to address the challenges posed by Dirichlet boundary disturbances to the application of the classical Lyapunov method, we utilize the generalized Lyapunov method to establish the ISS in the max-norm for the cascaded system involving Dirichlet boundary disturbances and two other types of disturbances. The obtained result indicates that even in the presence of different types of disturbances, ISS analysis can still be conducted within the framework of Lyapunov stability theory. For the well-posedness of the target system, it is conducted by using the technique of lifting and the semigroup method. Finally, numerical simulations are conducted to illustrate the effectiveness of the proposed control scheme and ISS properties for a cascaded system with different disturbances.

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arXiv2025

Local integral input-to-state stability for non-autonomous infinite-dimensional systems

In this paper, we prove comparison principles for nonlinear differential equations with time-varying coefficients and develop Lyapunov analytical tools for the integral input-to-state stability (iISS) analysis of nonlinear non-autonomous infinite-dimensional systems, which involve nonlinearities satisfying a superlinear growth, {bringing} difficulties to the iISS {analysis.} Specifically, our approach starts by establishing several forms of comparison principles for a wide range of ordinary differential equations having time-varying coefficients and superlinear terms, paving the way to conduct iISS assessment for general nonlinear non-autonomous infinite-dimensional systems within the Lyapunov stability framework. Then, by using the comparison principles, we prove a local {iISS} {(LiISS)} Lyapunov theorem for the nonlinear non-autonomous infinite-dimensional systems in the framework of Banach spaces. {Furthermore,} we provide sufficient conditions of the existence of a local iISS Lyapunonv functional (LiISS-LF) and construct LiISS-LFs for the systems in the framework of Hilbert spaces. Finally, we preset two examples to illustrate the proposed {Lyapunov} method for the LiISS analysis: one is to show how to obtain the LiISS of a nonlinear finite-dimensional system with time-varying coefficients and superlinear terms under linear state feedback control law while another one is to show how to employ the interpolation inequalities to handle superliner terms and establish the LiISS-LF for a class of multi-dimensional parabolic equations with space-time-varying coefficients. To demonstrate the validity of the results, numerical experiments are also conducted to verify the LiISS of these two classes of systems.

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arXiv2024

Input-to-State Stabilization of 1-D Parabolic PDEs under Output Feedback Control

This paper addresses the problem of input-to-state stabilization for a class of parabolic equations with time-varying coefficients, as well as Dirichlet and Robin boundary disturbances. By using time-invariant kernel functions, which can reduce the complexity in control design and implementation, an observer-based output feedback controller is designed via backstepping. By using the generalized Lyapunov method, which can be used to handle Dirichlet boundary terms, the input-to-state stability of the closed-loop system under output feedback control, as well as the state estimation error system, is established in the spatial $L^\infty$-norm. Numerical simulations are conducted to confirm the theoretical results and to illustrate the effectiveness of the proposed control scheme.

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