In this article, the backstepping method is employed to stabilize a coupled wave-ODE system with internal anti-damping by means of decoupling them into stable cascaded system. At same time, existence kernels in transformation and inverse proved iterative method.

In this paper, sliding mode control approach is used to stabilize a 2×2 system of first-order linear hyperbolic PDEs subject boundary input disturbance. Disturbance rejection achieved, and with the designed controller, resulting closed-loop admits unique (mild) solution without chattering. Convergence chosen infinite-dimensional surface state trajectories takes place in finite time. Then on surface, exponentially stable decay rate depending spatially varying coefficients. A simulation...

Accurate Lithium-ion (Li-ion) battery internal temperature information enables high-fidelity monitoring and safe operation in management systems, thus prevents thermal faults that could cause catastrophic failures. This paper proposes an online estimation scheme for cylindrical Li-ion batteries based on a one-dimensional semilinear parabolic partial differential equation (PDE) model subject to in-domain output uncertainties, using measurements at the surface only. The state observer design...

Abstract Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg–de Vries equation posed on finite interval <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>[</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> <m:mo>⁢</m:mo> <m:mi>π</m:mi> <m:msqrt> <m:mn>7</m:mn> <m:mo>/</m:mo> <m:mn>3</m:mn> </m:mrow> </m:msqrt> <m:mo>]</m:mo> </m:math> {[0,2\pi\sqrt{7/3}]} . The comes with Dirichlet boundary condition at the left end-point...

This paper considers the modelling and control design of multi-agent systems in 3-D space. The communication graph agents is a mesh-grid 2-D cylindrical surface. Different from most existing literatures, where are modelled by ordinary differential equations (ODEs), we treat as continuum this paper. More specifically, model collective dynamics two reaction–advection–diffusion partial (PDEs). PDE states represent agent positions, equilibria correspond to possible formation manifolds. These...

Accurate online state-of-charge (SoC) estimation is a basic need and also fundamental challenge for battery applications. In order to achieve accurate SoC the lithium-ion batteries, we employ coupled thermal-electrochemical model. This system of an ordinary differential equation (ODE) partial (PDE) simpler than Doyle-Fuller-Newman (DFN) model, more single particle model (SPM) alone. Thus, it could serve as better fit full state observer design estimation. PDE backstepping approach utilized...

In this paper, a backstepping control of the one-phase Stefan Problem, which is 1-D diffusion Partial Differential Equation (PDE) defined on time varying spatial domain described by an ordinary differential equation (ODE), studied. A new nonlinear transformation for moving boundary problem utilized to transform original coupled PDE-ODE system into target whose exponential stability proved. The full-state feedback controller ensures interface reference setpoint and ℋ <sub...

In this paper, backstepping boundary controllers are designed for a class of linearized Korteweg-de Vries systems with possible anti-diffusion, and the resulting closed-loop can achieve arbitrary exponential decay rate. Semigroup linear operators is constructed in analyzing well-posedness stability target systems, mathematical induction used proving existence kernel functions. An example also presented, which illustrates performance controller. The rate estimate derived paper not necessarily...

Abstract This paper considers the stabilization of a heat‐ODE system cascaded at boundary point and an intermediate point. The stabilizing feedback control law is designed by backstepping method. Based on novel transformation, we prove that all kernel functions in forward inverse transformations are class C 2 . Moreover, effectiveness controller design shown with numerical simulation. Finally, show coherence between controllability assumption main theorem this known one for special case λ =0.

A class of coupled PDE-ODE systems with delays at the input and two-directional interconnection interfaces (one single point) is discussed in this paper. Exponential stability sense corresponding norms for original closed-loop system derived controller obtained by finally transforming into an exponentially stable PDEs-ODE cascade a boundary feedback backstepping controller, result also rigidly proved.

This study proposes a constructive stabilisation and robust controller design method for stochastic non‐linear systems from novel dissipation analysis energy point of view. First, the authors propose sufficient condition Hamiltonian discuss property systems, which will be used stability feedback design. Then, show that system is (asymptotically) stable in probability if it (strictly) dissipative. By completing realisation proposed to stabilise under zero state detectability. For subjected...

In this article, we address adaptive output-feedback boundary control of coupled hyperbolic partial differential equations (PDEs) with spatially varying coefficients and on a time-varying domain, whose uncontrolled is disturbed ordinary equation (ODE), where multiple parameters in the state matrix amplitudes harmonic disturbance are unknown. The asymptotic convergence to zero ODE boundedness PDE states ensured. This article motivated by lateral vibration suppression mining cable elevator,...