Boundary observer design for hyperbolic PDE-ODE cascade systems

Static output feedback control via PDE boundary and ODE measurements in linear cascaded ODE-beam systems

https://hal.archives-ouvertes.fr/hal-01376564/document

Stabilization of coupled linear heterodirectional hyperbolic PDE–ODE systems

This paper discusses the synchronization problem for a class of reaction–diffusion neural networks with Dirichlet boundary conditions. Unlike other studies, a sampled-data controller with stochastic sampling is designed in order to synchronize the concerned neural networks with reaction–diffusion terms and time-varying delays, where $$m$$
 sampling periods are considered whose occurrence probabilities are given constants and satisfy the Bernoulli distribution. A novel discontinuous Lyapunov–Krasovskii functional with triple integral terms is introduced based on the extended Wirtinger’s inequality. Using Jensen’s inequality and reciprocally convex technique in deriving the upper bound for the derivative of the Lyapunov–Krasovskii functional, some new synchronization criteria are obtained in terms of linear matrix inequalities. Numerical examples are provided in order to show the effectiveness of the proposed theoretical results.

Synchronization of reaction–diffusion neural networks with time-varying delays via stochastic sampled-data controller

Stabilization of an ODE–Schrödinger Cascade

State and output feedback boundary control for a coupled PDE–ODE system☆

A control system of an ODE and a diffusion PDE is discussed in this paper. The novelty lies in that the system is coupled. The method of PDE backstepping as well as some special skills is resorted in stabilizing the coupled PDE–ODE control system, which is transformed into an exponentially stable PDE–ODE cascade with an invertible integral transformation. And a state feedback boundary controller is designed. Moreover, an exponentially convergent observer for anti-collocated setup is proposed, and the output feedback boundary control problem is solved. For both the state and output feedback boundary controllers, exponential stability analyses in the sense of the corresponding norms for the resulting closed-loop systems are given through rigid proofs.

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Stabilization for a coupled PDE–ODE control system

Boundary control to stabilize a system of coupled linear plant and reaction-diffusion process is considered. Backstepping transformations with a kernel function and a vector-valued function are introduced to design control laws. For the situation without heat resource, the kernel function and the vector-valued function of the transformation are obtained, and an explicit control law is established, and simulation results are presented through figures. For the general situation with heat resource, the existence of the kernel and the vector-valued function of the transformations is shown, and an control law is derived. Stability of the closed loops is achieved for both the situations.

Stabilization of coupled linear plant and reaction-diffusion process

A coupled system of an ODE and a diffusion PDE is considered in this paper. Special techniques as well as the method of PDE backstepping are employed to construct controllers. Through transforming the system into an exponentially stable PDE-ODE cascade, a state feedback boundary controller is established. Moreover, an observer for anti-collocated setup is proposed, and the observer error is shown to exponentially converge to zero, then an output feedback boundary controller is obtained. For a scalar coupled PDE-ODE system, the boundary controller and observer, as well as the solution of the closed-loop system are given explicitly.

/pdf/stabilization-of-a-coupled-pde-ode-system-by-boundary-h4ub6jk4m3.pdf

Stabilization of a coupled PDE-ODE system by boundary control

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

/pdf/stabilization-for-a-class-of-delayed-coupled-pde-ode-systems-4evocsryuv.pdf

Chengkang Xie

Papers

State and output feedback boundary control for a coupled PDE–ODE system☆

Stabilization for a coupled PDE–ODE control system

Stabilization of coupled linear plant and reaction-diffusion process

Stabilization of a coupled PDE-ODE system by boundary control

Stabilization for a class of delayed coupled PDE-ODE systems with boundary control