Regional gradient observability for semilinear hyperbolic systems: HUM approach

The paper aims to extend the notion of regional observability of the gradient to the semilinear hyperbolic case, in order to reconstruct the gradient of the initial conditions in a subregion $omega$ of the domain evolution $varOmega$. We start with an asymptotically linear system, the approach is based on an extension of the Hilbert uniqueness method (HUM) and Schauder''s fixed point theorem. The analysis leads to an algorithm which is successfully numerically implemented and illustrated with examples and simulations.     

线性混合系统的可观性分析

线性混合系统的控制输入(包括离散控制和连续控制)会影响混合系统的状态可观性．混合系统的可观性包括初始的离散状态和连续状态，以及离散状态的切换时间．对此．分析了系统的控制输入对线性混合系统状态(主要是离散状态)的影响，并论述这将有助于改善某些线性混合系统状态的可观性．通过分析给出了在这种情形下比较宽松的线性混合系统状态可观性条件及其秩检验条件，并给出说明性示例．     

Regional observability for distributed semi-linear hyperbolic systems

The objective of this paper is to study the notion of regional observability of hyperbolic semilinear systems. For the state reconstruction in a given subregion, we give a first approach which combines the extension of the HUM method and the fixed point techniques. The analytical case is then explored using sectorial property of the considered dynamic operator and converted to a fixed point problem. The two approaches lead to algorithms which are successfully implemented numerically and illustrated with examples and simulations.     

Analysis and stabilization for networked linear hyperbolic systems of rationally dependent conservation laws

In this paper, for a networked linear hyperbolic partial differential equations (PDEs) system of conservation laws, the propagation periods of which are rationally dependent, with coupled boundary conditions, we propose a novel approach to analyze its controllability and observability. In addition, we propose a design method of a stabilizing controller, where a boundary-input with boundary-valued feedback is considered. First, we characterize the control properties, such as controllability of such a PDE system, in terms of the corresponding ones of a finite-dimensional discrete-time system defined on the boundaries of the PDE system, which is derived by fully exploiting the method of characteristics. Since the obtained discrete-time system is low-dimensional, its analysis is relatively easier. Next, we propose a design method of a stabilizing controller based on this discrete-time system. Finally, numerical simulations are presented to show that the proposed method is effective.     

Observability of switching structured linear systems with unknown input. A graph-theoretic approach

This paper deals with the observability of the discrete mode, the internal state and the input of switching structured linear systems with unknown input. The proposed method, based on a graph-theoretic approach, assumes only the knowledge of the system’s structure. We express, in graphical terms, necessary and sufficient conditions for the generic observability of the discrete mode, the continuous internal state and the input of a switching structured linear system. These conditions can be implemented by classical graph theory algorithms based on finding particular paths and cycles in a digraph.     

A fourier series method for the numerical solution of hyperbolic equations

In this paper a Fourier series technique which reduces the given hyperbolic partial differential equation to a system of ordinary differential equations with one point boundary conditions is presented. The numerical results obtained indicate a considerable saving in time in addition to accuracy since no discretisation errors are incurred in the space variable.     

Observability of polynomially stable systems

For finite-dimensional systems the Hautus test is a well known and easily checkable condition for observability. Russell and Weiss [A general necessary condition for exact observability, SIAM J. Control Optim. 32 (1994) 1–23] suggested an infinite-dimensional version of the Hautus test, which is necessary for exact infinite-time observability and sufficient for approximate infinite-time observability of exponentially stable systems. In this paper the notion of observability is studied for polynomially stable systems. Several known results for exponentially stable systems are extended to the setting of polynomially stable systems. By means of an example the obtained results are illustrated.     

Differential Riccati equation‐based adaptive stabilization for switched linear systems

In this paper, a novel adaptive control design is proposed to stabilize a class of switched linear systems with parametric uncertainties and disturbances. In particular, a family of differential Riccati equations that holds for the finite switching intervals are established, of which the closed‐form solutions are exploited to develop the Lyapunov function for the closed‐loop system. This Lyapunov function is imposed to be decreasing at and between two arbitrary switching instants by solving a group of matrix inequalities, based on which the adaptive controllers for switched linear system with and without disturbances are proposed, respectively. In the nondisturbed setting, asymptotic stability of the adaptive switched linear system is achieved, while the system is bounded in a mean square sense in the disturbed setting. A numerical example of flight control for F4E fighter aircraft is used to illustrate the proposed adaptive control methodology.     

Observability analysis for structured bilinear systems: A graph-theoretic approach

This paper is devoted to the generic observability analysis for structured bilinear systems using a graph-theoretic approach. On the basis of a digraph representation, we express in graphic terms the necessary and sufficient conditions for the generic observability of structured bilinear systems. These conditions have an intuitive interpretation and are easy to check by hand for small systems and by means of well-known combinatorial techniques for large-scale systems.     

一类离散时间切换线性系统的无差拍控制

研究一类带多控制器和多传感器离散时间线性系统的无差拍控制.对能控系统,通过适当的状态坐标变换获得系统矩阵的块三角结构,再设计状态反馈和周期切换策略使得状态反馈矩阵在有限周期内为零,从而保证闭环系统的无差拍稳定.进一步,对能观系统,设计具有有限时间精确估计的动态输出反馈,通过适当的周期切换策略实现闭环系统的无差拍稳定.最后,给出一个例子以验证所提设计方法的有效性.     

Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially varying coefficients. Thereby, the ODE is coupled to the PDE in-domain and at the uncontrolled boundary, whereas the ODE is coupled with the latter boundary. For the state feedback design, a two-step backstepping approach is developed, which yields the conventional kernel equations and additional decoupling equations of simple form. In order to implement the state feedback controller, the design of observers for the PDE-ODE systems in question is considered, whereby anti-collocated measurements are assumed. Exponential stability with a prescribed convergence rate is verified for the closed-system pointwise in space. The resulting compensator design is illustrated for a 4 × 4 heterodirectional hyperbolic system coupled with a third-order ODE modelling a dynamic boundary condition.