This paper provides observer-based sampled-data and event-triggered boundary control strategies for a class of reaction-diffusion PDEs with collocated sensing and Robin actuation. Infinite-dimensional backstepping design is used as the underlying control approach. It is shown that the continuous-time output feedback boundary control applied in a sample-and-hold fashion ensures global closed-loop exponential stability, provided that the sampling period is sufficiently small. Further, robustness to perturbations of the sampling schedule is guaranteed. For the event-triggered implementation of the continuous-time controller, a dynamic triggering condition is utilized. The triggering condition determines the time instants at which the control input needs to be updated. Under the observer-based event-triggered boundary control, it is shown that there is a minimal dwell-time between two triggering instants independent of initial conditions. Further, the global exponential convergence of the closed-loop system to the equilibrium point is established. A simulation example is provided to validate the theoretical results.
Output Feedback Control of Inhomogeneous Parabolic PDEs with Point Actuation and Point Measurement using SOS and Semi-Separable Kernels
Illinois Institute of Technology（伊利诺伊理工学院）；Grenoble Image Parole Signal Automatique Lab., Université Joseph Fourier/Centre National de la Recherche Scientifique（格勒诺布尔图像语音信号自动实验室，约瑟夫·傅立叶大学/法国国家科学研究中心）；School of Engineering of Matter, Transport and Energy at Arizona State University（亚利桑那州立大学物质、运输与能源工程学院）
This paper addresses the topic of global output feedback stabilization of semilinear reaction-diffusion PDEs. The semilinearity is assumed to be confined into a sector condition. We consider two different types of actuation configurations, namely: bounded control operator and right Robin boundary control. The measurement is selected as a left Dirichlet trace. The control strategy is finite dimensional and is designed based on a linear version of the plant. We derive a set of sufficient conditions ensuring the global exponential stabilization of the semilinear reaction-diffusion PDE. These cond…
This paper presents an observer-based event-triggered boundary control strategy for a class of reaction-diffusion PDEs with Robin actuation. The observer only requires boundary measurements. The control approach consists of a backstepping output feedback boundary controller, derived using estimated states, and a dynamic triggering condition, which determines the time instants at which the control input needs to be updated. It is shown that under the proposed observer-based event-triggered boundary control approach, there is a minimal dwell-time between two triggering instants independent of in…
This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design strategy consists of a constant-delay predictor feedback designed based on the known nominal value of the control input delay and is synthesized on a finite-dimensional truncated model capturing the unstable modes of the original infinite-dimensional system. By using a small-gain argument, we show that the resulting closed-loop system is exponentially stable…
A network of agents, modeled by a class of wave PDEs, is under investigation. One agent in the network plays the role of a leader, and all the remaining "follower" agents are required to asymptotically track the state of the leader. Only boundary sensing of the agent's state is assumed, and each agent is controlled through the boundary by Neumann-type actuation. A linear interaction protocol is proposed and analyzed by means of a Lyapunov-based approach. A simple set of tuning rules, guaranteeing the exponential achievement of synchronization, is obtained. In addition, an exponential ISS relat…
A Convex Approach to Output Feedback Control of Parabolic PDEs Using Sum-of-Squares
Illinois Institute of Technology（伊利诺伊理工学院）；Grenoble Image Parole Signal Automatique Lab., Université Joseph Fourier/Centre National de la Recherche Scientifique（格勒诺布尔图像语音信号自动化实验室，约瑟夫·傅立叶大学/法国国家科学研究中心）；School of Engineering of Matter, Transport and Energy at Arizona State University（亚利桑那州立大学物质、运输与能源工程学院）
This paper deals with the backstepping design of observer-based compensators for parabolic ODE-PDE-ODE systems. The latter consist of n coupled parabolic PDEs with distinct diffusion coefficients and spatially-varying coefficients, that are bidirectionally coupled to ODEs at both boundaries. The actuation and sensing appears through these ODEs resulting in a challenging control problem. For this setup a systematic backstepping approach is proposed, in order to determine a state feedback controller and an observer. In particular, the state feedback loop and the observer error dynamics are mappe…
