Integral Inequalities for the Analysis of Distributed Parameter Systems: A complete characterization via the Least-Squares Principle

A wide variety of integral inequalities (IIs) have been proposed and studied for the stability analysis of distributed parameter systems using the Lyapunov functional approach. However, no unified mathematical framework has been proposed that could characterize the similarity and connection between these IIs, as most of them was introduced in a dispersed manner for the analysis of specific types of systems. Additionally, the extent to which the generality of these IIs can be expanded and the optimality of their lower bounds (LBs) remains open questions. In this work, we present two general classes of IIs that can generalize almost all IIs in the literature, whose integral kernels can contain a unlimited number of weighted L2 functions that are linearly independent in a Lebesgue sense. Moreover, we not only demonstrate the equivalence between the LBs of the proposed IIs under the same kernels and weighted functions, but also show that these LBs are guaranteed by the least squares principle, implying asymptotic convergence to the upper bound when the kernels functions constitutes a Schauder basis of the underlying Hilbert space. Given their general structures, the proposed IIs can be applied in various situations such as the stability analysis of coupled PDE-ODE systems or cybernetic systems that can be characterized by delay structures.Comment: Submitted to ACC 202

Local Stabilization for Discrete-Time Systems with Distributed State Delay and Fast-Varying Input Delay under Actuator Saturations

National Natural Science Foundation of China under Grant 61773156, Grant 61873148, and Grant 61933007; Program for Science and Technology Innovation Talents in the Universities of Henan Province of China under Grant 19HASTIT028, Research Fund for the Taishan Scholar Project of Shandong Province of China, Royal Society of the U.K.; Alexander von Humboldt Foundation of Germany

System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

Survey on time-delay approach to networked control

This paper provides a survey on time-delay approach to networked control systems (NCSs). The survey begins from a brief summary on fundamental network-induced issues in NCSs and the main approaches to the modelling of NCSs. In particular, a comprehensive introduction to time-delay approach to sampled-data and networked control is provided. Then, recent results on time-delay approach to event-triggered control are recalled. The survey highlights time-delay approach developed to modelling, analysis and synthesis of NCSs, under communication constraints, with a particular focus on Round-Robin, Try-once-discard and stochastic protocols. The time-delay approach allows communication delays to be larger than the sampling intervals in the presence of scheduling protocols. Moreover, some results on networked control of distributed parameter systems are surveyed. Finally, conclusions and some future research directions are briefly addressed

System level synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty – such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies