Resource Aware Control of Networked Control Systems A networked control system is a control system where the feedback loop is closed through a communication network. Networked control systems have different field of applications such as environment monitoring, industrial automation, healthcare applications, disaster management and military surveillance. One of the main challenges in networked control systems is resource constraints such as communication, computation and energy constraints. A popular control method widely used in networked control systems is event or self-triggered control. The main advantage of the event/self-triggered control method is the efficient utilization of resources while simultaneously achieving control objectives. In these control methods, sampling or communication times are determined implicitly by a state dependent triggering rule, which results in aperiodic transmissions or control updates based on need. Thus, event/self-triggered control is usually far more efficient in the usage of limited resources. However, as the update times are implicitly determined and aperiodic, higher-level planning and scheduling of shared resources is difficult. So, it is important to study about inter-event times for designing controllers that properly balance control objectives and constrained resources. For example, understanding the evolution of inter-event times helps to schedule multiple processes over a shared communication channel or to plan transmissions under constraints. Similarly, understanding inter-event times generated by an event/selftriggering rule can help in the analytical quantification of the improvement of average interevent times for an event/self-triggered controller over that of a time-triggered controller. However, very little research has been done on this problem. My current work deals with the analysis of evolution of inter-event times in linear systems under event-triggered control and region-based self-triggered control. In the first part of this work, we consider planar systems under control with a class of scale-invariant event triggering rules. In this setting, the inter-event time is a function of the
angle'' of the state at an event. This allows us to analyze the steady state convergence of inter-event times by studying the fixed points of theangle’’ map, which represents the evolution of the
angle'' of the state from one event to the next. For a specific triggering rule, we provide necessary conditions for the existence of a fixed point of the angle map. We also analyze stability and region of convergence of a fixed point of theangle’’ map. With the help of ergodic theory, we provide a sufficient condition for the asymptotic average inter-event time to be a constant for all initial states of the system. Then, we consider a special case where the
angle'' map is an orientation-preserving homeomorphism. Using rotation theory, we comment on the asymptotic behavior of the inter-event times, including on whether the inter-event times converge to a periodic sequence. We also analyze the asymptotic average inter-event time as a function of theangle’’ of the initial state of the system. In some special kind of scenarios, we also provide insights on how one could compute the asymptotic average inter-event time efficiently In the second part of this work, we consider n-dimensional systems under regionbased self-triggered control, in which the state space is partitioned into a finite number of conic regions and each region is associated with a fixed inter-event time. We analyze the evolution of inter-event times under the proposed self-triggered control method. In this framework, studying steady state behavior of the inter-event times is equivalent to studying the existence of a conic subregion, which is a positively invariant set under the map that gives the evolution of the state from one event to the next. We provide a sufficient condition for the existence of a special kind of positively invariant subregion called positively invariant ray. We also provide necessary and sufficient conditions for a positively invariant ray to be asymptotically stable. We also explore the existence of positively invariant subregions that do not include a positively invariant ray. We illustrate the proposed method of analysis and analytical results through numerical simulations. My research plans for the final year of my Ph. D. include the co-design of a controller and an event-triggering rule by using a reinforcement learning based approach to maximize the asymptotic average inter-event times.
Contributions to CNI during the academic year August 2021 – July 2022 • Volunteer for organizing CNI network seminar series