Resource-Aware State-Triggered Networked Control Systems

Abstract

State-triggered control is a popular control method in the field of networked control systems owing to its advantage of efficient utilization of resources while simultaneously achieving control objectives. In this control method, the communication times are op portunistic and implicitly determined by a triggering rule. In addition, state-triggered control can be designed with provable guarantees for a variety of systems, including non linear systems, distributed systems and multi-agent systems, and for a variety of control objectives, such as stabilization, filtering, trajectory tracking, multi-agent consensus and model predictive control. However, the question of how to theoretically analyze the resource usage by a state triggered control system is not well understood even in the simplest settings. Under standing inter-event times generated by a triggering rule is necessary for higher level planning and scheduling for control over shared or constrained resources as well as for the analytical quantification of the usage of communication or other resources compared to a time-triggered controller. This motivates the first part of the thesis, in which we provide a systematic way to analyze the evolution of inter-event times in planar linear systems, under a general class of scale-invariant event triggering rules. We provide a suf ficient condition for the convergence or non-convergence of inter-event times to a steady state value. We also provide a sufficient condition for the asymptotic average inter-event time to be a constant for all non-zero initial states of the system. Then, under a special case, we comment on the asymptotic behaviour of the inter-event times, including on whether the inter-event times converge to a periodic sequence. Later, we extend our analysis of inter-event times to linear systems under region-based self-triggered control. In this control method, the state space is partitioned into a finite number of conic regions and each region is associated with a fixed inter-event time. We provide several necessary conditions and sufficient conditions for the local convergence of inter-event times to a constant or to a given periodic sequence. In the second part of this thesis, we consider a design problem. Most of the exist ing event- or self-triggered controllers are designed using sampled-data zero-order-hold (ZOH) control input. However, many communication protocols used in networked con trol systems, such as TCP and UDP, have a minimum packet size. So, ZOH control may lead to under-utilization of each packet while also increasing the number of communi cation instances. On the other hand, use of non-ZOH control leads to better utilization of the minimum payload of each packet while also reducing the overall number of com munication instances. With these motivations, we propose a new control method called event-triggered parametrized control (ETPC). In this control method, between two con secutive events, each control input to the plant is a linear combination of a set of linearly independent scalar functions. At each event, the coefficients of the parameterized control input are chosen to minimize the error in approximating a continuous time control signal and then they are communicated to the actuator. We, first, showcase this method by focusing on the specific problem of stabilization of linear systems. We design two event triggering rules that guarantee global asymptotic stability of the origin of the closed loop system under some conditions on the model uncertainty. Later, we use a similar idea to propose an event-triggered polynomial control method for trajectory tracking by a unicycle robot and provide guarantees for uniform ultimate boundedness of the tracking error.