Utility Driven Sampled Data Control Under Imperfect Information

Computer based control systems, which are ubiquitous today, are essentially sampled data control systems. In the traditional time-triggered control systems, the sampling period is conservatively chosen, based on a worst case analysis. However, in many control systems, such as those implemented on embedded computers or over a network, parsimonious sampling and computation is helpful. In this context, state/data based aperiodic utility driven sampled data control systems are a promising alternative. This dissertation is concerned with the design of utility driven event-triggers in certain classes of problems where the information available to the triggering mechanisms is imperfect. In the first part, the problem of utility driven event-triggering under partial state information is considered - specifically in the context of (i) decentralized sensing and (ii) dynamic output feedback control. In the case of full state feedback, albeit with decentralized sensing, methods are developed for designing local and asynchronous event-triggers for asymptotic stabilization of an equilibrium point of a general nonlinear system. In the special case of Linear Time Invariant (LTI) systems, the developed method also holds for dynamic output feedback control, which extends naturally to control over Sensor-Controller-Actuator Networks (SCAN), wherein even the controller is decentralized. The second direction that is pursued in this dissertation is that of parsimonious utility driven sampling not only in time but also in space. A methodology of co-designing an event-trigger and a quantizer of the sampled data controller is developed. Effectively, the proposed methodology provides a discrete-event controller for asymptotic stabilization of an equilibrium point of a general continuous-time nonlinear system. In the last part, a method is proposed for designing utility driven event-triggers for the problem of trajectory tracking in general nonlinear systems, where the source of imperfect information is the exogenous reference inputs. Then, specifically in the context of robotic manipulators we develop utility driven sampled data implementation of an adaptive controller for trajectory tracking, wherein imperfect knowledge of system parameters is an added complication

On Asymptotic Behavior of Inter-Event Times in Planar Systems under Event-Triggered Control

This paper analyzes the asymptotic behavior of inter-event times in planar linear systems, under event-triggered control with a general 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 inter-event times by studying the fixed points of the ``angle'' map, which represents the evolution of the ``angle'' of the state from one event to the next. We provide a sufficient condition for the convergence or non-convergence of inter-event times to a steady state value under a scale-invariant event-triggering rule. With the help of ergodic theory, we 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, 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 the ``angle'' of the initial state of the system. We illustrate the proposed results through numerical simulations.Comment: The previous version of the paper now has been split into two separate papers, one on event-triggered control and one on self-triggered control. The updated part on self-triggered control may be accessed at arXiv:2212.1427