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

Event-Triggered Observers and Observer-Based Controllers for a Class of Nonlinear Systems

In this paper, we investigate the stabilization of a nonlinear plant subject to network constraints, under the assumption of partial knowledge of the plant state. The event triggered paradigm is used for the observation and the control of the system. Necessary conditions, making use of the ISS property, are given to guarantee the existence of a triggering mechanism, leading to asymptotic convergence of the observer and system states. The proposed triggering mechanism is illustrated in the stabilization of a robot with a flexible link robot.Comment: Proceedings of the 2015 American Control Conference - ACC 201

Input to State Stability of Bipedal Walking Robots: Application to DURUS

Bipedal robots are a prime example of systems which exhibit highly nonlinear dynamics, underactuation, and undergo complex dissipative impacts. This paper discusses methods used to overcome a wide variety of uncertainties, with the end result being stable bipedal walking. The principal contribution of this paper is to establish sufficiency conditions for yielding input to state stable (ISS) hybrid periodic orbits, i.e., stable walking gaits under model-based and phase-based uncertainties. In particular, it will be shown formally that exponential input to state stabilization (e-ISS) of the continuous dynamics, and hybrid invariance conditions are enough to realize stable walking in the 23-DOF bipedal robot DURUS. This main result will be supported through successful and sustained walking of the bipedal robot DURUS in a laboratory environment.Comment: 16 pages, 10 figure