In this paper, we consider the case when implementing a proportional-integral-derivative (PID) controller in the presence of non-periodic and intermittent sensor measurements. Current PID control design methods cannot accurately handle the case when the measurements arrive at isolated and potentially non-periodic time instants. We model the continuous-time plant being control, the impulsive measurement updates and the PID control law adapted to handle the measurement structure using a hybrid systems framework. By way of Lyapunov stability analysis for hybrid systems, we given sufficient conditions and a computationally tractable design method for the PID controller. We conclude by illustrating the results through numerical examples.

Effective attitude control is a key component of any Unmanned Aerial System (UAS).Typical PID based control operates on the euler angle representation of attitude. This representation is susceptible to the issue of gimbal lock – a phenomenon in which the rotation axes of a three-axis system align, causing a loss of one degree of freedom and potential loss of orientation information. Moreover, PID based attitude control of UAS’s suffer from the drawbacks associated with typical linear controllers. Namely, an ability to reliably control the system when not near the point of equilibrium. This thesis will cover an attitude control implementation directly on the Special Orthogonal group, SO(3), where neither of the aforementioned issues exist. This controller is implemented in both simulation and on hardware.

This dissertation focuses on developing tools for certifying temporal logic properties in hybrid dynamical systems that combine continuous and discrete dynamics. In particular, operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems are presented. Hybrid dynamical systems are given in terms of differential inclusions -- capturing the continuous dynamics -- and difference inclusions -- capturing the discrete dynamics or events -- with constraints. State trajectories (or solutions) to such systems are parameterized by a hybrid notion of time. Characterizations of temporal logic formulas in terms of dynamical properties of hybrid systems are presented -- in particular, forward invariance, conditional invariance, and finite time attractivity. These characterizations are exploited to formulate sufficient conditions assuring the satisfaction of temporal logic formulas --- when possible, these conditions do not involve solution information. Notions for specifying dynamical properties of systems with robustness to perturbations are proposed. Characterizations of basic signal temporal logic formulas are presented. Combining the results for formulas with a single operator, ways to certify more complex formulas are pointed out, in particular, via a decomposition using a finite state automaton. An object grasping application and academic examples are given to illustrate the results.