CONTROLLER SYNTHESIS UNDER INFORMATION AND FINITE-TIME LOGICAL CONSTRAINTS

Abstract

In robotics, networks, and many related fields, a typical controller design problem needs to address both logical and informational constraints. The logical constraints may arise due to the complex task description or decision making process, while the information-related constraints emerge naturally as a consequence of the limitations on communication and computation capabilities.

In the first part of the thesis, we consider the problem of synthesizing an event-based controller to address the information-related constraints in the controller design. We consider dynamical systems that are operating under continuous state feedback. This assumes that the measurements are continuously transmitted to the controller in order to generate the input and thus, increases the cost of communication by requiring huge communication resources. In many situations, it so happens that the measurement does not change fast enough that continuous transmission is required. Taking motivation from this, we consider the case where instead continuous feedback we seek an intermittent-feedback. As a result, the system trajectory will deviate from its ideal behavior. However, the question is how much would it deviate? Given the allowed bound on this deviation, can we design some controller that requires fewer measurements than the original controller and still manages to keep the deviation within this prescribed bound? Two important questions remain: 1) What will be the structure of the (optimal) controller? 2) How will the system know the (optimal) instances to transmit the measurement? When the system sends out measurement to controller, it is called as an ``event". Thus, we are looking for an event-generator and a controller to perform event-based control under the constraints on the availability of the state information.

The next part focuses on controller synthesis problems that have logical, spatio-temporal constraints on the trajectory of the system; a robot motion planning problem fits as a good example of these kind of finite-time logically constrained problems. We adopt an automata-based approach to abstract the motion of the robot into an automata, and verify the satisfaction of the logical constraints on this automata. The abstraction of the dynamics of the robot into an automata is based on certain reachability guarantee of the robot's dynamics. The controller synthesis problem over the abstracted automata can be represented as a shortest-path-problem.

In part III, we consider the problem of jointly addressing the logical and information constraints. The problem is approached with the notion of robustness of logical constraints.

We propose two different frameworks for this problem with two different notions of robustness and two different approaches for the controller synthesis. One framework relies on the abstraction of the dynamical systems into a finite transition system, whereas the other relies on tools and results from prescribed performance control to design continuous feedback control to satisfy the robust logical constraints. We adopt an hierarchical controller synthesis method where a continuous feedback controller is designed to satisfy the (robust) logical constraints, and later, that controller is replaced by a suitable event-triggered intermittent feedback controller to cope with informational constraints.