A Quantized State Systems Approach for Declarative Spacecraft Autonomy

Requirements for autonomous systems for the future will increase, requiring  more complex and independent systems. Model based methods such as Kalman  filtering techniques or Model Predictive Control (MPC) rely on an on-line model of the system that can be simulated on-line in faster than real-time. For complex models this is a significant challenge in implementing the mentioned methods, especially when the paradigm of modeling employed is that of hybrid systems where discrete and continuous dynamics co-exists.

The first objective of the PhD study is to design and implement an efficient software engine for on-line execution of models of non-linear hybrid systems. Contrary to traditional simulation/execution systems, where time is discrete, this engine operates on a quantised state-space where the update of states is determined by a projection onto the future points in time, where the trajectory enters a new region quantised interval. The design relies on theory developed by Bernard Zeigler and Ernesto Kofman. The designed engine executes models with expressivity similar to the definition of Hybrid systems by Michael S. Branicky.

The second objective is to develop declarative control methods for hybrid  plants including non-linear dynamics and multiple inputs and outputs. Declarative refers to a controller that will control the plant autonomously when provided with a plant model and a control objective. The solution uses Lyapunov functions to describe control objectives and the controller uses optimization theory to calculate a control signal that is locally optimal in the current region of the quantised system in terms of reducing the Lyapunov  function and avoiding system constraints encoded in the hybrid system formulation.

Example applications, which are demonstrated through simulation, are spacecraft supervisory control systems and trajectory control of autonomous underwater vehicles.