Advances in Disjunctive and Time-Optimal Predictive Control Methods

Abstract

This dissertation addresses two kinds of problems. The first kind, Disjunctive Sensing and Control (DSC), is a particular variant of a hybrid control problem type that arose from a complication when working on a small satellite attitude control system in which the magnetic actuators and sensors could not function at the same time as magnetic actuation would inject unacceptable levels of sensor noise. The second class of problems involves time-optimal waypoint-following Model Predictive Control (MPC), inspired by missions such as fast-slewing imaging spacecraft, which must capture as many ground images as possible before their orbit and the Earth's rotation move the target out of line of sight. In this dissertation, novel approaches are developed to address each problem, and simulations are presented to illustrate their effectiveness. Specific contributions are as follows.

Firstly, the small satellite problem is analyzed in detail. The control goal is defined, the Equations of Motion are derived, the magnetic actuator/sensor conflict is described, and a Linear Quadratic Regulator control scheme is developed that alternates between actuation and estimation, allowing these conflicting subsystems to still successfully achieve the mission objective. The spacecraft configuration with the additional passive stabilization mechanism in the form of panels that induce restorative air drag torques is considered as well as the design of an MPC controller to handle actuation constraints.

Secondly, inspired by the satellite problem, the DSC problem is treated in detail. The two subsystems, i.e., the sensing and actuation subsystems, are assumed to be linked by a binary decision variable that activates either subsystem at the expense of the other. Contractivity sufficient conditions are derived which can facilitate the construction of periodic switching sequences that guarantee boundness and convergence properties of the closed-loop system trajectories and of the error covariance as well as the enforcement of chance constraints in steady-state. Additional methods are proposed to speed up the search for periodic sequences that satisfy the contractivity conditions. Spacecraft relative motion simulation case studies are reported to demonstrate the effectiveness of the technique.

Next, time-optimal waypoint-following MPC is considered for which a Mixed-Integer Linear Program (MILP) approach is proposed. The MILP formulation complements the ability of MPC-based controllers to explicitly handle state constraints. Several different scenarios are considered for spacecraft attitude control, including multiple waypoints, exclusion zones, and the addition of flexible mode states to the attitude dynamics. Simulation results are reported.

Finally, the non-uniqueness of the solution to the time-optimal MPC problem in the discrete-time setting is addressed and it is shown that it can lead to the loss of closed-loop Lyapunov stability. As a remedy, a secondary objective function is minimized after the optimal time horizon has been determined; this lexicographic optimization yields a unique solution which is shown to restore Lyapunov stability. Spacecraft relative motion simulation case studies are reported which illustrate closed-loop stability and robustness to unmeasured disturbances of the minimum-time MPC with the lexicographic optimization.