Robust constrained model predictive control

Abstract

(cont.) multiple Uninhabited Aerial Vehicles (UAVs) demonstrate that the new DMPC algorithm offers significant computational improvement compared to its centralized counterpart. The controllers developed in this thesis are demonstrated throughout in simulated examples related to vehicle control. Also, some of the controllers have been implemented on vehicle testbeds to verify their operation. The tools developed in this thesis improve the applicability of MPC to problems involving uncertainty and high complexity, for example, the control of a team of cooperating UAVs.

This thesis extends Model Predictive Control (MPC) for constrained linear systems subject to uncertainty, including persistent disturbances, estimation error and the effects of delay. Previous work has shown that feasibility and constraint satisfaction can be guaranteed by tightening the constraints in a suitable, monotonic sequence. This thesis extends that work in several ways, including more flexible constraint tightening, applied within the prediction horizon, and more general terminal constraints, applied to ensure feasible evolution beyond the horizon. These modifications reduce the conservatism associated with the constraint tightening approach. Modifications to account for estimation error, enabling output feedback control, are presented, and we show that the effects of time delay can be handled in a similar manner. A further extension combines robust MPC with a novel uncertainty estimation algorithm, providing an adaptive MPC that adjusts the optimization constraints to suit the level of uncertainty detected. This adaptive control replaces the need for accurate a priori knowledge of uncertainty bounds. An approximate algorithm is developed for the prediction of the closed-loop performance using the new robust MPC formulation, enabling rapid trade studies on the effect of controller parameters. The constraint tightening concept is applied to develop a novel algorithm for Decentralized MPC (DMPC) for teams of cooperating subsystems with coupled constraints. The centralized MPC optimization is divided into smaller subproblems, each solving for the future actions of a single subsystem. Each subproblem is solved only once per time step, without iteration, and is guaranteed to be feasible. Simulation examples involving