Graph Based Approach to Nonlinear Model Predictive Control with Application to Combustion Control and Flow Control

Systems with a priori unknown, and time-varying dynamic behavior pose a significant challenge in the field of Nonlinear Model Predictive Control (NMPC). When both the identification of the nonlinear system and the optimization of control inputs are done robustly and efficiently, NMPC may be applied to control such systems. This dissertation presents a novel method for adaptive NMPC, called Adaptive Sampling Based Model Predictive Control (SBMPC), that combines a radial basis function neural network identification algorithm with a nonlinear optimization method based on graph search. Unlike other NMPC methods, it does not rely on linearizing the system or gradient based optimization. Instead, it discretizes the input space to the model via pseudo-random sampling and feeds the sampled inputs through the nonlinear model, producing a searchable graph. An optimal path is found using an efficient graph search method. Adaptive SBMPC is used in simulation to identify and control a simple plant with clearly visualized nonlinear dynamics. In these simulations, both fixed and time-varying dynamic systems are considered. Next, a power plant combustion simulation demonstrates successful control of a more realistic Multiple-Input Multiple-Output system. The simulated results are compared with an adaptive version of Neural GPC, an existing NMPC algorithm based on Netwon-Raphson optimization and a back propagation neural network model. When the cost function exhibits many local minima, Adaptive SBMPC is successful in finding a globally optimal solution while Neural GPC converges to a solution that is only locally optimal. Finally, an application to flow separation control is presented with experimental wind tunnel results. These results demonstrate real time feasibility, as the control updates are computed at 100 Hz, and highlight the robustness of Adaptive SBMPC to plant changes and the ability to adapt online. The experiments demonstrate separation control for a NACA 0025 airfoil with Reynolds Numbers ranging from 90,000 to 150,000 for both fixed and pitching (.33 deg/s) angles of attack.