Computational strategies for nonlinear model predictive control.

摘要

The primary purpose of this study is to develop a computationally efficient, numerically robust method for implementing model predictive control in real-time using nonlinear models. In addition to developing the algorithmic framework for the solution of these on-line optimization problems, the key differences between nonlinear and linear dynamic models are delineated in the context of optimization and closed-loop performance. A secondary goal of this research is to develop a freely available software package that incorporates the ideas of this work, as well as several relevant nonlinear models for benchmarking purposes.; The work presented in this thesis advocates a regulator without a terminal constraint, but with a terminal penalty based on the linear quadratic regulator at the target. The regulator is able to stabilize many difficult nonlinear examples.; Moving horizon estimation is used to estimate states from a history of input and output data. This strategy is shown to converge to the true state of the plant even when the current industrial standard, the extended Kalman filter, fails. Further, an approximate smoothing covariance is developed for nonlinear models that removes the periodic behavior of the filtering covariance update.; Both the regulator and state estimator employ specially tailored sequential quadratic programming algorithms to efficiently solve their respective nonlinear programs. The feasibility-perturbed SQP (FP-SQP) algorithm is introduced, which has the property of maintaining feasibility with respect to the state evolution equation and hard constraints at every iteration. The solution of the quadratic programs at each iteration is performed by a structured solver that scales linearly with horizon length, rather than cubically. The presented nonlinear programming method is demonstrated to be faster and more efficient than standard commercial software.; The closed-loop behavior of the nonlinear model predictive control system is investigated using the regulator, the estimator, and a nonlinear target calculation. Insight into the stability of disturbance models is gained, and superior performance to linear control is documented. Further, local minima are demonstrated for both the regulator and estimator. These minima may be avoided by shortening the horizon in the regulator, or by applying constraints in the estimator.