Enhanced Numerical Methods for Constrained Nonlinear Model Predictive Control

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

This research project will create new, rigorously grounded, methods for computationally efficient model predictive control. Model predictive control is based on computing system control inputs in response to sensor measurements through the use of real-time numerical optimization. It has proved invaluable in many important applications, including in the aerospace and automotive industries. Computational challenges stem from the need to optimize in real-time the response of large systems of constrained nonlinear dynamic equations in the presence of modeling errors and unpredictable disturbances. There are major difficulties in applying model predictive control to complex engineering systems, particularly when on-board computing power is limited. The most effective ways to address these challenges exploit problem-specific structure, in contrast to a "one size fits all" strategy. This project will produce classes of computationally efficient solution methods that can be appropriately tailored to specific problem characteristics. The developed theory and methods will be applied to control problems for automotive engines and aircraft propulsion systems, to address stringent performance requirements, growing system complexity, and numerous constraints. The implications for spacecraft orbital control will also be pursued to enable model predictive control solutions which expand spacecraft autonomy and resiliency. Project personnel will build on illustrations from automobile and aircraft engines and spacecraft missions to amplify STEM outreach efforts to local high school students from underrepresented groups. The aim of this research project is to develop advanced methods for reducing the computational cost of solving nonlinear model predictive control problems, while maintaining acceptable accuracy. Both a theoretical justification of these methods and their efficient algorithmic implementation will be pursued. Inexact sequential quadratic programming-type methods for solving variational inequalities/inclusions associated with appropriate necessary conditions for optimality will be developed. Some of these methods will compute derivatives just at the starting point or at some selected iterations, while others will utilize inexact Newton iterations. The interplay between cost functions, constraints, closed-loop stability and performance will be studied in the context of these kind of implementations. In addition, novel computational and constraint handling strategies will be developed based on the analysis of Lipschitz stability and sensitivity of nonlinear model predictive control problems considered. Theoretically justified approaches to both offline and online constraint transformations will also be developed as another general pathway to obtain computational simplifications based on sensitivity analysis. Homotopy procedures supplied with error analysis will be applied to achieve efficient computation of model predictive control solutions.