Real-time Predictive Control of Constrained Nonlinear Systems Using the IPA-SQP Approach.

Abstract

Model Predictive Control (MPC) is an effective control method that has been used for a diverse set of applications. Specifically, MPC for linear systems with quadratic cost functions is considered a mature technology. For nonlinear systems whose underlying dynamics are fast, however, the computational complexity of the numerical optimization has emerged as one of the main challenges in MPC applications.

An integrated perturbation analysis and sequential quadratic programming (IPA-SQP) algorithm has been developed to address the computational burden and to meet the real-time computation requirements in nonlinear MPC (NMPC). A parametric neighboring extremal (PNE) approach has also been developed. It provides a closed-form neighboring extremal (NE) solution for systems subject to initial state variation where a control sequence and a set of parameters are optimized.

Motivated by the effectiveness of the IPA-SQP and PNE approaches and by their possibilities of extending methodologically, this dissertation primarily focuses on development of methodological extension to the IPA-SQP and PNE approaches to deal with adaptive MPC (AMPC) and minimum-time MPC problems, respectively. An indirect AMPC algorithm is developed to effectively integrate adaptation and constrained dynamic optimization. The AMPC algorithm based on IPA-SQP facilitates fast updates of the control sequence when model parameters change. A methodological extension to the PNE approach has been developed for minimum-time MPC which is of interest due to its ability to improve robustness to model uncertainties and disturbances, satisfy constraints, and provide automatic control refinements near the target.

This dissertation also focuses on challenging real-time applications of the IPA-SQP algorithm. A novel optimization-based power management controller (PMC) is developed, analyzed, and tested on a physical test-bed platform with multiple power sources and loads. The development of model predictive controllers for spacecraft applications is also presented. A conventional linear quadratic MPC (LQ MPC) for spacecraft relative motion maneuvering is developed. The LQ MPC, however, does not enable the direct handling of nonlinear constraints. Hence the IPA-SQP MPC approach is applied to solve the NMPC problems arising in spacecraft relative motion maneuvers.