Carleman Linearization-based Nonlinear Model Predictive Control

Open Access
Fang, Yizhou
Graduate Program:
Chemical Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
August 13, 2015
Committee Members:
  • Antonios Armaou, Thesis Advisor
  • Process Control
  • Model Predictive Control
The need of tight operating conditions in chemical, pharmaceutical, and petroleum industries has given rise to the development of advanced process control. Model Predictive Control (MPC) started gaining attention three decades ago for optimal transitions between operating modes. Nonlinear MPC converts a constrained control problem of a nonlinear system into an optimization problem. This basic architecture makes Nonlinear MPC capable of handling large state-space multi-variable systems with constraints, and dealing with model-mismatches and disturbances readily. The computation time of control policy is required to be less than one sampling time for online operation. However, this requirement is most of the times impossible to meet when the system has high nonlinearity. That becomes one of the most significant reasons holding back the application of Nonlinear MPC. As a result, there is strong motivation to develop an advanced formulation of Nonlinear MPC that demands less computational effort and thus decides the control actions faster. The primary focus of this thesis is to develop an advanced formulation of Nonlinear MPC that decreases the amount of computational effort in order to circumvent feedback delay, to improve controller performance and to maintain stability of the system. Multiple mathematics tools combined with optimization techniques are implemented for the purpose of accelerated searching algorithms. The optimal control problem is formulated as a receding horizon one. An optimization problem is solved at each time the finite horizon moves on. Based on Carleman Linearization, the states of the system are extended to higher orders following the Kronecker product rule. The nonlinear dynamic process can thus be modeled with a bilinear representation while keeping nonlinear dynamic information. It enables analytical anticipation of system states and provides the searching algorithm with analytically computed sensitivity of the cost function to the control signals. The proposed method resembles both collocation and shooting methods for the following reasons. First, the states of the system are discretized explicitly in time while the sensitivity of the control signals is computed analytically. Second, the states are nonlinear functions of the control signals, releasing the optimization problem from equality constraints and reducing the number of design variables. This thesis presents an introduction to MPC, Carleman Linearization and detailed derivations of the proposed method in Chapter 1 and 2. It also provides detailed description of resetting extended states to compensate for the simulation errors caused by Carleman Linearization as an independent Chapter 3. Chapter 4 presents case-study examples to indicate the applications of the proposed method. Chapter 5 concludes the work and future plans. A part of the work presented in this thesis has been published at American Control Conference, Chicago, IL on July 1st, 2015.