Robust and Multi-Objective Model Predictive Control Design for Nonlinear Systems

摘要

The multi-objective trade-off paradigm has become a very valuable design tool in engineering problems that have conflicting objectives. Recently, many control designers have worked on the design methods which satisfy multiple design specifications called multi-objective control design. However,the main challenge posed for the MPC design lies in the high computation load preventing its application to the fast dynamic system control in real-time. To meet this challenge, this thesis has proposed several methods covering nonlinear system modeling, on-line MPC design and multi-objective optimization. First, the thesis has proposed a robust MPC to control the shimmy vibration of the landing gear with probabilistic uncertainty. Then, an on-line MPC method has been proposed for image-based visual servoing control of a 6 DOF Denso robot. Finally, a multi-objective MPC has been introduced to allow the designers consider multiple objectives in MPC design.
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\nIn this thesis, Tensor Product (TP) model transformation as a powerful tool in the modeling of the complex nonlinear systems is used to find the linear parameter-varying (LPV) models of the nonlinear systems. Higher-order singular value decomposition (HOSVD) technique is used to obtain a minimal order of the model tensor. Furthermore, to design a robust MPC for nonlinear systems in the presence of uncertainties which degrades the system performance and can lead to instability, we consider the parameters of the nonlinear systems with probabilistic uncertainties in the modeling using TP transformation. In this thesis, a computationally efficient methods for MPC design of image-based visual servoing, i.e. a fast dynamic system has been proposed. The controller is designed considering the robotic visual servoing system's input and output constraints, such as robot physical limitations and visibility constraints.
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\nThe main contributions of this thesis are: (i) design MPC for nonlinear systems with probabilistic uncertainties that guarantees robust stability and performance of the systems; (ii) develop a real-time MPC method for a fast dynamical system; (iii) to propose a new multi-objective MPC for nonlinear systems using game theory. A diverse range of systems with nonlinearities and uncertainties including landing gear system, 6 DOF Denso robot are studied in this thesis. The simulation and real-time experimental results are presented and discussed in this thesis to verify the effectiveness of the proposed methods.