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Real-time Model Predictive Control


M.N. Zeilinger

ETH Zurich

The main theme of this thesis is the development of real-time and soft constrained Model Predictive Control (MPC) methods for linear systems, providing the essential properties of closed-loop feasibility and stability. MPC is a successful modern control technique that is characterized by its ability to control constrained systems. In practical implementations of MPC, computational requirements on storage space or online computation time have to be considered in the controller design. As a result, the optimal MPC control law can often not be implemented and a suboptimal solution has to be provided that is tailored to the system and hardware under consideration and meets the computational requirements. Existing methods generally sacrifice guarantees on constraint satisfaction and/or closed-loop stability in such a real-time environment. In addition, enforcing hard state constraints in an MPC approach can be overly conservative or even infeasible in the presence of disturbances. A solution commonly applied in practice is to relax some of the constraints by means of so-called soft constraints. Current soft constrained approaches for finite horizon MPC, however, do not provide a guarantee for closed-loop stability. This thesis addresses these limitations and aims at reducing the gap between theory and practice in MPC by making three main contributions: A real-time MPC method based on a combination of explicit approximation and online optimization that offers new tradeoff possibilities in order to satisfy limits on the storage space and the available computation time and provides hard real-time feasibility and stability guarantees; a real-time MPC approach that is based on online optimization and provides these properties for any time constraint while allowing for extremely fast computation; a soft constrained method based on a finite horizon MPC approach that guarantees closed-loop stability even for unstable systems. First, two methods are presented that consider the application of MPC to high-speed systems imposing a hard real-time constraint on the computation of the MPC control law. There are generally two main paradigms for the solution of an MPC problem: In online MPC the control action is obtained by executing an optimization online, while in explicit MPC the control action is pre-computed and stored offline. Limits on the storage space or the computation time have therefore restricted the applicability of MPC in many practical problems. This thesis introduces a new approach, combining the two viii Abstract paradigms of explicit and online MPC in order to overcome their individual limitations. The use of an offline approximation together with warm-start techniques from online optimization allows for a tradeoff between the warm-start and online computational effort. This offers new possibilities in satisfying system requirements on storage space and online computation time. A preprocessing analysis is introduced that provides hard real-time execution, stability and performance guarantees for the proposed controller and can be utilized to identify the best solution method for a considered application and set of requirements. By using explicit approximations, the first real-time approach is best suited for small or medium size problems. In contrast, the second real-time MPC approach presented in this thesis is solely based on online optimization and can be practically implemented and efficiently solved for large-scale dynamic systems. A hard real-time constraint generally prevents the computation of the optimal solution to the MPC problem, which can lead to constraint violation, and more importantly, instability when using a general optimization solver. The proposed method is based on a robust MPC scheme and recovers guarantees on feasibility and stability in the presence of additive disturbances for any given time constraint. The approach can be extended from regulation to tracking of piecewise constant references, which is required in many applications. All computational details needed for an implementation of a fast MPC method are provided and it is shown how the structure of the resulting optimization problem can be exploited in order to achieve computation times equal to, or faster than those reported for methods without guarantees. One of the main difficulties in real-time MPC methods is the initialization with a feasible solution. This motivates the investigation of soft constrained MPC schemes and their robust stability properties in the final part of this thesis. The relaxation of state and/or output constraints in a standard soft constrained approach generally leads to a loss of the stability guarantee in MPC, relying on the use of a terminal state constraint. In this thesis a new soft constrained MPC method is presented that provides closed-loop stability even for unstable systems. The proposed approach significantly enlarges the region of attraction and preserves the optimal behavior with respect to the hard constrained MPC control law whenever all constraints can be enforced. By relaxing state constraints, robust stability in the presence of additive disturbances can be provided with an enlarged region of attraction compared to a robustMPC approach considering the same disturbance size. In order to allow for a more flexible disturbance handling, the proposed soft constrained MPC scheme can be combined with a robust MPC framework and the theoretical results directly extend to the combined case.


Type of Publication:

(03)Ph.D. Thesis

M. Morari

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2011:IFA_3977,
    author={M.N. Zeilinger},
    title={{Real-time Model Predictive Control}},
    address={ETH Zurich},
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