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Achieving a large domain of attraction with short-horizon linear MPC via polyhedral Lyapunov functions


S. Grammatico, G. Pannocchia

European Control Conference (ECC), Zurich, Switzerland

Polyhedral control Lyapunov functions (PCLFs) are exploited in this paper to propose a linear model predictive control (MPC) formulation that guarantees a “large” domain of attraction (DoA) even for short horizon. In particular, the terminal region of the proposed finite-horizon MPC formulation is chosen as a level set of an appropriate PCLF. For small dimensional systems, this terminal region can be explicitly computed as an arbitrarily close approximation to the entire (infinite-horizon) stabilizable set. Global stability of the origin is guaranteed by using an “inflated” PCLF as terminal cost. The proposed MPC scheme can be formulated as a (small dimensional) quadratic programming problem by introducing one additional scalar variable. Numerical examples show the main benefits and achievements of the proposed formulation in terms of trade-off between volume of the DoA, computational time and closed-loop performance.


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% Autogenerated BibTeX entry
@InProceedings { GraPan:2013:IFA_4386,
    author={S. Grammatico and G. Pannocchia},
    title={{Achieving a large domain of attraction with short-horizon
	  linear MPC via polyhedral Lyapunov functions}},
    booktitle={European Control Conference (ECC)},
    address={Zurich, Switzerland},
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