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A fixed-point iteration scheme for real-time model predictive control. (English) Zbl 1246.93042
Summary: A simple model predictive control (MPC) concept for nonlinear systems under input constraints is considered. The presented algorithm takes advantage of an MPC formulation without terminal constraints in order to solve the optimality conditions by a fixed-point iteration scheme that is easy to implement and of algorithmic simplicity. Sufficient conditions for the contraction of the fixed-point iterations are derived. To allow for a real-time implementation within an MPC scheme, a constant number of fixed-point iterations is used in each sampling step and sufficient conditions for asymptotic stability and incremental reduction of the suboptimality are presented.

MSC:
93B40 Computational methods in systems theory (MSC2010)
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
93D20 Asymptotic stability in control theory
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