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The role of sampling for stability and performance in unconstrained nonlinear model predictive control. (English) Zbl 1292.93061

Summary: We investigate the impact of sampling on stability and performance estimates in nonlinear model predictive control without stabilizing terminal constraints or costs. Interpreting the sampling period as a discretization parameter, the relation between continuous and discrete time estimates depending on this parameter is analyzed. The technique presented in this paper allows us to determine the sampling rate required in order to approximate the continuous time suboptimality bound arbitrarily well and, thus, gives insight into the trade-off between sampling time and guaranteed performance.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93C10 Nonlinear systems in control theory
93C20 Control/observation systems governed by partial differential equations
93C57 Sampled-data control/observation systems
93B05 Controllability
93D15 Stabilization of systems by feedback
93D20 Asymptotic stability in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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