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 |