Sliding Mode Approaches Considering Uncertainty for Reliable Control and Computation of Confidence Regions in State and Parameter Estimation
Robust control procedures are essential for a reliable functionality of technical applications. Therefore, firstly, the mathematical description of the system and, secondly, bounded as well as stochastic disturbances play a major role in control engineering. Bounded uncertainty occurs due to lack of knowledge about system parameters, manufacturing tolerances and measurement inaccuracy. Stochastic disturbances, namely process and measurement noise, play further a very important role in system dynamics. Both classes of uncertainty are considered in the presented control and estimation purposes by using interval arithmetics, where the estimator is necessary to reconstruct non-measurable system states. Interval representations of uncertain variables provide the possibility to stabilize dynamic (nonlinear) systems in a robust way. This is necessary because parameters and measured data are typically only known within given tolerance bounds. Therefore, this paper combines interval arithmetics with the advantages of sliding mode approaches for control and estimation of states and parameters taking into account also stochastic disturbances. The efficiency of these approaches is shown in terms of an application describing the longitudinal dynamics of a vehicle.
KeywordsSliding mode techniques Uncertainty Interval arithmetics
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