Indirect adaptive control of a class of interconnected non-linear dynamical systems

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Abstract
We consider the class of interconnected non-linear dynamic systems suggested by the problem of longitudinal and lateral control of a platoon of vehicles on automated highways. After describing the physical setting from which the control problem arises, we propose a local indirect adaptive control scheme for this class of interconnected non-linear systems. Then, we establish that the proposed local adaptive control scheme is suitable for monotonically decreasing the magnitude of deviations of each dynamic system's state from its sink manifold provided that (a) the exogenous input is varying sufficiently slowly and (b) the parameter error is sufficiently small. As a consequence, these deviations are bounded with a bound independent of the number of subsystems in the interconnection.

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