International Journal of applied mathematics and computer science

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Paper details

Number 4 - December 2019
Volume 29 - 2019

Fundamental limitations of the decay of generalized energy in controlled (discrete-time) nonlinear systems subject to state and input constraints

István Selek, Enso Ikonen

This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system’s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.

decay rate maximization, Lyapunov function, nonlinear control systems