On invariant ellipsoids for discrete-time systems by saturated optimal controls

Journal of Control Theory and Applications 10/2008; 6(4):415-420. DOI: 10.1007/s11768-008-7077-z


Analytical approximation of the maximal invariant ellipsoid for discrete-time linear systems with saturated optimal control
is established, which is less conservative than existing computationally un-intensive results. Simultaneously, necessary and
sufficient conditions for such approximation being equal to the real maximal invariant ellipsoid is presented. All results
are given analytically and can easily be implemented in practice. An illustrative example is given to show the effectiveness
of the proposed approach.

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    • "Equation (5) gives the radius of the invariant ellipsoid ε(P i , δ i ). The proof of (5) is given in [17], [20], [24], [25]. It is evident from (5), that with different input node (driver node) acting independently, the matrices P i and B i will change and this subsequently changes δ i and corresponding region of attraction. "
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    ABSTRACT: A network of discrete-time agents (nodes) which can be controlled by different nodes, acting independently, is considered. When a network can be controlled through several nodes, it is important to understand differences in choosing a particular node as driver node (node which control the entire network). This work considers limited actuator amplitude of driver node and characterizes driver node based on Region of Attraction (ROA) obtained corresponding to a particular chosen driver node. The presented theory and algorithms enable to find an appropriate node such that Region of Attraction maximizes. Theoretical developments are verified through numerical simulation.
    Proceedings of the 14th European Control Conference 2015 (ECC 2015), Linz, Austria, 15-17 July, 2015; 07/2015