Robust Equilibria in Indefinite Linear-Quadratic Differential Games

Abstract

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Disturbance attenuation problem using a differential game approach for feedback linear quadratic descriptor systems

“…Next, recall from, e.g., [8] that for all initial states in (1) there exists a smooth control that generates a smooth state trajectory if and only if (1) is impulse controllable 2 . Further, all impulsive modes of (1) can be transformed then into finite dynamic modes using static state feedback control.…”

“…Therefore, one of the biggest problems faced by a control designer is to design a controller that is capable to overcome various form of disturbances that might arise in the system [11]. One of the techniques to solve a disturbance attenuation problem uses a differential game approach [1], [2], and [14]. In this disturbance attenuation framework the control designer is the minimizing agent.…”

Bounded Nash type controls for uncertain linear systems

“…Injecting these two last expressions and the coupling conditions (16) into (19), inequalities (9) are satisfied.…”

“…Several approaches are proposed using Nash strategy to design robust controls for linear systems [14,8]. A way to treat uncertainty is to interpret perturbation as an exogenous input (a fictitious player) [7,19]. In [19], the definition of equilibria is ex-⋆ This paper was not presented at any IFAC meeting.…”

“…A way to treat uncertainty is to interpret perturbation as an exogenous input (a fictitious player) [7,19]. In [19], the definition of equilibria is ex-⋆ This paper was not presented at any IFAC meeting. Corresponding author M. Jungers.…”