Min-Max Robust Control in LQ-Differential Games

Jacob Engwerda

Dynamic Games and Applications, 2022, vol. 12, issue 4, No 10, 1279 pages

Abstract: Abstract In this paper, we consider the design of equilibrium linear feedback control policies in an uncertain process (e.g., an economy) affected by either one or more players. We consider a process which nominal (commonly believed) development in time is described by a linear system. Assuming every player is risk averse and has his own expectation about a worst-case development of the nominal process we model this problem using a linear quadratic differential game framework. Conditions under which equilibrium policies exist are studied. Assuming players have an infinite planning horizon, we provide a complete description in case the system is scalar, whereas for the multi-variable case, we provide existence results for some important classes of systems.

Keywords: Linear quadratic differential games; Linear feedback Nash equilibria; Coupled algebraic Riccati equations; Deterministic uncertainty (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13235-021-00421-z

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