Robust Optimal Control Design Using a Differential Game Approach for Open-Loop Linear Quadratic Descriptor Systems

Feedback saddle point equilibria for soft-constrained zero-sum linear quadratic descriptor differential game

“…HereJ ∞ γ denotes the upper value of the game (1,20). We also introduce the following algebraic Riccati equation corresponding to the Riccati differential equation 15A T 1…”

“…Next, we characterize FSP solutions for the infinite-horizon linear quadratic softconstrained differential game (1,20). One of the interesting questions in this situation is if (15) does not have a conjugate point on [0,t f ] for any t f and in case lim…”

“…[11]. Moreover, in optimal control theory it is well known that the issue to obtain robust control strategies to solve the disturbance attenuation problem can be approached as a dynamic game problem [1,16,3,20].…”

“…The general index case was studied in [26], where the theory of projector chains is used to decouple algebraic and differential parts of the descriptor system, and then the usual theory of ordinary differential games is applied to derive both necessary and sufficient conditions for the existence of feedback Nash equilibria for linear quadratic differential games. Moreover, the open-loop framework of soft-constrained descriptor differential game was studied in [20], also with its application in robust optimal control design.…”

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

“…Hence, by merging results obtained in [1] and [21], we will solve the robust optimal control problem for descriptor systems here. Further, [20] solved this problem for an open-loop information framework.…”