Non-cooperative intelligent Control agents (ICAs) with dedicated cost functions, can lead the system to poor performance and in some cases, closed-loop instability. A robust solution to this challenge is to place the ICAs at the feedback Nash equilibrium point (FNEP) of the differential game between them. This paper introduces the designation of a robust decentralized infinite horizon LQR Control system based on the FNEP for a linear time-invariant system. For this purpose, two Control strategies are defined. The first one is a centralized infinite horizon LQR (CIHLQR) problem (i.e. a supervisory problem), and the second one is a decentralized Control problem (i.e. an infinite horizon linear-quadratic differential game). Then, while examining the optimal solution of each of the above strategies on the performance of the other, the necessary and sufficient conditions for the equivalence of the two problems are presented. In the absence of the conditions, by using the least-squares error criterion, an approximated CIHLQR Controller is presented. It is shown that the theorems could be extended from a two-agent Control system to a multi-agent system. Finally, the results are evaluated using the simulation results of a Two-Area non-reheat power system.

This article investigates the problem of simultaneous attitude and vibration Control of a flexible spacecraft to perform high precision attitude maneuvers and reduce vibrations caused by the flexible panel excitations in the presence of external disturbances, system uncertainties, and actuator faults. Adaptive integral sliding mode Control is used in conjunction with an attitude actuator fault iterative learning observer (based on sliding mode) to develop an active fault tolerant algorithm considering rigid-flexible body dynamic interactions. The discontinuous structure of fault-tolerant Control led to discontinuous commands in the Control signal, resulting in chattering. This issue was resolved by introducing an adaptive rule for the sliding surface. Furthermore, the utilization of the sign function in the iterative learning observer for estimating actuator faults has not only enhanced its robustness to external disturbances through a straightforward design, but has also led to a decrease in computing workload. The strain rate feedback Control algorithm has been employed with the use of piezoelectric sensor/actuator patches to minimize residual vibrations caused by rigid-flexible body dynamic interactions and the effect of attitude actuator faults. Lyapunov's law ensures finite-time overall system stability even with fully coupled rigid-flexible nonlinear dynamics. Numerical simulations demonstrate the performance and advantages of the proposed system compared to other conventional approaches.

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