Degradation Tolerant Optimal Control Design for Stochastic Linear Systems

Safety-critical and mission-critical systems are often sensitive to functional degradation at the system or component level. Such degradation dynamics are often dependent on system usage (or control input), and may lead to significant losses and a potential system failure. Therefore, it becomes imperative to develop control designs that are able to ensure system stability and performance whilst mitigating the effects of incipient degradation by modulating the control input appropriately. In this context, this paper proposes a novel approach based on an optimal control theory framework wherein the degradation state of the system is considered in the augmented system model and estimated using sensor measurements. Further, it is incorporated within the optimal control paradigm leading to a control law that results in deceleration of the degradation rate at the cost of system performance whilst ensuring system stability. To that end, the speed of degradation and the state of the system in discrete time are considered to develop a linear quadratic tracker (LQT) and regulator (LQR) over a finite horizon in a mathematically rigorous manner. Simulation studies are performed to assess the proposed approach.