Solving a reliability-performance balancing problem for control systems with degrading actuators under model predictive control framework

In this paper, we formulate and study a reliability-performance balancing problem (RPBP) for long-term operational and unattended control systems with degrading actuators. It preliminarily explores a new type of autonomous maintenance method to extend the useful lifetime of the control system. The actuator, as the crucial component of a control system, executes calculated control actions and thereby is often exposed to the high-load working environment. As the actuator degrades, the control action will gradually alter with increasing magnitude to maintain the desired control performance, but this will accelerate the actuator degradation and thus reduce the useful lifetime (use reliability) of the control system. Therefore, conditionally balancing the control performance and use reliability is meaningful, for which a novel dynamic regulation strategy under the model predictive control (MPC) framework is proposed. Specifically, we model the actuator degradation using a diffusion Wiener process coupled with the control action or system state, and the corresponding actuator reliability is derived. By fusing the degradation model and system dynamics, a degradation-incorporated state space (DISS) model is formulated, in which the basic idea is to consider the actuator degradation as an extended state variable and to control it accordingly. Based on the DISS model, a mixed-index nonlinear MPC integrated with a weight tuning strategy is proposed to achieve a satisfactory balance between control performance and use reliability in the presence of actuator degradation. Further, the reference curve and the upper bound of actuator degradation are given for constructing the objective function and the constraint in the MPC optimization problem. An illustrative example is presented to demonstrate the availability of the proposed method.