MPC Trajectory Feasibility Constraints for Self-Powered Control Systems

A self-powered control system derives the energy to power its operation entirely from the dynamics of the plant in which it is embedded. Each actuator is a transducer capable of injecting energy into, as well as removing energy from, the plant. Removed energy is stored for reuse in rechargeable energy storage subsystems. Control inputs are physically constrained by the requirement that the system does not exhaust these energy storage subsystems. This article analyzes model-predictive control (MPC) trajectory feasibility for self-powered control systems. Specifically, we examine the case in which the MPC algorithm formulates a discrete-time zero-order-hold control trajectory, for which the energy constraints are approximately enforced by using response information only at discrete sample times. It is shown that continuous-time control feasibility can be ensured by conservatively overbounding the transmission loss model. The analysis is conducted both for the case in which future disturbances are known deterministically and the case in which they are uncertain but bounded. The methodology is demonstrated on an example pertaining to vibration control.