Risk prediction and its use for control of constrained systems with disturbances

In this paper, we consider a class of systems with measured (but unknown in advance) disturbances that can be operated in two modes. The first mode is a nominal mode in which the system has high efficiency and performance but in which the constraint violation is more likely. The second mode is the safe mode in which the performance/efficiency is lower but the constraint violation is less likely. For such systems approaches for predicting the risk of constraint violation based on linear and nonlinear discrete-time system models and disturbance scenarios based on steps and fluctuation near a constant values are described. Two examples of a mass spring damper system (linear system) and of an engine (nonlinear system) are presented in which the risk calculation is exploited to define the logic for activating the safe mode. Simulation results are reported.