Abstract-In robust model predictive control (MPC), modeling errors and disturbances are assumed to be unknown-butbounded quantities and the performance index is minimized with respect to the worst-case realization of the uncertainty (min-max approach). Instead, in stochastic MPC it is assumed that the underlying uncertainty is a random vector following some probability distribution. However, not always can the probability distribution be accurately estimated from available data, nor does it remain constant in time. Using the theory of risk measures, which originated in the field of stochastic finance, we seek to transcend the limitations of robust and stochastic optimal control by proposing a unifying framework that extends and contains both as special cases. We propose risk-averse formulations where the total cost of the MPC problem is expressed as a nested composition of conditional risk mappings. We focus on constrained nonlinear Markovian switching systems and draw parallels between dynamic programming and system theoretic properties to derive Lyapunovtype risk-averse stability conditions. Last, we cast the resulting risk-averse optimal control problem as a second-order cone program which can be solved efficiently.
In REF the authors provide a synthesis methodology for risk-averse MPC controllers for constrained nonlinear Markovian switching systems.
Risk-averse model predictive control
Automatica, vol. 100, pp. 281-288, Feb 2019
Mathematics Computer Science