Constraint-softening in model predictive control with off-line-optimized admissible sets for systems with additive and multiplicative disturbances

An approach to the softening of constraints is explored for a class of MPC algorithms that employ off-line-computed constraint-admissible sets for simplified on-line computations. The proposed approach relies on the use of exact penalty functions to ensure that the solution coincides with the actual optimal solution if the original MPC problem is feasible and that there are constraint violations at minimum possible levels if the original problem is infeasible. The approach is implemented for a class of linear systems with additive and multiplicative disturbances using a dynamic-policy-based MPC algorithm. Results specific to the cases of non-stochastic and stochastic disturbances are explored and assessed with simulation examples.