Handling State and Output Constraints in MPC Using Time-dependent Weights

On the design of exact penalty functions for MPC using mixed integer programming

“…In Hovd and Braatz (2001a) it was shown how to minimize this problem by using time-dependent weights in the optimization criterion.…”

“…Nevertheless, such constraints may introduce many complexities that an industrial MPC controller needs to address. There has been particular focus on the effect of hard output constraints on stability (Zafiriou & Marchal, 1991;de Oliveira & Biegler, 1994) as well as the use of soft constraint formulations to ensure a feasible optimization problem, see Scokaert and Rawlings (1999), Vada (2000), Hovd and Braatz (2001a) and references therein. This paper advances the ideas shown in Hovd (2011).…”

Stochastic model predictive control with joint chance constraints

“…Note that it is desired for the softconstrained optimal control problem to yield the same solution as the original hard-constrained problem when the latter is feasible. This can be achieved using the exact penalty function method (e.g., see [27,28,29,30] and the references therein for details). …”

“…Another practical method for a priori selecting ρ is to choose ρ as large as possible such that numerical issues do not occur when solving (28). The idea is that at some point ρ max < ∞, the weight will be so large that changes in the original value function are not numerically discernible in the optimizer.…”

Adaptive Control for Systems with Output Constraints Using an Online Optimization Method

“…However, when systems demonstrate non-minimum phase characteristics, constraint softening methods may have reduced performance. An extension of constraint softening which also employs time-dependent weightings on the objective functions to improve controller performance is found in [13]. However, these methods do not sufficiently consider the effects of unknown disturbances and/or uncertainties which are often present in complex systems.…”