An adaptive constraint tightening approach to linear MPC based on approximation algorithms for optimization

In this paper we propose a model predictive control scheme fo r discrete-time linear invariant systems based on inexact numerical optimization algorithms. We assume th at e solution of the associated quadratic program produced by some numerical algorithm is possibly ne ither optimal nor feasible, but the algorithm is able to provide estimates on primal suboptimality and prima l fe sibility violation. By adaptively tightening the complicating constraints we can ensure the primal feasi bility of the approximate solutions generated by the algorithm. We derive a control strategy that has the foll owing properties: the constraints on the states and inputs are satisfied, asymptotic stability of the closed -loop system is guaranteed, and the number of iterations needed for a desired level of suboptimality can b e determined. The proposed method is illustrated using a simulated longitudinal flight control problem. Copy right c © 2013 John Wiley & Sons, Ltd.

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