A quasi-min-max MPC algorithm for linear parameter varying systems with bounded rate of change of parameters

We (1999, 2000) have introduced a model predictive control (MPC) algorithm for polytopic linear parameter varying systems. The algorithm, called quasi-min-max MPC, separates the first stage cost from the infinite horizon quadratic objective function and bounds the rest of the cost by a quadratic term. For predictions the future state matrices are assumed to belong to a fixed polytope. In this paper it is assumed that the upper and lower bounds on the rate of change of the parameters are available. This allows the updating of the polytope for one time step in predictions and consequently the second stage cost can also be separated from the infinite horizon cost function. The modified quasi-min-max MPC can be solved by semi-definite programming and closed-loop stability is guaranteed when its feasible solutions are implemented in a receding horizon fashion. A numerical example demonstrates the superior performance of the new algorithm