On-line Tuning of Controllers for Systems with Constraints

Model Predictive Control (MPC) is traditionally applied to slow processes. Recently, an explicit solution to MPC was introduced, offering a possibility to extend the area of application to high-bandwidth processes. One of the main drawbacks of the explicit form of MPC is the loss of flexibility to adjust the objective of the controller on-line. We address this issue for constrained time-invariant discrete-time linear systems by defining a parameterized cost function based on piecewise linear norms. An explicit solution to MPC is obtained by solving a more general formulation of a multi-parametric linear program (mpLP), where both the cost and the constraints are parameter dependent. This fully parameterized explicit solution enables a re-adjustment of the parameters of the cost during the controller operation, without need for recomputation of the explicit solution. Furthermore, we show that the properties of the solution for the specific problem setup make stability analysis for a range of control parameters straightforward, providing bounds on the tunable parameters of the cost for which invariance and stability of the closed-loop system are preserved.