Robust Tube MPC Using Gain-Scheduled Policies for a Class of LPV Systems

This letter presents a method for robust model predictive control (MPC) of linear parameter varying (LPV) systems considering control policies that are affine functions of the parameter, which is possible when only the ‘A’ and not the ‘B’ matrix depends on the uncertain parameter (LPV-A systems). This is less conservative than formulations in which the policy is restricted to perturbations on a feedback law, as it includes such policies as a special case. State and input constraints are handled efficiently by bounding predicted states in a sequence of polyhedra (i.e., tube MPC), that are parameterised by variables in the online optimisation. The resulting controller can be implemented by online solution of a single quadratic programming problem and can exploit rate bounds on the LPV parameters, which requires a pre-processing step at each iteration. Recursive feasibility and exponential stability are proven and the approach is compared to existing methods in numerical examples drawn from other publications, showing reduced conservatism and improved regions of attraction.