Adaptive Model Predictive Control for Constrained Time Variying Systems

An approach to design feedback controllers for discrete-time, uncertain, linear time-varying systems subject to constraints is proposed. Building on previous contributions in the framework of time-invariant systems, in each sampling period a two-step procedure is carried out. In the first step, a set of linear models that are consistent with past input-output data and prior assumptions is built and refined. This set is guaranteed to contain also the true system dynamics if the considered working assumptions are valid. The time-varying nature of the plant is captured by assuming known bounds on the rate of change of the model parameters in time. In the second step, a robust finite-horizon optimal control problem is formulated and solved. The resulting optimal control sequence guarantees that the outputs of all possible plants inside the model set satisfy the operational constraints. The approach is showcased in numerical simulations on a three-tank system.