Practical Model Predictive Control for Nonlinear/Time-varying Systems Using Linear-Parameter Varying Models

The model predictive control (MPC) paradigm offers a unique ability to control constrained nonlinear (NL) and time-varying (TV) systems by solving a constrained NL optimization problem in each sampling interval based on future predictions of the system's behavior. However, to achieve a desired level of performance with a reasonable computational cost, an appropriate formulation of the MPC problem for NL/TV systems is necessary. Linear parameter-varying (LPV) systems provide a modeling framework for describing efficiently NL/TV systems in a linear setting via a so-called scheduling parameter, which is assumed available only at the current time instant. The strength of the LPVMPC approach lies in its ability to employ the linear MPC tools for controlling NL/TV systems. However, existing techniques have not yet exploited its full potentials to compromise the achievable control performance and the computational complexity. Its main difficulty is to properly handle the uncertainty of the future evolution of the scheduling parameter. During the first phase of this project a range of novel LPVMPC algorithms have been developed for controlling NL/TV systems with a reasonable computational burden, where the required future values of the scheduling parameter were treated according to given bounds on its rate of variation. However, the application of these algorithms to real systems have revealed two important issues: (1) The degradation of performance when long prediction horizons are considered without providing additional information about the future values of the scheduling parameter, and (2) the difficulties of establishing the recursive feasibility and stability properties when systems with high number of scheduling parameters are considered. Therefore, the first goal of this renewal project for enabling high performance LPVMPC is to anticipate the required future values of the scheduling parameter and incorporate them into the LPVMPC problem. For this purpose, we will adopt analytical and data-driven approaches based on advanced machine learning tools. Thus, deterministic, and stochastic MPC frameworks will be investigated. The second goal of the project is for establishing the control theoretic properties of the LPVMPC when highly complex LPV models are considered. We will overcome the associated computational complexity by employing equivalent/approximate LPV models with reduced number of scheduling parameters. When approximate models are considered, we will further analyze the validity of the chieved properties for the related full models and reformulate the LPVMPC design accordingly. Moreover, to employ the developed techniques for practical use, we will extend them to accommodate reference tracking and additive uncertainty problems. The developed techniques will be validated by experiments and simulations on applications of highly complex systems.