Data-driven subspace predictive control: Stability and horizon tuning

Data-driven Subspace Predictive Control (SPC) is an advanced model-free process control strategy in the presence of system constraints. Efficient implementation of SPC requires appropriate tuning of the controller horizons, which are called Prediction Horizon and Control Horizon. This tuning is a critical step to guarantee the SPC closed-loop stability and to enhance the closed-loop performance and robustness. In this paper we propose an optimal tuning method for unconstrained SPC, which can guarantee stability, computational efficiency and optimality of the unconstrained SPC closed-loop system and is applicable to non-minimum phase open-loop stable or marginally stable systems. Derivation of general form of closed-loop transfer function for unconstrained SPC, and providing a necessary and sufficient condition of the closed-loop stability is the primary contribution of this work. In addition, the stability analysis enabled us to propose an algorithm to determine the shortest-feasible-prediction-horizon and the feasible range of prediction horizon. Consequently, these results are used in proposing a new algorithm to determine the SPC horizons in optimal manner. Simulation results illustrate effectiveness and importance of our proposed stability analysis and horizons tuning algorithm for unconstrained SPC.