(188aa) Uniting Lyapunov-Based MPC with Closed-Loop Subspace Identification

Model Predictive Control (MPC) is a well established control method to handle process systems with constraints, nonlinearity, and uncertainty while recognizing performance objectives. One tool that imbues MPC approaches with excellent stability properties is use of control Lyapunov function in the control design [1, 2] to design Lyapunov-based MPC (LMPC). The success of LMPC (like other MPC designs) require a reasonable predictive model of the system. Often, a good first principles model is unavailable, however, sufficient historical data exists to possibly build a data driven model for the purpose of control.

The subspace identification methods (SIM) approach uses a set of input and output data, to estimate linear time-invariant models in a state space form [3]. These methods are based on the geometrical projections and numerical linear algebra, and have recently been adapted to handle data from batch processes [4]. Numerical robustness, fewer user parameters, MIMO systems identification, model order reduction make SIMs more favorable as compared to other identification methods like prediction error methods for the industrial applications. SIMs are usually non-iterative methods, which makes their application, computationally affordable, and, this simplicity would make the model update, affordable.

In the present work, we develop a framework to integrate LMPC with the subspace models. To make the model adaptive, an appropriate model re-identification trigger is included in the control design. Furthermore, the complexities arising out of the closed-loop nature of the data is also accounted for. Simulations on a nonlinear CSTR are used to illustrate the method.

Key Words: Lyapunov-Based Model Predictive Control, Subspace Identification Methods Continuous Stirred-Tank Reactor

[1] Mahmood, M. and Mhaskar, P. (2012). Lyapunov-based model predictive control of stochastic nonlinear systems. Automatica, 48(9), 2271-2276.

[2] Mahmood, M. and P. Mhaskar, Constrained Control Lyapunov Function Based Model Predictive Control Design, Int. J. Rob. & Nonl. Contr., 24, 374–388, 2014.

[3] Qin, S. J. (2006). An overview of subspace identification. Computers & chemical engineering, 30(10), 1502-1513.

[4] Rashid, M. M., Mhaskar, P., & Swartz, C. L. (2017). Handling multi‐rate and missing data in variable duration economic model predictive control of batch processes. AIChE Journal.