(681d) Data Driven Economic Model Predictive Control for Unstable Systems

Control systems designed to manage chemical process operations often faces numerous challenges such as inherent nonlinearity, process constraints and uncertainty. Model predictive control (MPC) is a well-established control method that can handle these challenges [1, 2]. In MPC, the control action is computed by solving an open-loop optimal control problem at each sampling instance over a time horizon, subject to the model that captures the dynamic response of the plant, and constraints.

With increasing recognition (and ability) of MPC designs to focus on economic objectives, the notion of Economic MPC (EMPC) was developed for linear and nonlinear systems [3, 4], and several important issues (such as input rate-of-change constraint and uncertainty) addressed.

Most of the existing MPC formulations, economic or otherwise, have been illustrated using first principles models. With growing availability of data, there exists the possibility of enhancing MPC implementation for situations where a first principles model may not be available, and simple `step-test', transfer-function based model identification approaches may not suffice. One of the widely utilized approaches in the general direction of model identification are, subspace-based system identification methods which have been adapted for the purpose of model identification, where state-space model from measured data are identified using projection methods [5]. To handle the resultant plant model mismatch with data-driven model based approaches, monitoring of the model validity becomes especially important.

In a direction, the focus more explicitly on the model behavior, in a recent result [6] an adaptive data-driven MPC was proposed to evaluate model prediction performance and trigger model identification in case of poor model prediction. Data driven MPC or EMPC approaches, that utilize appropriate modeling techniques to identify data from closed-loop tests to handle operation around nominally unstable equilibrium points remain unaddressed [4].

Motivated by the above considerations, in this work we address the problem of data driven model based predictive control at an unstable equilibrium point. In order to identify a model around an unstable equilibrium point, the system is perturbed under closed-loop operation. Having identified a model, a Lyapunov-based MPC is designed to achieve local and practical stability. The Lyapunov-based design is then used as the basis for a data driven Lyapunov-based EMPC design to achieve economical goals while ensuring boundedness.

Key Words: Model Predictive Control, Subspace Identification Methods, Lyapunov-Based MPC, Unstable Equilibrium Point

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[2] Garcia, C. E., Prett, D. M., & Morari, M. (1989). Model predictive control: theory and practice—a survey. Automatica, 25(3), 335-348.

[3] Alanqar, A., Ellis, M., & Christofides, P. D. (2015). Economic model predictive control of nonlinear process systems using empirical models. AIChE Journal, 61(3), 816-830.

[4] Kheradmandi, M., & Mhaskar, P. (2018). Data Driven Economic Model Predictive Control. Mathematics, 6(4), 51.

[5] Qin, S. J. (2006). An overview of subspace identification. Computers & chemical engineering, 30(10-12), 1502-1513.

[6] Kheradmandi, M., & Mhaskar, P. (2018). Model predictive control with closed-loop re-identification. Computers & Chemical Engineering, 109, 249-260.