(644d) Machine-Learning-Based Construction of Barrier Functions and Models for Safe Model Predictive Control

Process safety is one of the most critical priorities to industrial production and operation. As such, advanced control techniques such as Model Predictive Control (MPC) have been proposed to ensure smooth operation and to handle intricate multi-variable interactions, nonlinearities, and constraints on process variables and actuators. Moreover, Control Lyapunov-Barrier Function-based (CLBF) controllers have shown success in ensuring the stability and safety of a nonlinear system for all times ([1]). A Control Lyapunov-Barrier Function can be included as a part of the MPC formulation, where the predictive model within the MPC is either modeled using first-principles in the form of nonlinear ODE's ([2]), or modeled using machine-learning-based methods such as recurrent neural networks ([3]). CLBFs can be developed from the linear combination of Control Lyapunov Function (CLF) and Control Barrier Function (CBF), both of which satisfying certain stabilizability and safety properties ([1, 4]). Characterizing a CBF that satisfies its required properties for the unsafe and the safe operating regions distinctively still remains a difficult task especially for nonlinear processes with complex unsafe operating conditions which cannot be readily described with common explicit functions.

We propose a Control Lyapunov-Barrier Function-based Model Predictive Control method utilizing a feed-forward neural network specified Barrier Function and a recurrent neural network predictive model to stabilize the nonlinear systems with input constraints and to guarantee that safety requirements are met for all times. The nonlinear system is first modeled using recurrent neural network (RNN) techniques, and a Control Barrier Function is characterized by constructing a feed-forward neural network model (FNN) with unique structures and properties. The FNN is then trained based on discretized data within user-defined safe and unsafe operating regions. Given sufficiently small bounded modeling errors with the two NN models, the proposed control system is able to ensure closed-loop stability while preventing closed-loop states from entering any unsafe regions in the state-space under sample-and-hold control action implementation. We demonstrate the effectiveness of the proposed control strategy using a nonlinear chemical process example with a bounded unsafe region.

References:

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Lyapunov–barrier function. Automatica, 66:39–47, 2016.

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function-based model predictive control of nonlinear systems. Automatica, 109:108508,

2019.

[3] Z. Wu and P. D. Christofides. Control lyapunov-barrier function-based predictive control of

nonlinear processes using machine learning modeling. Computers & Chemical Engineering,

134:106706, 2020.

[4] M. Jankovic. Combining control Lyapunov and barrier functions for constrained stabilization

of nonlinear systems. In Proceedings of the American Control Conference, pages 1916–1922,

Seattle, Washington, 2017.