(118d) Data-Driven Dissipativity-Based Control

Data-driven control strategies aim to design controllers for process systems based on their historical, online or simulation data, thus providing alternatives to the difficulty of establishing and updating dynamic models in traditional model-based control [1]. The state-of-the-art data-driven control approaches can be classified into two main categories – those based on model identification and those based on approximate dynamic programming. The latter type of approaches, typically employing an online algorithm to train the controllers under the name of reinforcement learning, have been extensively studied in the recent years [2].

However, the application of currently existing data-driven control methods seems to be yet limited to small-scale systems with simple dynamics. This is due to the dependence of the identification performance on model complexity and the requirement of state information in reinforcement learning. For process systems with unobservable and high-dimensional states governed by complex dynamics, a data-driven control framework remains an open problem. A promising approach is to use only input-output data without involving state-space descriptions, and learn control-relevant properties of the system from these data rather than identifying the entire model. To this end, we note that the concept of dissipativity [3], as a characterization of input-output behavior of dynamical systems and a property typically possessed by process systems [4], has been widely exploited for output-feedback control.

In this work, we extend the concept of dissipativity-based control into a data-driven setting. First, we focus on the dissipativity learning. Specifically, the dissipativity property is captured by a storage function with parameters to be determined, called dissipativity parameters. With the data calculated from trajectory samples, we apply independent component analysis (ICA) to reduce the data dimensionality and project data onto individual components, and use probability density estimation (PDE) to infer a polyhedral confidence region of the trajectory data (similar to the idea of [6]). According to the dissipativity theory, the dual cone of such a confidence region turns out to be an estimated range of the dissipativity parameters, called dissipativity set. An early effort towards dissipativity learning using a more restrictive form of storage function parameterization appeared in [5].

The control performance, characterized by an upper bound of the L₂-gain from exogenous disturbances to control inputs and outputs, is related to the dissipativity parameters and the controller gain. The dissipativity set is subsequently used in an output-feedback controller synthesis formulation, which specifies the optimal controller gains and dissipativity parameters with respect to the L₂ control performance. The problem is a semidefinite program that is multi-convex in the controller gains and the dissipativity parameters, which we propose to solve by iteratively optimizing these two groups of variables.

We point out that the proposed data-driven dissipativity-based control approach can be applied to both regulating and tracking control tasks, and can be used for the design of P, PI or PID controllers. This is illustrated by two case studies on the regulating control of a polymerization reactor and the tracking control of an oscillatory reactor. In the case studies, we also discuss how to choose the only two hyper-parameters, namely the number of independent components and the confidence level, involved in the dissipativity learning procedure.

References

[1] Hou, Z. S., & Wang, Z. (2013). From model-based control to data-driven control: Survey, classification and perspective. Information Sciences, 235, 3-35.

[2] Lee, J. H., Shin, J., & Realff, M. J. (2018). Machine learning: Overview of the recent progresses and implications for the process systems engineering field. Computers & Chemical Engineering, 114, 111-121.

[3] Brogliato, B., Lozano, R., Maschke, B., & Egeland, O. (2007). Dissipative systems analysis and control: Theory and applications. Springer.

[4] Hioe, D., Bao, J., & Ydstie, B. E. (2013). Dissipativity analysis for networks of process systems. Computers & Chemical Engineering, 50, 207-219.

[5] Romer, A., Montenbruck, J. M., & Allgöwer, F. (2017). Determining dissipation inequalities from input-output samples. IFAC-PapersOnLine, 50(1), 7789-7794.

[6] Ning, C., & You, F. (2018). Data-driven decision making under uncertainty integrating robust optimization with principal component analysis and kernel smoothing methods. Computers & Chemical Engineering, 112, 190-210.