Controllability test for nonlinear datatic systems
Controllability is a fundamental property of control systems, serving as the prerequisite for controller design. While controllability test is well established in modelic (i.e., model-driven) control systems, extending it to datatic (i.e., data-driven) control systems is still a challenging task due...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-12-01
|
| Series: | Communications in Transportation Research |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S277242472400026X |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Controllability is a fundamental property of control systems, serving as the prerequisite for controller design. While controllability test is well established in modelic (i.e., model-driven) control systems, extending it to datatic (i.e., data-driven) control systems is still a challenging task due to the absence of system models. In this study, we propose a general controllability test method for nonlinear systems with datatic description, where the system behaviors are merely described by data. In this situation, the state transition information of a dynamic system is available only at a limited number of data points, leaving the behaviors beyond these points unknown. Different from traditional exact controllability, we introduce a new concept called ϵ-controllability, which extends the definition from point-to-point form to point-to-region form. Accordingly, our focus shifts to checking whether the system state can be steered to a closed state ball centered on the target state, rather than exactly at that target state. Given a known state transition sample, the Lipschitz continuity assumption restricts the one-step transition of all the points in a state ball to a small neighborhood of the subsequent state. This property is referred to as one-step controllability backpropagation, i.e., if the states within this neighborhood are ϵ-controllable, those within the state ball are also ϵ-controllable. On its basis, we propose a tree search algorithm called maximum expansion of controllable subset (MECS) to identify controllable states in the dataset. Starting with a specific target state, our algorithm can iteratively propagate controllability from a known state ball to a new one. This iterative process gradually enlarges the ϵ-controllable subset by incorporating new controllable balls until all ϵ-controllable states are searched. Besides, a simplified version of MECS is proposed by solving a special shortest path problem, called Floyd expansion with radius fixed (FERF). FERF maintains a fixed radius of all controllable balls based on a mutual controllability assumption of neighboring states. The effectiveness of our method is validated in three datatic control systems whose dynamic behaviors are described by sampled data. |
|---|---|
| ISSN: | 2772-4247 |