| Abstract: |
| We introduce three types of stabilizability for controlled forward-backward stochastic differential equations (FBSDEs): weak stabilizability, stabilizability and strong stabilizability. To investigate the weak stabilizability and stabilizability of FBSDEs, we focus on the partial stabilizability of the associated controlled linear systems, which can be characterized by some linear matrix inequality. Similarly, to address the strong stabilizability of FBSDEs, we define the concept of invariant stabilizability for controlled linear systems, which is described by some mild algebraic criteria. In addition, the stabilizability of game-based control systems (GBCSs) is studied, and by virtue of using the maximum principle, we reduce the analysis of these stabilizability types for GBCSs to the corresponding stabilizability of controlled FBSDEs. Finally, for the specific GBCS, we give the corresponding numerical
simulation results to verify the accuracy of our theoretical results. |
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