Asymptotical Feedback Stabilization and Controllability of Probabilistic Logic Networks With State-Dependent Constraints

This study investigates the asymptotical feedback set stabilization and asymptotical feedback controllability of probabilistic logic control networks (PLCNs) with state-dependent constraints. First, based on the properties of the semi-tensor product (STP) of matrices and the vector representation of logic, a PLCN with state-dependent constraints is expressed as the algebraic form. Second, using a state-dependent input transformation, a PLCN with state-dependent constraints is transformed into one with free control input. The equivalence between the stabilizability and controllability of the original constrained PLCN and those of the resulting PLCN with free input is established. Based on these, we propose the necessary and sufficient conditions for both asymptotical feedback stabilizability and asymptotical feedback controllability. Finally, two examples are presented to demonstrate the application of the obtained results.