Nonconvex projection activated zeroing neurodynamic models for time-varying matrix pseudoinversion with accelerated finite-time convergence

Zeroing dynamics (ZD, or termed Zhang dynamics after its inventor), being a special type of neurodynamic methodology, has shown powerful abilities to solve a great variety of time-varying problems with monotonically increasing odd activation functions. In this paper, two limitations of existing ZD are identified, i.e., the convex restriction on projection operations of activation functions and the low convergence speed with relatively redundant formulations on activation functions. This work breaks them by proposing modified ZD models, allowing nonconvex sets for projection operations in activation functions and possessing accelerated finite-time convergence. Theoretical analyses reveal that the proposed ZD models are of global stability with timely convergence. Finally, illustrative simulation examples, including an application to the motion generation of a robot manipulator, are provided and analyzed to substantiate the efficacy and superiority of the proposed ZD models for real-time varying matrix pseudoinversion.