Discrete-time formulation, control, solution and verification of pendulum systems with zeroing neural dynamics

Abstract As a typical kind of nonlinear system, pendulum systems have drawn attention of numerous researchers for a very long time. This paper focuses mainly on dealing with the discrete-time tracking control problem of both the simple pendulum system and inverted-pendulum-on-a-cart (IPOAC) system. Based on zeroing neural dynamics (ZND), controllers of z2 type are designed respectively for the effective tracking control of the above two pendulum systems. Then, with the aim of possible digital hardware implementation, a 4-node discretization (4ND) formula, which is of square precision in terms of truncation error, is employed to discretize the continuous-time pendulum systems with high precision (i.e., with discretization error being proportional to the cube of the sampling gap). By comparing with Euler-type discretization, simulative results further substantiate the feasibility, accuracy and superiority of the discrete-time control of both the simple pendulum system and IPOAC system with the 4ND formula.