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Future quadratic programming (FQP) is an interesting and challenging topic due to its unknown future information and time-dependent feature. In this paper, a continuous-time zeroing neurodynamics (CTZN) model for quadratic programming is first obtained via zeroing neurodynamics (ZN) method. Then, a general four-step Zhang et al. discretization formula is presented and adopted to discretize the above CTZN model, and thus the general four-step discrete-time ZN (DTZN) algorithm for the FQP is developed. For comparison, a three-step DTZN algorithm and a one-step DTZN algorithm for the FQP are also presented. It is worth noting that there is an important parameter termed stepsize in the DTZN algorithms, which is closely related to their stability. If the value of stepsize is outside its effective interval, the DTZN algorithms are impossible to achieve convergence in terms of residual errors, which leads to failure of the FQP problem solving. By utilizing bilinear transformation and Routh stability criterion, the effective stepsize interval of the general four-step DTZN algorithm is confirmed via theoretical proof. Besides, numerical results substantiate the effectiveness and superiority of the general four-step DTZN algorithm as well as the accuracy of the effective stepsize interval. Finally, the general four-step DTZN algorithm is applied to fulfill the path-tracking control of different robot manipulators, with the effectiveness and superiority further validated. [ABSTRACT FROM AUTHOR]