Abstract: Non-anticipativity is a critical principle in power dispatching, ensuring that uncertain future parameters do not affect current decisions. All-scenario feasibility refers to the ultimate objective in power dispatching, where every possible realization of uncertain parameters has a corresponding feasible decision. These become vital in power dispatching, especially with integrating renewable energy sources introducing uncertainties. Thus, this paper explores the mechanisms of non-anticipativity and all-scenario feasibility, constructing non-anticipativity constraints and a finite scenario set that satisfies all-scenario feasibility. Based on them, this paper establishes a scenario-based all-scenario feasible unit commitment model with non-anticipativity to provide unit commitment solutions that satisfy all-scenario feasibility. Further, recognizing the computational challenges posed by the above model, this paper transforms the model using affine transformations and robust equivalent constraints. It introduces an affine-adjustable robust all-scenario feasible unit commitment model with non-anticipativity in decision-making. This model reduces the computational complexity and demonstrates advantages in solving efficiency. Finally, the paper conducts case studies using a modified IEEE-118 test system. These case studies thoroughly examine the importance of non-anticipativity in decision-making and the necessity of decisions fulfilling all-scenario feasibility in power dispatching, then evaluate the efficiency of the proposed affine-adjustable robust all-scenario feasible unit commitment model with non-anticipativity in the decision-making process.