The paper gives an overview of an algebraic approach based on differential 1-forms, developed for the study of nonlinear control systems. The purpose of the paper is to describe the approach, comment on the necessary assumptions made, and demonstrate the effectiveness and limitations of the approach. Two very important aspects of the approach are as follows: (1) one works with differentials and not with functions, meaning that computations are, up to integration similar to the linear case and (2) the approach is used to study generic properties of control systems that hold for almost every point of a suitable domain. The first point means that solutions to various problems are found in terms of 1-forms and the integrability properties allow transformation of the solution back to the level of functions. The study of generic properties simplifies the presentation of the solutions, since there is no need to specify the working point and its neighbourhood. Finally, the paper includes an extensive list of publications, where the approach of 1-forms is studied or applied to solve different control problems.
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