Hüseyin, Anar2023-06-232023-06-2329.11.2022N. Huseyin, A. Huseyin, Kh.G. Guseinov. Approximations of the set of trajectories and integral funnel of the nonlinear control systems with L_p norm constraints on the control functions. IMA Journal of Mathematical Control and Information. 2022, vol.39, no.4, pp.1213-1231.1471-6887https://hdl.handle.net/20.500.12418/13999In this paper, approximations of the set of trajectories and integral funnel of the control system described by non-linear ordinary differential equation with integral constraint on the control functions are considered. The set of admissible control functions is replaced by a set, consisting of a finite number of piecewise-constant control functions. It is shown that the set of trajectories generated by a finite number of piecewise-constant control functions is an internal approximation of the set of trajectories. Further, each trajectory generated by a piecewise-constant control function is substituted by appropriate Euler’s broken line and it is proved that the set consisting of a finite number of Euler’s broken lines is an approximation of the set of trajectories of given control system. An approximation of the system’s integral funnel by a set consisting of a finite number of points is obtained.en10.1093/imamci/dnac028info:eu-repo/semantics/openAccessArticle394123112132-s2.0-85156109945Q2WOS:000886405400001Q2