APPROXIMATIONS OF THE SET OF TRAJECTORIES, ATTAINABLE SETS AND INTEGRAL FUNNEL OF NONLINEAR CONTROL SYSTEMS WITH MIXED CONSTRAINTS ON THE CONTROL FUNCTIONS

Anar Huseyin     (Sivas Cumhuriyet University, 58140 Merkez, Sivas, Turkey)
Nesir Huseyin     (Sivas Cumhuriyet University, 58140 Merkez, Sivas, Turkey)

Abstract


In this paper, approximations of the set of trajectories, attainable sets and integral funnel of a control system described by a nonlinear ordinary differential equation with mixed constraints on the control functions are discussed. The set of admissible control functions is replaced by a set consisting of a finite number of piecewise-constant control functions. Then, each trajectory generated by a piecewise-constant control function is replaced by its Euler's broken line, and  it is proved that, in appropriate settings of the discretization parameters, the Hausdorff distance between the set of trajectories, attainable sets, integral funnel, and their approximations can be made sufficiently small.

Keywords


Nonlinear control system, Mixed constraints, Set of trajectories, Attainable set, Integral funnel, Approximation

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References


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DOI: http://dx.doi.org/10.15826/umj.2026.1.004

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