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Approximation of the attainable sets of the nonlinear control systems with integral constraint on controls. (English) Zbl 1162.93005

Summary: The attainable sets of a control system are investigated. It is assumed that the behavior of the control system is described by a differential equation which is nonlinear with respect to the phase state vector and control vector. The admissible control functions are chosen from the closed ball centered at the origin with radius \(\mu _{0}\) in \(L_p([t_0,\theta];\mathbb R^m)\) with \(p\in (1,+\infty \)). An approximation method has been obtained for numerical construction of the attainable sets.

MSC:

93B03 Attainable sets, reachability
49M25 Discrete approximations in optimal control
34H05 Control problems involving ordinary differential equations
93C10 Nonlinear systems in control theory
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