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A systematic method for establishment of exact and approximate controllability of dynamic systems with nonlinear state constraints within infinite time is developed. Using the recently developed Green's function approach, we derive necessary and sufficient conditions for exact controllability, as well as sufficient conditions for approximate controllability. Conditions for null‐controllability and lack of controllability are established as well. Several possibilities of deriving explicit form for resolving controls are described. Possibilities of heuristic determination of resolving controls is studied in details. The advantages and drawbacks of the method are revealed on specific examples of nonlinear wave and diffusion equations in unbounded domains.

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