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The initiation, termination, and control of internal transport barriers associated with E × B flow shear near local minima of magnetic shear are examined for burning plasmas to determine if the positive feedback loops between profiles, instability, transport, and flow shear operate in regimes with fusion self-heating. A five-field transport model for the evolution of profiles of density, ion and electron temperature, ion and electron fluctuations, and radial electric field is utilized to examine the efficacy of controls associated with external inputs of heat and particles, including neutral beam injection, RF, pellets, and gas puffing. The response of the plasma to these inputs is studied in the presence of self-heating. The latter is affected by the external inputs and their modification of profiles and is, therefore, not an external control. Provided sufficient external power is applied, internal transport barriers can be created and controlled, both in ion and electron channels. Barrier control is sensitive to the locations of power deposition and pellet ablation, as well as temporal sequencing of external inputs.