An exhaust gas control apparatus comprising: a dust collection device configured to apply a direct current voltage between a charging electrode and a counter electrode, and to collect particulate matter on an oxidation substrate that is arranged inside the counter electrode, the charging electrode being arranged in a flow channel for exhaust gas containing particulate matter, and the counter electrode constituting at least a part of an inner wall surface of the flow channel; an oxidation treatment device configured to apply an alternating current voltage between an oxidation electrode and the counter electrode, and to subject the particulate matter deposited on the oxidation substrate to an oxidation treatment, the oxidation electrode being provided in the oxidation substrate and being at least partially covered with a dielectric; and an electronic control unit configured to control the dust collection device and the oxidation treatment device, the electronic control unit being configured to estimate a distribution of a deposition amount of the particulate matter deposited on the oxidation substrate in a flow direction of exhaust gas, based on input information including at least a flow rate of exhaust gas and a mass of the particulate matter in exhaust gas, setting information including at least an electric field intensity between the charging electrode and the counter electrode, and history information on the oxidation treatment by the oxidation treatment device, the electronic control unit being configured to carry out the oxidation treatment by the oxidation treatment device when the deposition amount of at least a part of the deposited particulate matter exceeds a threshold (α1), wherein the electronic control unit is further configured to perform a comparison with a preset threshold at a plurality of charging positions, each charging position corresponding to one out of a plurality of regions into which the oxidation substrate is divided, and wherein the control apparatus is configured to carry out the oxidation treatment when the threshold is exceeded in at least one of the charging positions. a dust collection device configured to apply a direct current voltage between a charging electrode and a counter electrode, and to collect particulate matter on an oxidation substrate that is arranged inside the counter electrode, the charging electrode being arranged in a flow channel for exhaust gas containing particulate matter, and the counter electrode constituting at least a part of an inner wall surface of the flow channel; an oxidation treatment device configured to apply an alternating current voltage between an oxidation electrode and the counter electrode, and to subject the particulate matter deposited on the oxidation substrate to an oxidation treatment, the oxidation electrode being provided in the oxidation substrate and being at least partially covered with a dielectric; and an electronic control unit configured to control the dust collection device and the oxidation treatment device, the electronic control unit being configured to estimate a distribution of a deposition amount of the particulate matter deposited on the oxidation substrate in a flow direction of exhaust gas, based on input information including at least a flow rate of exhaust gas and a mass of the particulate matter in exhaust gas, setting information including at least an electric field intensity between the charging electrode and the counter electrode, and history information on the oxidation treatment by the oxidation treatment device, the electronic control unit being configured to carry out the oxidation treatment by the oxidation treatment device when the deposition amount of at least a part of the deposited particulate matter exceeds a threshold (α1), wherein the electronic control unit is further configured to perform a comparison with a preset threshold at a plurality of charging positions, each charging position corresponding to one out of a plurality of regions into which the oxidation substrate is divided, and wherein the control apparatus is configured to carry out the oxidation treatment when the threshold is exceeded in at least one of the charging positions.