1. A control apparatus for an internal combustion engine that controls an internal combustion engine provided with an EGR device having an EGR passage that recirculates part of an exhaust gas as an EGR gas and an EGR valve that is provided in the EGR passage and that can adjust an EGR amount, which is a flow rate of the EGR gas, the control apparatus comprising: a controller that performs the following control of: estimating state parameters of the internal combustion engine that affect a behavior of the EGR gas within a predetermined period of time; setting constraints on the EGR amount within the predetermined period of time on the basis of an approximated dynamics obtained by approximating a true dynamics, which is a transition of the EGR amount within the predetermined period of time, so that approximated values do not exceed the true dynamics; determining a target value of the EGR amount according to the estimated state parameters within a range of the EGR amount on which the constraints have been set; and controlling the EGR valve so that the EGR amount becomes the determined target value, wherein the controller sets at least one of a constraint arising from a physical limitation on an opening degree of the EGR valve, a constraint arising from a physical limitation on an opening degree variation rate of the EGR valve, and a constraint arising from a misfire limitation on the internal combustion engine as the constraints on the EGR amount.