In this work, we present an optimal control formulation for the bidomain model in order to estimate maximal conductance parameters in cardiac electrophysiology multiscale modelling. We consider a general Hodgkin-Huxley formalism to describe the ionic exchanges at the microscopic level. We treat the desired parameters as control variables in a cost function minimizing the gap between the measured and the computed transmembrane potentials. First, we establish the existence of an optimal control solution and we formally derive the optimality system. Second, we propose a strategy for solving the estimation problem for both single and multiple parameters cases. Our algorithm is based on a gradient descent method, where the gradient is obtained by solving an adjoint problem. Both the state and the adjoint problems are solved using the finite element method. Numerical simulations for single and multiple conductances estimations show the capability of this approach to identify the values of sodium, calcium and potassium ion channels conductances of the Luo Rudy phase I model.