A suboptimal solution to nonconvex optimal control problems involving input - affine dynamic models

This papers presents a convex approximation method for the solution of nonconvex optimal control problems involving input-affine dynamic models. The method relies in the availability of full reference state trajectories. By using these states references as real states trajectories, the dynamic model is approximated such that the resulting problem becomes convex. The convexified problem is solved by efficient convex methods delivering a suboptimal solution. This solution is used to linearize the original nonconvex problem such that the minimizer is refined by solving a new convex problem. Consequently, the solution to the original problem is obtained in two steps. An assessment of the errors in the approximation as a function of the mismatch between state reference trajectories and a perfect traceable trajectory is provided. The method is exemplified by formulating the optimal control problem of an isothermal continuous stirred tank reactor with Van den Vusse reactions.