A logical network approximation to optimal control on a continuous domain and its application to HEV control

The finite-time horizon optimal control problem is investigated for discrete-time dynamical systems defined on a continuous domain. First, the original optimal control problem in the continuous domain is approximated as one on a finite-valued domain based on a special quantification process. Under suitable assumptions, convergence analysis of the approximate optimal cost of the quantified system to the optimal cost of the original system was established with error estimation. Thereafter, the approximate problem is solved using a logical network-based method that is proposed based on the semi-tensor product of the matrix. Finally, the proposed scheme is applied to deal with the optimal control problem of a hybrid electric vehicle (HEV) powertrain system, and its effectiveness is shown by a series of simulation results.