The optimization of the supervisory control of hybrid electric vehicles over predetermined driving cycles has been used as a previous study for determining on-line strategies and also for design and sizing purposes. This problem may be posed as an optimal control problem, in which the energy in the bank of batteries is often the state variable, and the power from any of the system sources is, the control action. As both of these quantities are bounded, the optimal control problem has control constraints or state constraints or both. Usually, the charge-sustaining mode of operation is ensured just by imposing a transversality condition, i.e. a fixed final energy, or including an additional term in the cost functional that penalizes the moving away of the state variable from the nominal value. We considered the problem where the state is allowed to move freely within a band. This led to an optimal control problem with control and state constraints. In this work we describe the difficulties that arise while solving the equations given by the Pontryagin’s Maximum Principle and how these difficulties can be overcome by using the so-called Direct Transcription approach that consists of a programming tool to solve the resultant large-scale finite dimensional optimization problem.
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