On the optimal trajectory generation for servomotors: a Hamiltonian approach

This note considers the energy optimal trajectory generation of servo systems through open-loop optimal control design approach. Solving the exact optimal solution is challenging because of the nonlinear and switching cost function, and various constraints. The minimum principle is applied to establish piecewise necessary optimality conditions. An approximate optimal control is proposed to circumvent the difficulty due to the nonlinearity of the cost function. Simulation is performed to illustrate the generation of the approximate optimal trajectory.