| Optimal control with mixed control actions is a relatively new area of research. In flight mechanics, electrophysics, medicine, and economics, we often encounter dynamic systems that admit discontinuous trajectories generated by impulse controls. In the system response there hence exists some instantaneous jumps. We then have to solve a generalized optimization problem. Both piecewise continuous control and impulse control will be considered in the optimization task.;Given is a thorough overview about parameter optimal control. We have developed not only necessary conditions but also sufficient conditions to all our stated problems. The theoretical derivations can all be proved by the associated numerical algorithms. Applications to ascending rocket, lunar orbit injection, and four-terminal networks, all satisfied the necessary and sufficient conditions and gave reasonable results. A new algorithm for solving optimal control problem with mixed control actions has been developed and demonstrated by using a two-link robot manipulator model to solve a minimal-time problem.;The discussion of the existence of optimal control of linear systems with mixed control actions is first considered and then extended to nonlinear systems. The results ensure the existence of time-optimal mixed control actions for example. Based on this foundation we established a preliminary approach for the time-varying linear control systems. |
