1D couple’s state: Views investigation, lovebirds trajectories, and you will stabilizing
Given x0, the control paths (i = 1, 2) obtained from (SM1) constitute an open-loop numerical solution of the couple’s effort problem. The scheme (SM2) allows us to compare the stabilizing solution with the unperturbed solution.
The 1D types of brand new couple’s effort state is sensed for the , whom turned-out the current presence of a different sort of solution to your “lovebirds disease”, that is, considering an initial feeling x(0) = x
One or two systems of couple’s energy problem are thought second. First, the newest 1D make of the issue is analysed. The viewpoints approach provides right here beneficial complementary information to your (open-loop) control-theoretical procedures in . Next, the study of your own dyadic (2D) brand of the problem is handled.
A similar parameter philosophy can be used in numerical education. They truly are found in Table step one. The new electric and you can disutility functions employed for the analysis, specifically (14) are the same because the the individuals sensed inside the . This method is good to extend its unlock-cycle analysis of your situation. The fresh new electricity and you can disutility functions a lot more than match the design criteria called for in the last part. The numerical efficiency exhibited within this part are robust relating to various requisite of your own design inputs.
Furthermore, for any initial feeling x0, the corresponding optimal trajectory (c ? (t), x ? (t)) converges towards the unique equilibrium of the following dynamical system, which is obtained from Pontryagin’s maximum principle, (15) The equilibrium is a saddle point, so the optimal trajectory lies on the stable manifold of the system (see or Theorem 1 in ). (more…)