Analyzing one example of LC circuit in [8], show its Lagrange problem only have other type critical points except for minimum type and maximum type under many circumstances. One novel variational principle is established instead of Pontryagin maximum principle or other extremal principles to be suitable for all types of critical points in nonlinear LC circuits. The generalized Euler-Lagrange eq...

For optimal control problems, described by the Gursat-Darboux stochastic system, a number of first-order necessary optimality conditions are formulated and proved, which analogue - Pontryagin maximum principle, linearized principle Euler equation.

We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls two-level quantum systems by means piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in cases with one and two controls. Exact speed limits established as a function sampling period. observe numerically exponential convergence towards minimum time continuous limit...

In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary conditions we derive the corresponding transversality conditions. Our proof is based on Ekeland’s variational principle. Our statement and comments clearly show th...

In this paper, we carry out the dynamics-based optimization of sagittal gait cycles of a planar seven-link biped using the Pontryagin maximum principle. Special attention is devoted to the double-support phase of the gait, during which the movement is subjected to severe limiting conditions. In particular, due to the fact that the biped moves as a closed kinematic chain, overactuation must be c...