Exact(8)
Here, we need to invoke regular synthesis constructions (see Appendix A.3) as they are described in [34, Sect. 6.3].
Either way, straightforward modifications of regular synthesis type arguments give the optimality of the above field of extremals.
The feedback control laws are rigorously shown to produce only time-optimal trajectories, by constructing a regular synthesis for each control law.
The foundations of geometric control can be dated back to the Chow's theorem and to [24, 25], where Brunovsky found that it was possible to derive regular synthesis results by using geometric considerations for a large class of control systems.
Alternatively, the constructions in [35], where a regular synthesis argument has been generalized to problems with order 1 state space constraints, could be modified to apply to cases where the state space constraint is active at the terminal time.
The first series of silica nanoparticles, 1a-h, was prepared using the recently developed W/O microemulsion method proposed by Bagwe et al. [28] This regular synthesis involved the use of Triton X100, n-hexanol, cyclohexane and water to prepare the microemulsion.
Similar(52)
The optimality of this control follows from regular synthesis-type sufficient conditions for optimality, and we briefly outline the reasoning.
Alleviating this issue is a highly nontrivial technical matter, which has led to regular synthesis-type arguments for optimality [39].
We outline regular synthesis-type sufficient conditions for optimality and how they apply to the optimal control problems considered in this paper.
Although the discontinuity of the value impedes on the application of most HJB-type sufficient conditions for optimality, this is not the case for regular synthesis-type constructions (see Appendix A.3), and the optimality of the synthesis follows from Theorem 6.3.3 in [34].
They solved the common and regular module, synthesis subband with relative improvements.
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