In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints whose costs are general, possibly nonsmooth finite coherent risk measures. Unlike preexisting contributions covering situation, our analysis holds classical differential equations driven by standard Brownian motions. addition, it ...

We consider a class of cooperative differential games with continuous updating making use the Pontryagin maximum principle. It is assumed that at each moment, players have or information about game structure defined in closed time interval fixed duration. Over time, will be updated. The subject current paper to construct players’ strategies, their trajectory, characteristic function, and soluti...

1.1 Duality is a frequently occurring principle for understanding a mathematical structure. The Fourier transformation is a classical example which leads to the Pontryagin duality of topological abelian groups. A more geometric example is the Fourier-Mukai ∗Mathematisches Institut, Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, GERMANY, [email protected], [email protected] s...

We obtain a discrete time analog of E. Noether’s theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasiinvariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations a...

The minimum description length (MDL) principle states that one should prefer the model that yields the shortest description of the data when the complexity of the model itself is also accounted for. MDL provides a versatile approach to statistical modeling. It is applicable to model selection and regularization. Modern versions of MDL lead to robust methods that are well suited for choosing an ...

This article formulates the optimal pacing of a cyclist on hilly terrain time trials as minimum-time control problem. The maximal power serves time-varying constraint and depends fatigue recovery which are captured via dynamic models proposed early in article. Experimental protocols for identifying individualized parameters detailed results six human subjects shown. In an analytical treatment n...