On a maximum principle in potential theory

Pontryagin's maximum principle in geometric function theory

We discuss an innnite-dimensional version of Pontrya-gin's maximum principle as a uniied variational method in many familiar classes of analytic functions, and its interrelation with classical variational methods in geometric function theory.

Optimal Control Theory - Module 3 - Maximum Principle

subject to (tf , x(tf )) ∈ S = [t0,∞)× S1 where S1 is a k dimensional manifold in Rn S1 = {x ∈ R : h1(x) = h2(x) = · · · = hn−k(x) = 0} where hi are C1 functions from Rn to R subject to ẋ = f(x, u), x(t0) = x0 for u ∈ C[t0, T ] and u(t) ∈ U ⊂ Rm with f and L being C1 functions. Let u∗ : [t0, tf ] → R be an optimal control with state trajectory x∗ : [t0, tf ] → Rn and a constant. Then there exis...

Large deviation principle in logarithmic potential theory

Remarks on the Maximum Entropy Principle with Application to the Maximum Entropy Theory of Ecology

In the first part of the paper we work out the consequences of the fact that Jaynes’ Maximum Entropy Principle, when translated in mathematical terms, is a constrained extremum problem for an entropy function H(p) expressing the uncertainty associated with the probability distribution p. Consequently, if two observers use different independent variables p or g(p), the associated entropy functio...

Geometric aspects of the maximum principle in control theory

In a previous paper [1] we have proven a geometric formulation of the maximum principle for time dependent optimal control problems with fixed endpoint conditions. As a side result we obtained a necessary and sufficient condition for a control to be a (strictly) abnormal extremal. As an application of that result we consider in this paper two known examples of optimal control systems having abn...