منابع مشابه
The Pontryagin Maximum Principle
Theorem (PontryaginMaximum Principle). Suppose a final time T and controlstate pair (û, x̂) on [τ, T ] give the minimum in the problem above; assume that û is piecewise continuous. Then there exist a vector of Lagrange multipliers (λ0, λ) ∈ R × R with λ0 ≥ 0 and a piecewise smooth function p: [τ, T ] → R n such that the function ĥ(t) def =H(t, x̂(t), p(t), û(t)) is piecewise smooth, and one has ̇̂ ...
متن کاملStochastic maximum principle
The Pontrjagin maximum principle solves the problem of optimal control of a continuous deterministic system. The discrete maximum principle solves the problem of optimal control of a discrete-time deterministic system. The maximum principle changes the problem of optimal control to a two point boundary value problem which can be completely solved only in special tasks. It was probably the reaso...
متن کاملSimplified multitime maximum principle
Many science and engineering problems can be formulated as optimization problems that are governed by m-flow type PDEs (multitime evolution systems) and by cost functionals expressed as multiple integrals or curvilinear integrals. Our paper discuss the m-flow type PDEconstrained optimization problems, focussing on a simplified multitime maximum principle. This extends the simplified single-time...
متن کاملFractional convexity maximum principle∗
We construct an anisotropic, degenerate, fractional operator that nevertheless satisfies a strong form of the maximum principle. By applying such an operator to the concavity function associated to the solution of an equation involving the usual fractional Laplacian, we obtain a fractional form of the celebrated convexity maximum principle devised by Korevaar in the 80’s. Some applications are ...
متن کاملThe Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle
We give a simple proof of the Maximum Principle for smooth hybrid control systems by reducing the hybrid problem to an optimal control problem of Pontryagin type and then by using the classical Pontryagin Maximum Principle.
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1979
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700014890