کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1707022 1012494 2009 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Dynamic programming and Lagrange multipliers for active relaxation of resources in nonlinear non-equilibrium systems
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مکانیک محاسباتی
پیش نمایش صفحه اول مقاله
Dynamic programming and Lagrange multipliers for active relaxation of resources in nonlinear non-equilibrium systems
چکیده انگلیسی

In power production problems maximum power and minimum entropy production and inherently connected by the Gouy–Stodola law. In this paper various mathematical tools are applied in dynamic optimization of power-maximizing paths, with special attention paid to nonlinear systems. Maximum power and/or minimum entropy production are governed by Hamilton–Jacobi–Bellman (HJB) equations which describe the value function of the problem and associated controls. Yet, in many cases optimal relaxation curve is non-exponential, governing HJB equations do not admit classical solutions and one has to work with viscosity solutions. Systems with nonlinear kinetics (e.g. radiation engines) are particularly difficult, thus, discrete counterparts of continuous HJB equations and numerical approaches are recommended. Discrete algorithms of dynamic programming (DP), which lead to power limits and associated availabilities, are effective. We consider convergence of discrete algorithms to viscosity solutions of HJB equations, discrete approximations, and the role of Lagrange multiplier λ associated with the duration constraint. In analytical discrete schemes, the Legendre transformation is a significant tool leading to original work function. We also describe numerical algorithms of dynamic programming and consider dimensionality reduction in these algorithms. Indications showing the method potential for other systems, in particular chemical energy systems, are given.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematical Modelling - Volume 33, Issue 3, March 2009, Pages 1457–1478
نویسندگان
,