Measure Driven Differential Inclusions

Necessary conditions of optimality for measure driven differential inclusions

Minimize h(x(0), x(1)) subject to dx(t) ∈ F (t, x(t))dt + G(t, x(t))dμ(t) ∀t∈[0, 1] (x(0), x(1)) ∈ C ⊂ IR × IR l(t, x(t)) ≤ 0 ∀t∈[0, 1] dμ ∈ K where h : IR × IR → IR, and l : [0, 1]× IR → IR are given functions, F : [0, 1]× IR → P(IRn), and G : [0, 1] × IR → P(IRn×q) are given set-valued maps, K ⊂ C∗([0, 1];K) is the set of control measures supported on [0, 1] with range in a given set K ⊂ IR, ...

Measure differential inclusions - between continuous and discrete

*Correspondence: [email protected] 2Faculty of Electrical Engineering and Computer Science, ’Stefan cel Mare’ University of Suceava, Universitatii 13, Suceava, Romania Full list of author information is available at the end of the article Abstract The paper is devoted to the study of the measure-driven differential inclusions dx(t) ∈ G(t, x(t))dμ(t), x(0) = x0 for arbitrary finite Borel m...

On Stability of Measure Driven Differential Equations

We consider the problem of stability in a class of differential equations which are driven by a differential measure associated with the inputs of locally bounded variation. After discussing some existing notions of solution for such systems, we derive conditions on the system’s vector fields for asymptotic stability under a specific class of inputs. These conditions present a trade-off between...

THE FULL AVERAGING OF FUZZY DIFFERENTIAL INCLUSIONS

In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations.

Improving the Solution of Fuzzy Differential Inclusions