Nonholonomic approach of multitime maximum principle

Many science and engineering problems can be formulated as optimization problems that are governed by contact distributions (multitime Pfaff evolution systems) and by cost functionals expressed as multiple integrals or curvilinear integrals. Our paper discuss the contact distribution constrained optimization problems, focussing on a nonholonomic approach of multitime maximum principle. This principle extends the work of Pontryaguin in the ODEs case to include the case of normal PDEs or, more general, the distribution case. In Section 1 a multitime maximum principle for the case of multiple integral functionals is stated and proved. Section 2 is devoted to the multitime maximum principle for the case of curvilinear integral functionals. Section 3 deals with a multitime maximum principle approach of variational calculus in the case of nonintegrability. M.S.C. 2000: 93C20, 93C35, 49K20, 49J20, 53C44.