The optimal path planning for two flexible cooperating manipulators carrying a solid object on a prescribed tip trajectory has been studied using kinematic resolution. The formulation has been derived using the Pontryagin minimum principle that results in a two-point boundary value problem. Also, a numerical technique based on converting the abstract optimization to parametric optimization prob...

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove strong necessary optimality condition of Pontryagin type. The possibility that admissible are subject to pointwise constraints is new requires more sophisticated techniques include maximality condition. start by proving results continuity solutions due needle-like pe...

In this paper, an attempt to unify two important lines of thought in applied optimization is proposed. We wish integrate the well-known (dynamic) theory Pontryagin optimal control with Pareto (of static type), involving maximization/minimization a non-trivial number functions or functionals, offers definitive theoretical device for dynamic realization objectives be optimized. The undoubtedly le...

classical control methods such as pontryagin maximum principle and bang-bang principle and other methods are not usually useful for solving opti-mal control systems (ocs) specially optimal control of nonlinear systems (ocns). in this paper, we introduce a new approach for solving ocns by using some combination of atomic measures. we define a criterion for controllability of lumped nonlinear con...

In this paper, the authors study an optimal control problem for quasilinear elliptic PDEs with pointwise state constraints. Weak and strong optimality conditions of Pontryagin maximum principle type are derived. In proving these results, we penalized the state constraints and respectively use the Ekeland variational principle and an exact penalization method. In this paper, our aim is to prove ...

It well known that the Pontryagin maximum principle is a necessary optimality condition for control problems. For linear control problems, it is also a sufficient condition, but for a nonlinear control problems in common form, it is not. We found a class of nonlinear control problems for which the Pontryagin maximum principle is also a sufficient optimality condition. This is a class of problem...

In 1696, Johann Bernoulli solved the brachistochrone problem by an ingenious method of combining Fermat’s principle of minimum time, Snell’s law of refraction and “finite element” discretization. This appears to be the first application of a “direct method.” By taking the limits of these “broken-line solutions,” Bernoulli arrived at an equation for the cycloid. About fifty years later (1744), E...

In this paper, finding Dynamic Load Carrying Capacity (DLCC) of flexible link manipulators in point to-point motion was formulated as an optimal control problem. The finite element method was employed for modelling and deriving the dynamic equations of the system. The study employed indirect solution of optimal control for system motion planning. Due to offline nature of the method, many diffic...