In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature fo...

Recently, an approach to derive solutions of HamiltonJacobi equation with high accuracy, called stable manifold theory, is proposed. So far some researches about nonlinear optimal control via stable manifold are subjected. However, research of robustness for nonlinear optimal control is not reported. This report proposes a new framework to enhance robustness to the nonlinear optimal control sys...

this paper presents optimal control method to path planning of mobile robots with flexible joints. dynamic equations are derived and additional kinematic constraints are used to solve the extra dofs arose from base mobility. then with modeling the elasticity at each joint as a linear torsinal spring, the set of equations are formed. the hamiltonian function is formed and the necessary condition...

This paper concerns a study on the optimal control for nonlinear systems. An appropriate alternative in order to alleviate the nonlinearity of a system is the exact linearization approach. In this fashion, the nonlinear system has been linearized using input-output feedback linearization (IOFL). Then, by utilizing the well developed optimal control theory of linear systems, the compensated ...

this paper concerns a study on the optimal control for nonlinear systems. an appropriate alternative in order to alleviate the nonlinearity of a system is the exact linearization approach. in this fashion, the nonlinear system has been linearized using input-output feedback linearization (iofl). then, by utilizing the well developed optimal control theory of linear systems, the compensated nonl...

In this paper, the min-time optimal control problem is mainly investigated in the linear time invariant (LTI) continuous-time control system with a constrained input. A high order dynamical LTI system is firstly considered for this purpose. Then the Pontryagin principle and some necessary optimality conditions have been simultaneously used to solve the optimal control problem. These optimality ...

In this paper, we attempt to solve the time-optimal control problem for single-degree-of-freedom (DOF) mechanical systems with friction, while taking into account not only the velocity-dependent control input constraint but also the state constraint. Direct application of the Pontryagin’s maximum principle (PMP) leads to a sixth-order nonlinear two-point boundary-value problem (TPBVP) which is ...

in this paper, simultaneous control of source terms is considered in a vibrational string problem.in the considered problem, the terms to be controlled are the force and the initial velocity functions. we statethe generalized (weak) solution about the considered problem. the existence and uniqueness of the solutionfor optimal control problem is investigated. the frechet derivative of the functi...