Abstract: A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian approach. Both the free and fixed final state cases have been considered. Numerical examples...

In the first part of this two-paper series, we presented a conceptual algorithm for the optimal control of constrained switched systems and proved that this algorithm generates a sequence of points that converge to a necessary condition for optimality. However, since our algorithm requires the exact solution of a differential equation, the numerical implementation of this algorithm is impractic...

This paper is devoted to the analysis of a bilinear optimal control problem subject to the Fokker-Planck equation. The control function depends on time and space and acts as a coefficient of the advection term. For this reason, suitable integrability properties of the control function are required to ensure well-posedness of the state equation. Under these low regularity assumptions and for a g...

This paper deals with optimal control problems for systems affine in the control variable. We have nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we get a second order sufficient condition for the scalar control case. The results use in an essential way t...

In this paper, we consider an optimal control problem for a linear infinite order hyperbolic system. One from the initial conditions is given by control function. Sufficient conditions for the existence of a unique solution of such hyperbolic equations with the Dirichlet boundary conditions are presented. The performance functional has the quadratic form. The time horizon T is fixed. Finally, w...

A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers’ equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the ...

In this paper we derive necessary optimality conditions involving Mordukhovich coderivatives for optimal control problems of strongly monotone variational inequalities.

For optimal control problems involving ordinary differential equations and functional inequality state constraints, the maximum principle may degenerate, producing no useful information about minimizers. This is known as the degeneracy phenomenon. Several non-degenerate forms of the maximum principle, valid under different constraint qualifications, have been proposed in the literature. In this...

In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagintype Maximum Principle (MP) for optimal control processes governed by hybrid dynamics with autonomous location transitions, we extend the necessary optimality conditions to a class of Impulsive Hyb...

The aim of this article is to study an optimal control problem for a system of nonlinear elliptic equations with Dirichlet boundary conditions, u x a x x c x u x eu x u x x , Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . x , 1.1 Ž . x b x u x d x x f x u x x , Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . x , u x x 0, on , Ž . Ž . 1, 2 The authors were supported in part by CICYT, Ministry of Education and Culture,...