Existence, uniqueness, and stability of solutions to singular linear quadratic optimal control problems

Existence and Uniqueness of Solutions for Boundary Value Problems to the Singular One-Dimension p-Laplacian

Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems

In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.

Haar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems

‎In this paper‎, ‎Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems‎. ‎Firstly‎, ‎using necessary conditions for optimality‎, ‎the problem is changed into a two-boundary value problem (TBVP)‎. ‎Next‎, ‎Haar wavelets are applied for converting the TBVP‎, ‎as a system of differential equations‎, ‎in to a system of matrix algebraic equations‎...

On the Essential Boundedness of Solutions to Problems in Piecewise Linear-quadratic Optimal Control

Primal and dual problems of optimal control with linear, quadratic or piecewise linear-quadratic convex objective are considered in which a linear dynamical system is subjected to linear inequality constraints that could jointly involve states and controls. It is shown that when such constraints, except for the ones on controls only, are represented by penalty terms, and a mild coercivity condi...

Existence and Uniqueness of Solutions for Singular Higher Order Continuous and Discrete Boundary Value Problems