Approximate Penalty Method in Optimal Control Problems for Nonsmooth Singular Systems

Rend. Circ. Mat. Palermo

Mokhtar-Kharroubi

2010

We consider an abstract optimal control problem with additional equality and inequality state and control constraints, we use the exterior penalty function to transform the constrained optimal control problem into a sequence of unconstrained optimal control problems, under conditions in control lie in L 1 , the sequence of the solution to the unconstrained problem contains a subsequence converging of the solution of constrained problem, this convergence is strong when the problem is non convex, and is weak if the problem is convex in control. This generalizes the results of P.Nepomiastcthy [4] where he considered the control in the Hilbert space L 2 (I, R m ).

mentioning

confidence: 99%

“…In [4], it is shown that this convergence when the control lie in the Hilbert space L 2 (I, R m ) and piecewise equilipschitizian. In [5], it shown that the approximate penalty method can be used to find an approximate (in the weak sens) solution of an abstract optimal control problem linear in the control, with additional constraints and nonsmooth terms.…”

mentioning

confidence: 99%

Exterior penalty in optimal control problem with state-control constraints

Rend. Circ. Mat. Palermo

Mokhtar-Kharroubi

2010

A class of optimal control problems governed by singular systems via Balakrishnan’s method

Makreloufi

IMA Journal of Mathematical Control and Information

2020

The purpose of this paper is to discuss, by the use of the Balakrishnan’s epsilon method, a class of optimal control problems governed by continuous linear time invariant singular systems which have only a finite dynamic mode. The linear differential algebraic equation is handled using the epsilon technique to obtain a sequence of the calculus of variations problems. A convergence theorem is given to obtain approximate and, in the limit, an optimal solution of this class of optimal control problem by the use of the necessary optimality conditions of Euler–Lagrange type. A correspondence has been also shown between this penalty function and duality for this class of optimal control problems considered. As an application, an example of optimal linear quadratic problem is also given.

Optimal Control with Time Delays via the Penalty Method

Mathematical Problems in Engineering

Torres

2014

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.