Several recent works have been devoted to the analysis of this field for the error estimates, for example, Cao and Yang got the a priori error estimates using Ciarlet-Raviart mixed finite element methods for the fourth order control problems governed by the first bi-harmonic equation (see [24]).
By choosing this composite variable so that the implicit differential equation is stable, high order control problems can be reduced to first-order problems, amenable to qualitative feedback strategies, typically organized in intermittent manner.
The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant "no spill-over property" of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result.
And to make the proposed method can be applied in a more general situation of synchronization of chaotic systems, a special second order system control problem with double control coefficients was researched first.
It is well known that the reduced-order H∞ control problem is equivalent to the problem of checking the feasibility of three LMI constraints as well as a rank constraint.
Tricaud and Chen have solved fractional order optimal control problems by means of rational approximation [3].
Firstly, we discuss the semi-discrete mixed finite element approximation for the fourth order parabolic optimal control problem in Section 2.
In order to solve this control problem, two controllers are designed, an artificial neural network, whose input is the setpoint, is used to provide the steady state control command, and a fuzzy inference system, whose input is the error of the system, is used to provide the transient control command.
For instance in [21] an efficient linear programming formulation is proposed for a class of fractional-order optimal control problems with delay argument.
In this paper, a fourth order quadratic parabolic optimal control problem is analyzed.
