3 research outputs found
Boundary element method for convex boundary control problems
summary:In this paper, we discuss the numerical methods for a class of convex boundary control problems. The boundary element method is applied for the approximations of the problems. The a posteriori error estimators for the boundary element approximations are presented, which can be applied as the indicators of the adaptive mesh refinement of the related boundary element methods
Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint
The aim of this work is to study the semidiscrete finite element discretization for a class of semilinear parabolic integrodifferential optimal control problems. We derive a posteriori
error estimates in L2(J;L2(Ω))-norm and L2(J;H1(Ω))-norm for both the control and coupled state approximations. Such estimates can be used to construct reliable adaptive finite element approximation for semilinear parabolic integrodifferential optimal control problem. Furthermore, we introduce an adaptive algorithm to guide the mesh refinement. Finally, a numerical example is given to demonstrate the theoretical results
Optimal control of systems with memory
The “Optimal Control of Systems with memory” is a PhD project that is borne
from the collaboration between the Department of Mechanical and Aerospace
Engineering of Sapienza University of Rome and CNR-INM the Institute for Marine
Engineering of the National Research Council of Italy (ex INSEAN). This project is
part of a larger EDA (European Defence Agency) project called ETLAT: Evaluation
of State of the Art Thin Line Array Technology. ETLAT is aimed at improving
the scientific and technical knowledge of potential performance of current Thin
Line Towed Array (TLA) technologies (element sensors and arrays) in view of
Underwater Surveillance applications.
A towed sonar array has been widely employed as an important tool for naval
defence, ocean exploitation and ocean research. Two main operative limitations
costrain the TLA design such as: a fixed immersion depth and the stabilization of
its horizontal trim. The system is composed by a towed vehicle and a towed line
sonar array (TLA). The two subsystems are towed by a towing cable attached to
the moving boat. The role of the vehicle is to guarantee a TLA’s constant depth of
navigation and the reduction of the entire system oscillations. The vehicle is also
called "depressor" and its motion generates memory effects that influence the proper
operation of the TLA. The dynamic of underwater towed system is affected by
memory effects induced by the fluid-structure interaction, namely: vortex shedding
and added damping due to the presence of a free surface in the fluid. In time
domain, memory effects are represented by convolution integral between special
kernel functions and the state of the system. The mathematical formulation of the
underwater system, implies the use of integral-differential equations in the time
domain, that requires a nonstandard optimal control strategy. The goal of this
PhD work is to developed a new optimal control strategy for mechanical systems
affected by memory effects and described by integral-differential equations. The
innovative control method presented in this thesis, is an extension of the Pontryagin
optimal solution which is normally applied to differential equations. The control is
based on the variational control theory implying a feedback formulation, via model
predictive control.
This work introduces a novel formulation for the control of the vehicle and cable
oscillations that can include in the optimal control integral terms besides the more
conventional differential ones. The innovative method produces very interesting
results, that show how even widely applied control methods (LQR) fail, while the
present formulation exhibits the advantage of the optimal control theory based on
integral-differential equations of motion