2 research outputs found
An efficient hybrid pseudo-spectral method for solving optimal control of Volterra integral systems
In this paper, a new pseudo-spectral (PS) method is developed for solving optimal controproblems governed by the non-linear Volterra integral equation(VIE). The novel method is based upon approximating the state and control variables by the hybrid of block pulse functions and Legendre polynomials. The properties of hybrid functions are presented. The numerical integration and collocation method is utilized to discretize the continuous optimal control problem and then the resulting large-scale finite-dimensional non-linear programming (NLP) is solved by the existing well-developed algorithm in Mathematica software. A set of sufficient conditions is presented under which optimal solutions of discrete optimal control problems converge to the optimal solution of the continuous problem. The error bound of approximation is also given. Numerical experiments confirm efficiency of the proposed method especially for problems with non-sufficiently smooth solutions belonging to class or
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