602 research outputs found
Solving Optimal Control Problem Via Chebyshev Wavelet
Over the last four decades, optimal control problem are solved using direct and indirect methods. Direct methods are based on using polynomials to represent the optimal problem. Direct methods can be implemented using either discretization or parameterization. The proposed method in my thesis is considered as a direct method in which the optimal control problem is directly converted into a mathematical programming problem. A wavelet-based method is presented to solve the non-linear quadratic optimal control problem. The Chebyshev wavelets functions are used as the basis functions. The proposed method is also based on the iteration technique which replaces the nonlinear state equations by an equivalent sequence of linear time-varying state equations which is much easier to solve. Numerical examples are presented to show the effectiveness of the method, several optimal control problems were solved, and the simulation results show that the proposed method gives good and comparable results with some other methods
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Analysis and control of power systems using orthogonal expansions
In recent years, considerable attention has been focused on the application of
orthogonal expansions to system analysis, parameter identification, model reduction
and control system design. However, little research has been done in applying their
useful properties to Power System analysis and control. This research attempts to
make some inroads in applying the so called " orthogonal expansion approach " to
analysis and control of Power systems, especially the latter.
A set of orthogonal functions commonly called Walsh functions in system
science after it's discoverer J.L. Walsh [1923] have been successfully used for
parameter identification in the presence of severe nonlinearities. The classical optimal
control problem is applied to a synchronous machine infinite bus system via the
orthogonal expansion approach and a convenient method outlined for designing PID
controllers which can achieve prespecified closed loop response characteristics. The
latter is then applied for designing a dynamic series capacitor controller for a single
machine infinite bus system
A novel Chebyshev wavelet method for solving fractional-order optimal control problems
This thesis presents a numerical approach based on generalized fractional-order Chebyshev wavelets for solving fractional-order optimal control problems. The exact value of the Riemann– Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets is computed by applying the regularized beta function. We apply the given wavelets, the exact formula, and the collocation method to transform the studied problem into a new optimization problem. The convergence analysis of the proposed method is provided. The present method is extended for solving fractional-order, distributed-order, and variable-order optimal control problems. Illustrative examples are considered to show the advantage of this method in comparison with the existing methods in the literature
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
A theory of intense-field dynamic alignment and high harmonic generation from coherently rotating molecules and interpretation of intense-field ultrafast pump-probe experiments
A theory of ultra-fast pump-probe experiments proposed by us earlier [F.H.M.
Faisal et al., Phys. Rev. Lett. 98, 143001 (2007) and F.H.M. Faisal and A.
Abdurrouf, Phys. Rev. Lett. 100, 123005 (2008)] is developed here fully and
applied to investigate the phenomena of dynamic alignment and high harmonic
generation (HHG) from coherently rotating linear molecules. The theory provides
essentially analytical results for the signals that allow us to investigate the
simultaneous dependence of the HHG signals on the two externally available
control parameters, namely, the relative angle between the polarizations, and
the delay-time between the two pulses. It is applied to investigate the
characteristics of high harmonic emission from nitrogen and oxygen molecules
that have been observed experimentally in a number of laboratories. The results
obtained both in the time-domain and in the frequency-domain are compared with
the observed characteristics as well as directly with the data and are found to
agree remarkably well. In addition we have predicted the existence of a "magic"
polarization angle at which all modulations of the harmonic emission from
nitrogen molecule changes to a steady emission at the harmonic frequency. Among
other things we have also shown a correlation between the existence of the
"magic" or critical polarization angles and the symmetry of the active
molecular orbitals, that is deemed to be useful in connection with the "inverse
problem" of molecular imaging from the HHG data.Comment: 31 pages, 22 figures, and 140 equation
Analogue neuromorphic systems.
This thesis addresses a new area of science and technology, that of neuromorphic
systems, namely the problems and prospects of analogue neuromorphic systems. The
subject is subdivided into three chapters.
Chapter 1 is an introduction. It formulates the oncoming problem of the creation
of highly computationally costly systems of nonlinear information processing (such as
artificial neural networks and artificial intelligence systems). It shows that an analogue
technology could make a vital contribution to the creation such systems. The basic principles
of creation of analogue neuromorphic systems are formulated. The importance
will be emphasised of the principle of orthogonality for future highly efficient complex
information processing systems.
Chapter 2 reviews the basics of neural and neuromorphic systems and informs on
the present situation in this field of research, including both experimental and theoretical
knowledge gained up-to-date. The chapter provides the necessary background for
correct interpretation of the results reported in Chapter 3 and for a realistic decision on
the direction for future work.
Chapter 3 describes my own experimental and computational results within the
framework of the subject, obtained at De Montfort University. These include: the
building of (i) Analogue Polynomial Approximator/lnterpolatoriExtrapolator, (ii) Synthesiser
of orthogonal functions, (iii) analogue real-time video filter (performing the
homomorphic filtration), (iv) Adaptive polynomial compensator of geometrical distortions
of CRT- monitors, (v) analogue parallel-learning neural network (backpropagation
algorithm).
Thus, this thesis makes a dual contribution to the chosen field: it summarises the
present knowledge on the possibility of utilising analogue technology in up-to-date and
future computational systems, and it reports new results within the framework of the
subject. The main conclusion is that due to its promising power characteristics, small
sizes and high tolerance to degradation, the analogue neuromorphic systems will playa
more and more important role in future computational systems (in particular in systems
of artificial intelligence)
Bifurcation and Chaos in Fractional-Order Systems
This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics
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