383 research outputs found
Expected Utility Maximization and Conditional Value-at-Risk Deviation-based Sharpe Ratio in Dynamic Stochastic Portfolio Optimization
In this paper we investigate the expected terminal utility maximization
approach for a dynamic stochastic portfolio optimization problem. We solve it
numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which
is transformed by means of the Riccati transformation. We examine the
dependence of the results on the shape of a chosen utility function in regard
to the associated risk aversion level. We define the
Conditional value-at-risk deviation () based Sharpe ratio for
measuring risk-adjusted performance of a dynamic portfolio. We compute optimal
strategies for a portfolio investment problem motivated by the German DAX 30
Index and we evaluate and analyze the dependence of the -based Sharpe
ratio on the utility function and the associated risk aversion level
Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming
© 2019, Springer-Verlag London Ltd., part of Springer Nature. In this paper, a novel application of biologically inspired computing paradigm is presented for solving initial value problem (IVP) of electric circuits based on nonlinear RL model by exploiting the competency of accurate modeling with feed forward artificial neural network (FF-ANN), global search efficacy of genetic algorithms (GA) and rapid local search with sequential quadratic programming (SQP). The fitness function for IVP of associated nonlinear RL circuit is developed by exploiting the approximation theory in mean squared error sense using an approximate FF-ANN model. Training of the networks is conducted by integrated computational heuristic based on GA-aided with SQP, i.e., GA-SQP. The designed methodology is evaluated to variants of nonlinear RL systems based on both AC and DC excitations for number of scenarios with different voltages, resistances and inductance parameters. The comparative studies of the proposed results with Adam’s numerical solutions in terms of various performance measures verify the accuracy of the scheme. Results of statistics based on Monte-Carlo simulations validate the accuracy, convergence, stability and robustness of the designed scheme for solving problem in nonlinear circuit theory
A novel design of fractional Mayer wavelet neural networks with application to the nonlinear singular fractional Lane-Emden systems
In this study, a novel stochastic computational frameworks based on fractional Meyer wavelet artificial neural network (FMW-ANN) is designed for nonlinear-singular fractional Lane-Emden (NS-FLE) differential equation. The modeling strength of FMW-ANN is used to transformed the differential NS-FLE system to difference equations and approximate theory is implemented in mean squared error sense to develop a merit function for NS-FLE differential equations. Meta-heuristic strength of hybrid computing by exploiting global search efficacy of genetic algorithms (GA) supported with local refinements with efficient active-set (AS) algorithm is used for optimization of design variables FMW-ANN., i.e., FMW-ANN-GASA. The proposed FMW-ANN-GASA methodology is implemented on NS-FLM for six different scenarios in order to exam the accuracy, convergence, stability and robustness. The proposed numerical results of FMW-ANN-GASA are compared with exact solutions to verify the correctness, viability and efficacy. The statistical observations further validate the worth of FMW-ANN-GASA for the solution of singular nonlinear fractional order systems.This paper is partially supported by Ministerio de Ciencia, Innovación y Universidades grant number PGC2018-097198-BI00
and Fundación Séneca de la Región de Murcia grant number 20783/PI/18
Design Optimization, Analysis, and Control of Walking Robots
Passive dynamic walking refers to the dynamical behavior of mechanical devices that are able to naturally walk down a shallow slope in a stable manner, without using actuation or sensing of any kind. Such devices can attain motions that are remarkably human-like by purely exploiting their natural dynamics. This suggests that passive dynamic walking machines can be used to model and study human locomotion; however, there are two major limitations: they can be difficult to design, and they cannot walk on level ground or uphill without some kind of actuation.
This thesis presents a mechanism design optimization framework that allows the designer to find the best design parameters based on the chosen performance metric(s). The optimization is formulated as a convex problem, where its solutions are globally optimal and can be obtained efficiently.
To enable locomotion on level ground and uphill, this thesis studies a robot based on a passive walker: the rimless wheel with an actuated torso. We design and validate two control policies for the robot through the use of scalable methodology based on tools from mathematical analysis, optimization theory, linear algebra, differential equations, and control theory
A control-theoretic approach to dynamic optimization of metabolic networks
The characterization of general control principles that underpin metabolic dynamics
is an important part of systems analysis in biology. It has been long argued
that many biological regulatory mechanisms have evolved so as to optimize cellular
adaptation in response to external stimuli. In this thesis we use an optimal control
framework to solve dynamic optimization problems associated with metabolic
dynamics. The analysis is based on a nonlinear control-ane model of a metabolic
network with the enzyme concentrations as control inputs.
We consider the optimization of time-dependent enzyme concentrations to activate
an unbranched network and reach a prescribed metabolic
ux. The solution
accounts for time-resource optimality under constraints in the total enzymatic
abundance. We identify a temporal pattern in the solution that is consistent with
previous experimental and numerical observations. Our analysis suggests that this
behaviour may appear in a broader class of networks than previously considered.
In addition, we address the optimization of time-dependent enzyme expression
rates for a metabolic network coupled with a model of enzyme dynamics. The formulation
accounts for the transition between two metabolic steady states in networks
with arbitrary stoichiometries and enzyme kinetics. We consider a nite horizon
quadratic cost function that weighs the deviations of metabolites, enzymes and
their expression rates from their target values, together with the time-derivative
of the expression rates. The problem is recast as an iterative sequence of Linear
Quadratic Tracking problems, and we derive conditions under which the iterations
converge to a suboptimal solution of the original problem. Additionally, if constant
metabolite concentrations are enforced, the nonlinear system can be written as a
linear Dierential-Algebraic system. In the innite horizon case the problem can be
recast as a standard Linear Quadratic Regulator problem for a lower-dimensional
system, the solution of which is readily available
A control-theoretic approach to dynamic optimization of metabolic networks
The characterization of general control principles that underpin metabolic dynamics
is an important part of systems analysis in biology. It has been long argued
that many biological regulatory mechanisms have evolved so as to optimize cellular
adaptation in response to external stimuli. In this thesis we use an optimal control
framework to solve dynamic optimization problems associated with metabolic
dynamics. The analysis is based on a nonlinear control-ane model of a metabolic
network with the enzyme concentrations as control inputs.
We consider the optimization of time-dependent enzyme concentrations to activate
an unbranched network and reach a prescribed metabolic
ux. The solution
accounts for time-resource optimality under constraints in the total enzymatic
abundance. We identify a temporal pattern in the solution that is consistent with
previous experimental and numerical observations. Our analysis suggests that this
behaviour may appear in a broader class of networks than previously considered.
In addition, we address the optimization of time-dependent enzyme expression
rates for a metabolic network coupled with a model of enzyme dynamics. The formulation
accounts for the transition between two metabolic steady states in networks
with arbitrary stoichiometries and enzyme kinetics. We consider a nite horizon
quadratic cost function that weighs the deviations of metabolites, enzymes and
their expression rates from their target values, together with the time-derivative
of the expression rates. The problem is recast as an iterative sequence of Linear
Quadratic Tracking problems, and we derive conditions under which the iterations
converge to a suboptimal solution of the original problem. Additionally, if constant
metabolite concentrations are enforced, the nonlinear system can be written as a
linear Dierential-Algebraic system. In the innite horizon case the problem can be
recast as a standard Linear Quadratic Regulator problem for a lower-dimensional
system, the solution of which is readily available
Nonlinear Systems
Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems
Optimal PMU-based monitoring architecture design for power systems
International audienceThis paper is dedicated to a new methodology for designing an optimal monitoring architecture by using a limited number of PMUs (Phasor Measurement Units) and PDCs (Phase Data Concentrators). The optimal design problem consists in defining the optimal location of both PMUs and PDCs by maximizing the expected value of the trace of the observability gramian of the power system over a large number of set point scenarios, while minimizing some communication infrastructure costs. Furthermore, a nonlinear dynamical state-observer, based on the Extended Kalman Filter, is proposed. This state-observer allows to take transient phenomena into account for wide-area power systems described by algebraic-differential equations, without needing nonlinear inversion techniques. The overall approach is illustrated with the IEEE 10 generator 39 bus New England power system
Identification and Optimal Linear Tracking Control of ODU Autonomous Surface Vehicle
Autonomous surface vehicles (ASVs) are being used for diverse applications of civilian and military importance such as: military reconnaissance, sea patrol, bathymetry, environmental monitoring, and oceanographic research. Currently, these unmanned tasks can accurately be accomplished by ASVs due to recent advancements in computing, sensing, and actuating systems. For this reason, researchers around the world have been taking interest in ASVs for the last decade. Due to the ever-changing surface of water and stochastic disturbances such as wind and tidal currents that greatly affect the path-following ability of ASVs, identification of an accurate model of inherently nonlinear and stochastic ASV system and then designing a viable control using that model for its planar motion is a challenging task. For planar motion control of ASV, the work done by researchers is mainly based on the theoretical modeling in which the nonlinear hydrodynamic terms are determined, while some work suggested the nonlinear control techniques and adhered to simulation results. Also, the majority of work is related to the mono- or twin-hull ASVs with a single rudder. The ODU-ASV used in present research is a twin-hull design having two DC trolling motors for path-following motion.
A novel approach of time-domain open-loop observer Kalman filter identifications (OKID) and state-feedback optimal linear tracking control of ODU-ASV is presented, in which a linear state-space model of ODU-ASV is obtained from the measured input and output data. The accuracy of the identified model for ODU-ASV is confirmed by validation results of model output data reconstruction and benchmark residual analysis. Then, the OKID-identified model of the ODU-ASV is utilized to design the proposed controller for its planar motion such that a predefined cost function is minimized using state and control weighting matrices, which are determined by a multi-objective optimization genetic algorithm technique. The validation results of proposed controller using step inputs as well as sinusoidal and arc-like trajectories are presented to confirm the controller performance. Moreover, real-time water-trials were performed and their results confirm the validity of proposed controller in path-following motion of ODU-ASV
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