A Simple Technique for the Minimum Mass Design of Continuous Structural Members

1977 ◽  
Vol 44 (2) ◽  
pp. 285-290 ◽  
Author(s):  
M. Foley ◽  
S. J. Citron
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimization Problem ◽  
Simple Technique ◽  
Minimum Mass ◽  
Structural Members ◽  
State Variables ◽  
Simply Supported ◽  
Euler Buckling

A technique for determining the minimum mass design of continuous structural members is presented. The method involves formulating the minimum mass design problem as an optimal control problem, transforming the differential equations modeling the member into a penalty function, and then representing the state variables in terms of a Ritz-type expansion and discretizing to reduce the original optimal control problem to a parameter optimization problem. The technique is applied to determine the optimal design of a simply supported beam with fixed fundamental frequency of free vibration and a fixed-free column with specified Euler buckling load.

scholarly journals Robust Tracking Control of Mobile Robot Formation with Obstacle Avoidance

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Tiantian Yang ◽  
Zhiyuan Liu ◽  
Hong Chen ◽  
Run Pei
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Formation Control ◽  
Optimization Problem ◽  
Reference Trajectory ◽  
Robust Tracking Control ◽  
Wheeled Mobile Robots ◽  
Lmi Optimization ◽  
Control Scheme

We consider the formation control problem of multiple wheeled mobile robots with parametric uncertainties and actuator saturations in the environment with obstacles. First, a nonconvex optimization problem is introduced to generate the collision-free trajectory. If the robots tracking along the reference trajectory find themselves moving close to the obstacles, a new collision-free trajectory is generated automatically by solving the optimization problem. Then, a distributed control scheme is proposed to keep the robots tracking the reference trajectory. For each interacting robot, optimal control problem is generated. And in the framework of LMI optimization, a distributed moving horizon control scheme is formulated as online solving each optimal control problem at each sampling time. Moreover, closed-loop properties inclusive of stability andH∞performance are discussed. Finally, simulation is performed to highlight the effectiveness of the proposed control law.

scholarly journals Optimal Control of Mechanical Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Vadim Azhmyakov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimization Problem ◽  
Multiobjective Programming ◽  
Optimal Control Problems ◽  
Auxiliary Problem ◽  
Control Problems ◽  
Hamilton Equations ◽  
Variational Structure

In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm.

scholarly journals Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Kin Wei Ng ◽  
Ahmad Rohanin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conjugate Gradient ◽  
Optimization Problem ◽  
Numerical Solutions ◽  
Gradient Methods ◽  
Parabolic Partial Differential Equation ◽  
Conjugate Gradient Methods ◽  
Monodomain Model

We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes-Stiefel-Dai-Yuan (HS-DY) method and the Liu-Storey-Conjugate-Descent (LS-CD) method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.

scholarly journals Sparse Optimal Control for Fractional Diffusion

2018 ◽  
Vol 18 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Enrique Otárola ◽  
Abner J. Salgado
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
A Priori ◽  
Control Variable ◽  
Fractional Diffusion ◽  
State Equation ◽  
Solution Technique ◽  
State Variables ◽  
Regularity Results

AbstractWe consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity results together with first-order optimality conditions. In order to propose a solution technique, we realize fractional diffusion as the Dirichlet-to-Neumann map for a nonuniformly elliptic operator and consider an equivalent optimal control problem with a nonuniformly elliptic equation as state equation. The rapid decay of the solution to this problem suggests a truncation that is suitable for numerical approximation. We propose a fully discrete scheme: piecewise constant functions for the control variable and first-degree tensor product finite elements for the state variable. We derive a priori error estimates for the control and state variables.

scholarly journals Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 452 ◽  
Author(s):  
Madiha Sana ◽  
Muhammad Mustahsan
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
State Variables ◽  
B Splines ◽  
Regularity Of Solution ◽  
Distinct Aspect

In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivatives of state variables, which decrease the regularity of solution. A meshless FEM is proposed using WEB-splines, defined on the usual grid over the domain, R 2 . The weighted extended B-spline method (WEB method) absorbs the regularity problem as the degree of the B-splines is increased. Convergence analysis is also performed by some numerical examples.

scholarly journals Solvability of optimization problem for the oscillation processes with optimal vector controls

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1369-1379
Author(s):  
Elmira Abdyldaeva ◽  
Akylbek Kerimbekov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Unique Solvability ◽  
Optimization Problem ◽  
Complete Solution ◽  
Sufficient Condition ◽  
Optimal Process ◽  
Optimal Vector

The optimal control problem is investigated for oscillation processes, described by integrodifferential equations with the Fredholm operator when functions of external and boundary sources nonlinearly depend on components of optimal vector controls. Optimality conditions having specific properties in the case of vector controls were found. A sufficient condition is established for unique solvability of the nonlinear optimization problem and its complete solution is constructed in the form of optimal control, an optimal process, and a minimum value of the functional.

scholarly journals Solving Optimal Control Linear Systems by Using New Third kind Chebyshev Wavelets Operational Matrix of Derivative

2014 ◽  
Vol 11 (2) ◽  
pp. 229-234
Author(s):  
Baghdad Science Journal
Keyword(s):  
Optimal Control ◽  
Linear System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Operational Matrix ◽  
Control Problems ◽  
State Variables ◽  
Algebraic Equations ◽  
Chebyshev Wavelets

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

Choosing the number of time intervals for solving a model predictive control problem of nonlinear systems

2021 ◽  
pp. 014233122110073
Author(s):  
Jasem Tamimi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Model Predictive Control ◽  
Control Problem ◽  
Predictive Control ◽  
Optimization Problem ◽  
The State ◽  
Nonlinear Program ◽  
Box Constraints ◽  
Time Intervals

Model predictive control (MPC) is a control strategy that can handle state and control multi-variables at same time. To use the MPC using direct methods for solving the a dynamic optimization problem, one needs, for example, to transform the optimization problem into a nonlinear programming (NLP) problem by dividing the prediction horizon into equal time intervals. In this work, we suggest a tool and procedures for helping to choose a ‘compromise’ number of time intervals with a needed accuracy, objective cost, number of turned NLP iterations and computational time. On the other hand, we offer a simplified nonlinear program to ensure the convergence of a class of finite optimal control problem by modifying the state box constraints. In particular, a special type of box constraints were used to the constrained optimal control problem to enforce the state trajectories to reach the desired stationary point. These box constraints are characterized by some parameters that are easily optimized by our proposed nonlinear program. Our proposed tools are tested using two case studies; nonlinear continuous stirred tank reactor (CSTR) and nonlinear batch reactor.

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