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.

Experimental Study on Optimal Tracking Control of a Micro Ground Vehicle

2017 ◽  
Vol 29 (4) ◽  
pp. 757-765 ◽  
Author(s):  
Soichiro Watanabe ◽  
◽  
Masanori Harada
Keyword(s):  
Experimental Study ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Predictive Control ◽  
Tracking Control ◽  
Reference Trajectory ◽  
Ground Vehicle ◽  
Optimal Tracking ◽  
Tracking Controller

This paper investigates the application of optimal control to a micro ground vehicle (MGV) experimentally. The model predictive control (MPC) technique is used for the overall tracking controller during the maneuver. The reference trajectory for MPC is preliminarily obtained by numerical computation of the optimal control problem, which is prescribed as a minimum-time maneuver. The results provide nominal tracking performance and validate the feasibility of the approach.

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.

Optimal Tracking Control of a Micro Ground Vehicle

2015 ◽  
Vol 27 (6) ◽  
pp. 653-659 ◽  
Author(s):  
Soichiro Watanabe ◽  
◽  
Masanori Harada
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Coordinate System ◽  
Predictive Control ◽  
Tracking Control ◽  
Minimum Time ◽  
Reference Trajectory ◽  
Ground Vehicle ◽  
Optimal Tracking

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00270006/07.jpg"" width=""300"" /> Coordinate system of MGV</div>This paper investigates the application of optimal micro ground vehicle (MGV) control involving overall tracking by model-predictive control (MPC) during a minimum-time maneuver. The MPC’s reference trajectory is obtained beforehand by numerically calculating an optimal control problem described as a minimum-time maneuver. Results provide nominal tracking performance and confirm the feasibility of our approach.

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 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.

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.

Route-dependent optimal control of the after-treatment system of diesel engines

2019 ◽  
Vol 22 (1) ◽  
pp. 64-76
Author(s):  
Fuguo Xu ◽  
Hideki Matsunaga ◽  
Atsushi Kato ◽  
Yuji Yasui ◽  
Tielong Shen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nitrogen Oxide ◽  
Diesel Engines ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Nitrogen Oxide Emission ◽  
Control Scheme ◽  
Oxide Trap

In this article, the optimal control problem for nitrogen oxide emission reduction is investigated for diesel engines with a lean nitrogen oxide trap. First, a control-oriented model is developed based on conservation laws. Then, the optimal control problem is formulated as a multistage decision problem and solved using a dynamic programming algorithm under dynamical model constraints. A trade-off between fuel economy and nitrogen oxide emission is considered in the cost function of optimization. To demonstrate the obtained optimal control scheme, the parameters of the lean nitrogen oxide trap model are identified with data obtained from a GT-power-based diesel engine simulator. The numerical simulation results for two standard driving cycles and a stochastically generated driving cycle in comparison to a conventional logic-based control scheme are provided using the identified model in the MATLAB/Simulink platform.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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