scholarly journals Optimal control problems in transport dynamics

2017 ◽  
Vol 27 (03) ◽  
pp. 427-451 ◽  
Author(s):  
Mattia Bongini ◽  
Giuseppe Buttazzo
Keyword(s):  
Optimal Control ◽  
Population Dynamics ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Unmanned Aerial Vehicles ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Transport Dynamics ◽  
Aerial Vehicles ◽  
The Cost

In the present paper, we deal with an optimal control problem related to a model in population dynamics; more precisely, the goal is to modify the behavior of a given density of individuals via another population of agents interacting with the first. The cost functional to be minimized to determine the dynamics of the second population takes into account the desired target or configuration to be reached as well as the quantity of control agents. Several applications may fall into this framework, as for instance driving a mass of pedestrian in (or out of) a certain location; influencing the stock market by acting on a small quantity of key investors; controlling a swarm of unmanned aerial vehicles by means of few piloted drones.

scholarly journals Numerical Optimal Control of HIV Transmission in Octave/MATLAB

2019 ◽  
Vol 25 (1) ◽  
pp. 1 ◽  
Author(s):  
Carlos Campos ◽  
Cristiana J. Silva ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Initial Value

We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin’s maximum principle. For that, we consider a normalized HIV/AIDS transmission dynamics model based on the one proposed in our recent contribution (Silva, C.J.; Torres, D.F.M. A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde. Ecol. Complex. 2017, 30, 70–75), given by a system of four ordinary differential equations. An HIV initial value problem is solved numerically using the ode45 GNU Octave function and three standard methods implemented by us in Octave/MATLAB: Euler method and second-order and fourth-order Runge–Kutta methods. Afterwards, a control function is introduced into the normalized HIV model and an optimal control problem is formulated, where the goal is to find the optimal HIV prevention strategy that maximizes the fraction of uninfected HIV individuals with the least HIV new infections and cost associated with the control measures. The optimal control problem is characterized analytically using the Pontryagin Maximum Principle, and the extremals are computed numerically by implementing a forward-backward fourth-order Runge–Kutta method. Complete algorithms, for both uncontrolled initial value and optimal control problems, developed under the free GNU Octave software and compatible with MATLAB are provided along the article.

Local generalization of transversality conditions for optimal control problem

2019 ◽  
Vol 14 (3) ◽  
pp. 310
Author(s):  
Beyza Billur İskender Eroglu ◽  
Dіlara Yapişkan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Hamiltonian Formalism ◽  
Variational Calculus ◽  
Control Problems ◽  
Conformable Derivative ◽  
Transversality Conditions ◽  
Control Functions

In this paper, we introduce the transversality conditions of optimal control problems formulated with the conformable derivative. Since the optimal control theory is based on variational calculus, the transversality conditions for variational calculus problems are first investigated and then supported by some illustrative examples. Utilizing from these formulations, the transversality conditions for optimal control problems are attained by using the Hamiltonian formalism and Lagrange multiplier technique. To illustrate the obtained results, the dynamical system on which optimal control problem constructed is taken as a diffusion process modeled in terms of the conformable derivative. The optimal control law is achieved by analytically solving the time dependent conformable differential equations occurring from the eigenfunction expansions of the state and the control functions. All figures are plotted using MATLAB.

Sensitivity analysis for optimal control problems described by nonlinear fractional evolution inclusions

2018 ◽  
Vol 21 (6) ◽  
pp. 1439-1470 ◽  
Author(s):  
Xiuwen Li ◽  
Yunxiang Li ◽  
Zhenhai Liu ◽  
Jing Li
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Mild Solutions ◽  
Control Problems ◽  
Initial Condition ◽  
Evolution Inclusions ◽  
Technical Details

Abstract In this paper, a sensitivity analysis of optimal control problem for a class of systems described by nonlinear fractional evolution inclusions (NFEIs, for short) on Banach spaces is investigated. Firstly, the nonemptiness as well as the compactness of the mild solutions set S(ζ) (ζ being the initial condition) for the NFEIs are obtained, and we also present an extension Filippov’s theorem and whose proof differs from previous work only in some technical details. Finally, the optimal control problems described by NFEIs depending on the initial condition ζ and the parameter η are considered and the sensitivity properties of the optimal control problem are also established.

scholarly journals A global method for some class of optimization and control problems

2000 ◽  
Vol 23 (9) ◽  
pp. 605-616 ◽  
Author(s):  
R. Enkhbat
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Convex Function ◽  
Control Problem ◽  
Optimality Condition ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Global Method ◽  
Optimization And Control ◽  
And Control

The problem of maximizing a nonsmooth convex function over an arbitrary set is considered. Based on the optimality condition obtained by Strekalovsky in 1987 an algorithm for solving the problem is proposed. We show that the algorithm can be applied to the nonconvex optimal control problem as well. We illustrate the method by describing some computational experiments performed on a few nonconvex optimal control problems.

scholarly journals CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS

2009 ◽  
Vol 06 (07) ◽  
pp. 1221-1233 ◽  
Author(s):  
MARÍA BARBERO-LIÑÁN ◽  
MIGUEL C. MUÑOZ-LECANDA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Control Problems ◽  
Affine System

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.

scholarly journals A space–time pseudospectral discretization method for solving diffusion optimal control problems with two-sided fractional derivatives

2018 ◽  
Vol 25 (5) ◽  
pp. 1080-1095 ◽  
Author(s):  
Mushtaq Salh Ali ◽  
Mostafa Shamsi ◽  
Hassan Khosravian-Arab ◽  
Delfim F. M. Torres ◽  
Farid Bozorgnia
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Original Problem ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Processing Unit ◽  
Quadratic Optimization Problem ◽  
Central Processing ◽  
Main Challenge

We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is discretized by using the Jacobi–Gauss pseudospectral discretization and, in this way, the original problem is transformed into a classical integer–order optimal control problem. The main challenge, which we faced in this step, is to derive the left and right fractional differentiation matrices. In this respect, novel techniques for derivation of these matrices are presented. In the second step, the Legendre–Gauss–Radau pseudospectral method is employed. With these two steps, the original problem is converted into a convex quadratic optimization problem, which can be solved efficiently by available methods. Our approach can be easily implemented and extended to cover fractional optimal control problems with state constraints. Five test examples are provided to demonstrate the efficiency and validity of the presented method. The results show that our method reaches the solutions with good accuracy and a low central processing unit time.

Periodic Control of Unmanned Aerial Vehicles Based on Differential Flatness

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Oladapo Ogunbodede ◽  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Unmanned Aerial Vehicles ◽  
Differential Flatness ◽  
Marine Animals ◽  
Periodic Control ◽  
Aerial Vehicles ◽  
Locomotory Behavior ◽  
Long Endurance

Unmanned aerial vehicles (UAVs) are making increasingly long flights today with significantly longer mission times. This requires the UAVs to have long endurance as well as have long range capabilities. Motivated by locomotory patterns in birds and marine animals which demonstrate a powered-coasting-powered periodic locomotory behavior, an optimal control problem is formulated to study UAV trajectory planning. The concept of differential flatness is used to reformulate the optimal control problem as a nonlinear programing problem where the flat outputs are parameterized using Fourier series. The Π test is also used to verify the existence of a periodic solution which outperforms the steady-state motion. An example of an Aerosonde UAV is used to illustrate the improvement in endurance and range costs of the periodic control solutions relative to the equilibrium flight.

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.

Trajectory planning with mid-air collision avoidance for quadrotor unmanned aerial vehicles

2021 ◽  
pp. 095441002110440
Author(s):  
Yuhang Jiang ◽  
Shiqiang Hu ◽  
Christopher J Damaren
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Unmanned Aerial Vehicles ◽  
Collision Avoidance ◽  
Trajectory Planning ◽  
Pseudospectral Method ◽  
Planning Problem ◽  
Aerial Vehicles ◽  
Optimal Control Algorithms

Flight collision between unmanned aerial vehicles (UAVs) in mid-air poses a potential risk to flight safety in low-altitude airspace. This article transforms the problem of collision avoidance between quadrotor UAVs into a trajectory-planning problem using optimal control algorithms, therefore achieving both robustness and efficiency. Specifically, the pseudospectral method is introduced to solve the raised optimal control problem, while the generated optimal trajectory is precisely followed by a feedback controller. It is worth noting that the contributions of this article also include the introduction of the normalized relative coordinate, so that UAVs can obtain collision-free trajectories more conveniently in real time. The collision-free trajectories for a classical scenario of collision avoidance between two UAVs are given in the simulation part by both solving the optimal control problem and querying the prior results. The scalability of the proposed method is also verified in the simulation part by solving a collision avoidance problem among multiple UAVs.

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