A Numerical Computation Approach for the Optimal Control of ASP Flooding Based on Adaptive Strategies

A numerical computation approach based on constraint aggregation and pseudospectral method is proposed to solve the optimal control of alkali/surfactant/polymer (ASP) flooding. At first, all path constraints are aggregated into one terminal condition by applying a Kreisselmeier-Steinhauser (KS) function. After being transformed into a multistage problem by control vector parameter, a normalized time variable is introduced to convert the original problem into a fixed final time optimal control problem. Then the problem is discretized to nonlinear programming by using Legendre-Gauss pseudospectral method, whose numerical solutions can be obtained by sequential quadratic programming (SQP) method through solving the KKT optimality conditions. Additionally, two adaptive strategies are applied to improve the procedure: (1) the adaptive constraint aggregation is used to regulate the parameter ρ in KS function and (2) the adaptive Legendre-Gauss (LG) method is used to adjust the number of subinterval divisions and LG points. Finally, the optimal control of ASP flooding is solved by the proposed method. Simulation results show the feasibility and effectiveness of the proposed method.

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Pseudospectral Real-Time Optimal Energy Control with Safety Constraints for Heavy-Haul Trains

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2017.p0258 ◽

2017 ◽

Vol 21 (2) ◽

pp. 258-265

Author(s):

Rui Zhang ◽

◽

Jun Peng ◽

Bin Chen ◽

Hongtao Liao ◽

...

Keyword(s):

Optimal Control ◽

Real Time ◽

Closed Loop ◽

Pseudospectral Method ◽

Heavy Haul Train ◽

Heavy Haul ◽

Time Optimal ◽

Safety Constraints ◽

Heavy Haul Trains ◽

Control Principle

Heavy-haul trains must be energy-efficient and safe during their operations. Owing to the multidimensional high-order nonlinear characteristic of heavy-haul trains, which include numerous cars, this paper proposes a uniform pseudospectral real-time closed-loop optimal control framework to minimize the energy consumption with control inputs and state constraints based on the Radau Pseudospectral Method (RPM). In the framework, in order to ensure safe running of the heavy-haul train, the desired in-train force and speed limit requirements are formulated as constraints of optimal control. Simultaneously, a constrained closed-loop optimal control is constructed by using the receding horizon control principle and pseudospectral observer, in which RPM is leveraged to obtain real-time optimal solutions. The effectiveness of the proposed approach is verified from simulation results.

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Numerical Analysis of Constrained, Time-Optimal Satellite Reorientation

Mathematical Problems in Engineering ◽

10.1155/2012/769376 ◽

2012 ◽

Vol 2012 ◽

pp. 1-19 ◽

Cited By ~ 2

Author(s):

Robert G. Melton

Keyword(s):

Numerical Analysis ◽

High Intensity ◽

Numerical Solutions ◽

Pseudospectral Method ◽

Optimal Solutions ◽

Path Constraints ◽

Time Optimal ◽

Stage Process ◽

Legendre Pseudospectral Method ◽

Method Show

Previous work on time-optimal satellite slewing maneuvers, with one satellite axis (sensor axis) required to obey multiple path constraints (exclusion from keep-out cones centered on high-intensity astronomical sources) reveals complex motions with no part of the trajectory touching the constraint boundaries (boundary points) or lying along a finite arc of the constraint boundary (boundary arcs). This paper examines four cases in which the sensor axis is either forced to follow a boundary arc, or has initial and final directions that lie on the constraint boundary. Numerical solutions, generated via a Legendre pseudospectral method, show that the forced boundary arcs are suboptimal. Precession created by the control torques, moving the sensor axis away from the constraint boundary, results in faster slewing maneuvers. A two-stage process is proposed for generating optimal solutions in less time, an important consideration for eventual onboard implementation.

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Time Optimal Trajectories for a Mobile Robot Under Nonsliding and Radius-of-Turn Constraints

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4046331 ◽

2020 ◽

Vol 142 (6) ◽

Author(s):

Joseph Z. Ben-Asher ◽

Michael Wetzler ◽

Elon D. Rimon

Keyword(s):

Optimal Control ◽

Mobile Robot ◽

Numerical Solutions ◽

Optimal Path ◽

Linear Acceleration ◽

Optimal Trajectories ◽

Hodograph Method ◽

Minimal Radius ◽

Time Optimal ◽

Target States

Abstract The time-optimal path problem for a point mass mobile robot is considered. Given initial and target states, we seek the time optimal path subject to the following constraints: (1) A limitation on its maximal linear acceleration; (2) a speed-dependent nonsliding condition; and (3) a minimal radius of turn. The paper formulates and analyzes the time optimal path problem using standard optimal control formulation with extensive use of the classical Hodograph method. Based on the analysis, the time optimal path consists of five path primitives. Numerical solutions are obtained to support and illustrate the analysis.

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A pseudospectral method for budget-constrained infinite horizon optimal control problems

ESAIM Proceedings and Surveys ◽

10.1051/proc/202171145 ◽

2021 ◽

Vol 71 ◽

pp. 145-154

Author(s):

Angie Burtchen ◽

Valeriya Lykina ◽

Sabine Pickenhain

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Numerical Solutions ◽

Infinite Horizon ◽

Pseudospectral Method ◽

Linear Quadratic Regulator ◽

Approximate Solutions ◽

Control Problems ◽

Linear Quadratic ◽

Weighted Functional Spaces

In this paper a generalization of the indirect pseudo-spectral method, presented in [17], for the numerical solution of budget-constrained infinite horizon optimal control problems is presented. Consideration of the problem statement in the framework of weighted functional spaces allows to arrive at a good approximation for the initial value of the adjoint variable, which is inevitable for obtaining good numerical solutions. The presented method is illustrated by applying it to the budget-constrained linear-quadratic regulator model. The quality of approximate solutions is demonstrated by an example.

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Numerical Computation for a Kind of Time Optimal Control Problem for the Tubular Reactor System

Mathematical Problems in Engineering ◽

10.1155/2018/9580470 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9

Author(s):

Detang Zeng ◽

Xin Yu ◽

Jingfang Huang ◽

Chunqing Tan

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Numerical Computation ◽

Optimal Parameter ◽

Tubular Reactor ◽

Parameter Selection ◽

Time Optimal Control ◽

Time Optimal ◽

Time Optimal Control Problem

This paper is devoted to the study of numerical computation for a kind of time optimal control problem for the tubular reactor system. This kind of time optimal control problem is aimed at delaying the initiation time τ of the active control as late as possible, such that the state governed by this controlled system can reach the target set at a given ending time T. To compute the time optimal control problem, we firstly approximate the original problem by finite element method and get a new approximation time optimal control problem governed by ordinary differential equations. Then, through the control parameterization method and time-scaling transformation, the approximation problem becomes an optimal parameter selection problem. Finally, we use Sequential Quadratic Program algorithm to solve the optimal parameter selection problem. A numerical simulation is given for illustration.

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