OCP Benchmarks

Main.MoreDynamicOptimizationBenchmarks History

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March 06, 2025, at 04:49 AM by 10.35.117.248 -

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!!!! [[https://apmonitor.com/wiki/index.php/Apps/ElectricVehicleEnergy|Electric Vehicle Energy]]

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!!!! [[https://apmonitor.com/wiki/index.php/Apps/AircraftControl|Aircraft Control]]

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March 26, 2023, at 04:34 AM by 136.36.4.38 -

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!!!! [[https://apmonitor.com/wiki/index.php/Apps/DroneFlight|Drone Flight]]

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March 26, 2023, at 04:17 AM by 136.36.4.38 -

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March 26, 2023, at 03:26 AM by 136.36.4.38 -

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Optimal Control Problem (OCP) solvers are a powerful tool for designing control strategies that optimize a given objective function subject to constraints. They are widely used in engineering, economics, finance, and management, and are applied to a wide range of problems to find optimal solutions that minimize costs, maximize profits, reduce risk, or achieve other desired outcomes. The control strategy is typically represented as a function of time that maps the control input (manipulated variable) to the state of the system. The state of the system is determined by a set of differential equations, and the objective function is a measure of the system performance over a time horizon.

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'''Objective:''' Set up and solve several ~~optimal control problem (OCP)~~ benchmarks. Create a program to optimize and display the results. ''Estimated Time (each): 30 minutes''

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'''Objective:''' Set up and solve several OCP benchmarks. Create a program to optimize and display the results. ''Estimated Time (each): 30 minutes''

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March 26, 2023, at 03:11 AM by 136.36.4.38 -

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March 26, 2023, at 03:10 AM by 136.36.4.38 -

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(:title ~~Optimal Control Benchmark Problems II~~:)

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(:title OCP Benchmarks:)

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'''Objective:''' Set up and solve several optimal control ~~benchmark problems~~. Create a program to optimize and display the results. ''Estimated Time (each): 30 minutes''

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'''Objective:''' Set up and solve several optimal control problem (OCP) benchmarks. Create a program to optimize and display the results. ''Estimated Time (each): 30 minutes''

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March 26, 2023, at 03:09 AM by 136.36.4.38 -

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Attach:download.png [[Attach:dynamic_optimization_catalyst.zip|Catalyzed Reaction Optimized in MATLAB ~~and Python~~]] and [[https://youtu.be/jB7WWGHFNIw|Video]]

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Attach:download.png [[Attach:dynamic_optimization_catalyst.zip|Catalyzed Reaction Optimized in MATLAB]] and [[https://youtu.be/jB7WWGHFNIw|Video]]

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March 26, 2023, at 03:08 AM by 136.36.4.38 -

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Attach:download.png [[Attach:dynamic_optimization_alychan.zip|Dynamic Optimization Aly-Chan Solution in MATLAB and ~~Python~~]]

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Attach:download.png [[Attach:dynamic_optimization_alychan.zip|Dynamic Optimization Aly-Chan Solution in MATLAB]] and [[https://youtu.be/tY8kyJq4BEY|Video]]

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Attach:download.png [[Attach:dynamic_optimization_aly.zip|Aly Singular Control Solution in MATLAB ~~and Python~~]]

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<iframe width="560" height="315" src="https://~~www~~.~~youtube.com~~/~~embed/~~cd0TkFtXfWs" frameborder="0" allowfullscreen></iframe>
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Attach:download.png [[Attach:dynamic_optimization_aly.zip|Aly Singular Control Solution in MATLAB]] and [[https://youtu.be/cd0TkFtXfWs|Video]]

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Attach:download.png [[Attach:dynamic_optimization_catalyst.zip|Catalyzed Reaction Optimized in MATLAB and Python]]

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<iframe width="560" height="315" src="https://~~www~~.~~youtube.com~~/~~embed/~~jB7WWGHFNIw" frameborder="0" allowfullscreen></iframe>
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Attach:download.png [[Attach:dynamic_optimization_catalyst.zip|Catalyzed Reaction Optimized in MATLAB and Python]] and [[https://youtu.be/jB7WWGHFNIw|Video]]

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March 26, 2023, at 03:02 AM by 136.36.4.38 -

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!!!! [[https://apmonitor.com/wiki/index.php/Apps/BatchReactor|Batch Reactor]]

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!!!! [[https://apmonitor.com/wiki/index.php/Apps/BrysonDenhamProblem|Bryson-Denham Problem]]

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!!!! [[Main/IntegralObjective|Integral Objective (Luus)]]

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!!!! [[Main/EconomicDynamicOptimization|Maximize Profit (Commercial Fishery)]]

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!!!! [[Main/MinimizeFinalTime|Minimize Final Time (Jennings)]]

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!!!! [[Main/EconomicDynamicOptimization|Maximize Profit (Commercial Fishery)]]

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!!!! [[Main/MinimizeFinalTime|Minimize Final Time (Jennings)]]

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!!!! [[Main/IntegralObjective|Integral Objective (Luus)]]

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!!!! [[https://apmonitor.com/wiki/index.php/Apps/BrysonDenhamProblem|Bryson-Denham Problem]]

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!!!! [[https://apmonitor.com/wiki/index.php/Apps/BatchReactor|Batch Reactor]]

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March 25, 2023, at 11:46 PM by 136.36.4.38 -

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!!!! [[https://apmonitor.com/wiki/index.php/Apps/BatchReactor|Batch Reactor]]

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November 17, 2021, at 12:55 AM by 10.35.117.248 -

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plt.plot(m.time,x1.value,'k:',~~LineWidth~~=2,label=r'$x_1$')
plt.plot(m.time,x2.value,'b-',~~LineWidth~~=2,label=r'$x_2$')
plt.plot(m.time,x2.value,'k-',~~LineWidth~~=2,label=r'$x_3$')

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plt.plot(m.time,x1.value,'k:',lw=2,label=r'$x_1$')
plt.plot(m.time,x2.value,'b-',lw=2,label=r'$x_2$')
plt.plot(m.time,x2.value,'k-',lw=2,label=r'$x_3$')

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plt.plot(m.time,u.value,'r--',~~LineWidth~~=2,label=r'$u$')
plt.plot(t,-np.sin(t),'k:',~~LineWidth~~=2,label='Exact')

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plt.plot(m.time,u.value,'r--',lw=2,label=r'$u$')
plt.plot(t,-np.sin(t),'k:',lw=2,label='Exact')

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May 15, 2021, at 05:02 AM by 136.36.4.38 -

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(:title ~~More~~ Optimal Control Problems:)

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(:title Optimal Control Benchmark Problems II:)

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June 21, 2020, at 02:01 PM by 136.36.211.159 -

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# Beal, L.D.R., Hill, D., Martin, R.A., and Hedengren, J. D., ''GEKKO Optimization Suite'', Processes, Volume 6, Number 8, 2018, doi: 10.3390/pr6080106. [[https://www.mdpi.com/2227-9717/6/8/106|Article]]

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June 21, 2020, at 02:01 PM by 136.36.211.159 -

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'''Objective:''' Set up and solve several optimal control benchmark problems. Create a program ~~as shown in reference [1]~~ to optimize and display the results. ''Estimated Time (each): 30 minutes''

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'''Objective:''' Set up and solve several optimal control benchmark problems. Create a program to optimize and display the results. ''Estimated Time (each): 30 minutes''

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* Solve the following nonlinear and constrained problem ~~as shown in reference [2]~~.

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* Solve the following nonlinear and constrained problem.

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June 21, 2020, at 02:00 PM by 136.36.211.159 -

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'''Objective:''' Set up and solve several optimal control benchmark problems. Create a program'^1^' to optimize and display the results. ''Estimated Time (each): 30 minutes''

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'''Objective:''' Set up and solve several optimal control benchmark problems. Create a program as shown in reference [1] to optimize and display the results. ''Estimated Time (each): 30 minutes''

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!!!! Aly-Chan Singular Control Problem~~'^2^'~~
* Solve the following nonlinear and constrained problem.

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!!!! Aly-Chan Singular Control Problem
* Solve the following nonlinear and constrained problem as shown in reference [2].

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June 21, 2020, at 01:59 PM by 136.36.211.159 -

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!!!! [[https://apmonitor.com/wiki/index.php/Apps/BrysonDenhamProblem|Bryson-Denham Problem]]

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March 08, 2018, at 02:24 PM by 45.56.3.173 -

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!!!! [[Main/EconomicDynamicOptimization|~~Commercial~~ Fishery]]

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!!!! [[Main/EconomicDynamicOptimization|Maximize Profit (Commercial Fishery)]]

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March 07, 2018, at 06:55 PM by 10.37.83.132 -

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!!!! Commercial Fishery

~~Attach:download.png [[Attach:dynamic_optimization_fishery.zip|Economic Optimization of Fishery in MATLAB and Python~~]]

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!!!! [[Main/EconomicDynamicOptimization|Commercial Fishery]]

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February 26, 2018, at 07:58 PM by 10.37.5.186 -

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!!!! Jennings Problem

Attach:download.png [[Attach:dynamic_optimization_jennings.zip|Jennings Problem in MATLAB and Python]]

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!!!! [[Main/MinimizeFinalTime|Minimize Final Time (Jennings)]]

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February 22, 2018, at 10:29 PM by 10.5.113.199 -

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(:toggle hide gekko button show="Show GEKKO (Python) Code":)
(:div id=gekko:)
(:source lang=python:)
import numpy as np
import matplotlib.pyplot as plt
from gekko import GEKKO

m = GEKKO()

nt = 1001
t = np.linspace(0,np.pi/2,nt)
m.time = t

# Variables
x1 = m.Var(value=0)
x2 = m.Var(value=1)
x3 = m.Var(value=0)

u = m.MV(value=0,ub=1,lb=-1)
u.STATUS = 1
u.DCOST = 0

p = np.zeros(nt)
p[-1] = 1.0
final = m.Param(value=p)

# Equations
m.Equation(x1.dt()==x2)
m.Equation(x2.dt()==u)
m.Equation(2*x3.dt()==x2**2-x1**2)

# Objective Function
m.Obj(x3*final)

m.options.IMODE = 6
m.options.NODES = 4
m.solve()

plt.figure(1)
plt.subplot(2,1,1)
plt.plot(m.time,x1.value,'k:',LineWidth=2,label=r'$x_1$')
plt.plot(m.time,x2.value,'b-',LineWidth=2,label=r'$x_2$')
plt.plot(m.time,x2.value,'k-',LineWidth=2,label=r'$x_3$')
plt.subplot(2,1,2)
plt.plot(m.time,u.value,'r--',LineWidth=2,label=r'$u$')
plt.plot(t,-np.sin(t),'k:',LineWidth=2,label='Exact')
plt.legend(loc='best')
plt.xlabel('Time')
plt.ylabel('Value')
plt.show()
(:sourceend:)
(:divend:)

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February 13, 2018, at 01:43 PM by 45.56.3.173 -

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(:title More Optimal Control Problems:)
(:keywords nonlinear control, optimal control, dynamic optimization, engineering optimization, MATLAB, Python, GEKKO, differential, algebraic, modeling language, university course:)
(:description More optimal control problems solved with Dynamic Optimization in MATLAB and Python.:)

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February 13, 2018, at 01:39 PM by 45.56.3.173 -

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'''Objective:''' Set up and solve several ~~[[Attach:Dynamic_Optimization_Benchmarks.pdf|dynamic optimization~~ benchmark problems]]. Create a program'^1^' to optimize and display the results. ''Estimated Time (each): 30 minutes''

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'''Objective:''' Set up and solve several optimal control benchmark problems. Create a program'^1^' to optimize and display the results. ''Estimated Time (each): 30 minutes''

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February 13, 2018, at 01:38 PM by 45.56.3.173 -

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!!!! Luus Problem

Attach:download.png [[Attach:dynamic_optimization_luus.zip|Luus ~~Problem in MATLAB and Python~~]]

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<iframe width="560" height="315" src="https://www.youtube.com/embed/WIe31dTaW6g" frameborder="0" allowfullscreen></iframe>
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!!!! [[Main/IntegralObjective|Integral Objective (Luus)]]

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February 10, 2016, at 07:04 AM by 174.148.96.184 -

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February 10, 2016, at 06:39 AM by 174.148.96.184 -

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(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/yuj217itTa8" frameborder="0" allowfullscreen></iframe>
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!!!! Luus Problem

Attach:download.png [[Attach:dynamic_optimization_luus.zip|Luus Problem in MATLAB and Python]]

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February 10, 2016, at 06:36 AM by 174.148.96.184 -

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February 10, 2016, at 06:11 AM by 174.148.96.184 -

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Attach:download.png [[Attach:dynamic_optimization_catalyst.zip|~~Dynamic Optimization Catalyst Solution~~ in MATLAB and Python]]

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Attach:download.png [[Attach:dynamic_optimization_catalyst.zip|Catalyzed Reaction Optimized in MATLAB and Python]]

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Attach:download.png [[Attach:dynamic_optimization_fishery.zip|~~Dynamic~~ Optimization Fishery ~~Solution~~ in MATLAB and Python]]

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Attach:download.png [[Attach:dynamic_optimization_fishery.zip|Economic Optimization of Fishery in MATLAB and Python]]

(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/MA53XPp-a7I" frameborder="0" allowfullscreen></iframe>
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!!!! Jennings Problem

Attach:download.png [[Attach:dynamic_optimization_jennings.zip|Jennings Problem in MATLAB and Python]]

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February 10, 2016, at 12:59 AM by 174.148.92.107 -

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~~->Attach:dynopt_alychan.png~~

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February 10, 2016, at 12:59 AM by 174.148.92.107 -

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February 10, 2016, at 12:39 AM by 174.148.92.107 -

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!!!! Commercial Fishery

Attach:download.png [[Attach:dynamic_optimization_fishery.zip|Dynamic Optimization Fishery Solution in MATLAB and Python]]

(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/jB7WWGHFNIw" frameborder="0" allowfullscreen></iframe>
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February 09, 2016, at 01:22 PM by 174.148.118.172 -

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See [[https://youtu.be/5qY7WyngRbo|estimation example]] using the same model to explain estimator objectives.

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February 09, 2016, at 01:19 PM by 174.148.118.172 -

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February 09, 2016, at 12:49 PM by 174.148.118.172 -

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!!!! Aly-Chan Problem'^2^'

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!!!! Aly-Chan Singular Control Problem'^2^'

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!!!! Catalyzed Reaction

Attach:download.png [[Attach:~~dynamic_optimization_catalyst~~.~~zip|Dynamic Optimization Catalyst~~ Solution in MATLAB and Python]]

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!!!! Aly Singular Control Problem

Attach:download.png [[Attach:dynamic_optimization_aly.zip|Aly Singular Control Solution in MATLAB and Python]]

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~~<iframe width="560" height="315" src="https://www.youtube.com/embed/jB7WWGHFNIw" frameborder="0" allowfullscreen></iframe>~~

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!!!! Catalyzed Reaction

Attach:download.png [[Attach:dynamic_optimization_catalyst.zip|Dynamic Optimization Catalyst Solution in MATLAB and Python]]

(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/jB7WWGHFNIw" frameborder="0" allowfullscreen></iframe>
(:htmlend:)

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February 09, 2016, at 06:33 AM by 174.148.220.36 -

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~~!!!! Solution to Catalyzed Reaction Problem~~

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February 09, 2016, at 06:31 AM by 174.148.220.36 -

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~~!!!! Solution to Aly-Chan Problem~~

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!!!! Catalyzed Reaction

!!!! Solution to Catalyzed Reaction Problem
Attach:download.png [[Attach:dynamic_optimization_catalyst.zip|Dynamic Optimization Catalyst Solution in MATLAB and Python]]

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January 25, 2016, at 05:20 PM by 45.56.3.184 -

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January 25, 2016, at 04:49 PM by 45.56.3.184 -

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!!!! Aly-Chan ~~Problem~~

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!!!! Aly-Chan Problem'^2^'

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* The objective is to minimize final state ''x_3_(pi/2)'' by adjusting the value of ''u''.

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* The objective is to minimize final state ''x'_3_'(pi/2)'' by adjusting the value of ''u''.

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January 25, 2016, at 04:27 PM by 45.56.3.184 -

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* ~~Nonlinear, constrained, minimize final state~~

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* Solve the following nonlinear and constrained problem.
* The objective is to minimize final state ''x_3_(pi/2)'' by adjusting the value of ''u''.
* Compare to the exact solution of ''u(t)= -sin(t)''.

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January 25, 2016, at 04:19 PM by 45.56.3.184 -

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!!!! Exercise

'''Objective:''' Set up and solve several [[Attach:Dynamic_Optimization_Benchmarks.pdf|dynamic optimization benchmark problems]]. Create a program'^1^' to optimize and display the results. ''Estimated Time (each): 30 minutes''

!!!! Aly-Chan Problem
* Nonlinear, constrained, minimize final state
->Attach:dynopt_alychan.png
!!!! Solution to Aly-Chan Problem
Attach:download.png [[Attach:dynamic_optimization_alychan.zip|Dynamic Optimization Aly-Chan Solution in MATLAB and Python]]

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!!!! References

# Hedengren, J. D. and Asgharzadeh Shishavan, R., Powell, K.M., and Edgar, T.F., Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers and Chemical Engineering, Volume 70, pg. 133–148, 2014. [[https://dx.doi.org/10.1016/j.compchemeng.2014.04.013|Article]]

# Aly G.M. and Chan W.C. Application of a modified quasilinearization technique to totally singular optimal problems. International Journal of Control, 17(4): 809-815, 1973.

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