Main

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!!!! Luus Problem

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

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

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

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

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<iframe width="560" height="315" src="https://www.youtube.com/embed/tY8kyJq4BEY" frameborder="0" allowfullscreen></iframe>

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## More Dynamic Optimization Benchmarks

## Main.MoreDynamicOptimizationBenchmarks History

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!!!! Luus Problem

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

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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]]

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!!!! Jennings Problem

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

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!!!! Jennings Problem

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

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!!!! Commercial Fishery

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

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!!!! Commercial Fishery

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

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

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<iframe width="560" height="315" src="https://www.youtube.com/embed/cd0TkFtXfWs" frameborder="0" allowfullscreen></iframe>

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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]]

Attach:download.png [[

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!!!! Aly Singular Control Problem

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

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

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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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!!!! 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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!!!! 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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!!!! 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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* ~~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)''.

* 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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!!!! 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. [[http://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.

'''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. [[http://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.