in process control in engineering, of course in many situations we need to control a system under a performance index (optimal control), where the system is exposed to uncertainty ( parameter uncertainty or disturbance or noise). and sometimes we need some constrained on the state of the system.
there are two approaches: robust optimal control, stochastic optimal control.
when we use robust optimal control (because some bounds on the uncertainty is known) we consider the worst case scenario, and we can use optimal control and hard constraints on the states can be satisfied.I think this is a practical approach
on the other hand, when we can not specify some bounds on the uncertainty and the probability distribution of uncertainty is known, we must use stochastic optimal control. In this case, the hard constraint can not be defined, and we should use the definition of chance constraints, meaning the constraint can be satisfied with some level of probability.
now my question is, does such definition a practical definition in real-world application?and is it really applied in industry?
Most of the constraints are for safety. for example we want the temperature of the boiler to be bounded. it is dangerous if we want the temperature of the boiler to be bounded with some probability. so I want to know that, is chance constrain a practical definition in real-world application in engineering?
Dear Ali,
I suggest you to see links in topic.
-Chance Constrained Finite Horizon Optimal Control with Nonconvex ...
https://pdfs.semanticscholar.org/.../5b4f1b28eb809675f76ec57da5...
-Chance-Constrained Dynamic Programming with ... - Stanford University
https://web.stanford.edu/~pavone/.../Ono.Pavone.ea.AURO14.pdf
-The Scenario Approach for Stochastic Model Predictive Control with ...
https://arxiv.org/pdf/1307.5640
-Mixed Strategy for Finite-Horizon Stochastic Optimal Control
https://hiroono.com/wp-content/.../request.dl.php?api...
-A Tutorial on Stochastic Programming - ISyE
https://www.isye.gatech.edu/people/faculty/Alex.../TutorialSP.pdf
Best regards
Dear Ali,
I suggest you to see links in topic.
- R. Bellman, Dynamic programming, Courier Corporation, (2013).
- J. Yong and X. Zhou, Stochastic controls: Hamiltonian systems and HJB equations, Springer Science and Business Media, 43 (1999).
Best regards
In real world applications you should use, when possible, more than one model. If this is not possible, in any case do sensitivity analysis, and if possible, simulate your answers. Do for instance scenario analysis. In principle, there is nothing wrong with using chance constraints, but if you do that, vary in any case the chosen probabilities, and , always, have a look at the optimal solution/policy, and try to find out, whether this solution makes sense. And, you could use this solution as a starting point.
Dear Dr. Nieuwenhuis , Dr.Lafifi and Dr. Mahrouf
what I want to know here is that I believe the chance constraint is accepted by theorists, but what about experimentalists? do they really use it?
for an engineer, does chance-constrain really has a meaning?
is it really used in process control or even in engineering approaches nowadays?
Have a look at the following presentation:
https://pdfs.semanticscholar.org/presentation/3b85/36a2674f3291e92d59085c114843c703f261.pdf
Kind regards, J.W.Nieuwenhuis.
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