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Pontryagin Minimum Principle
Published in Desineni Subbaram Naidu, Optimal Control Systems, 2018
The previous relation, which means that the necessary condition for the constrained optimal control system is that the optimal control should minimize the Hamiltonian, is the main contribution of the Pontryagin Minimum Principle. We note that this is only the necessary condition and is not in general sufficient for optimality.
Pontryagin’s Minimum Principle
Published in Simant Ranjan Upreti, Optimal Control for Chemical Engineers, 2016
Pontryagin’s minimum principle is a statement of necessary conditions for the control to be optimal. The main conclusion of this principle is that the optimal control minimizes the Hamiltonian at each point in the time interval whether or not the control there is continuous.
Linear quadratic optimal control problem with fuzzy variables via neural network
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2021
Sohrab Effati, Amin Mansoori, Mohammad Eshaghnezhad
Motivated by the former discussion, we are going to solve the quadratic optimal control problem via fuzzy variables. We consider linear time-invariant systems with the fuzzy condition and the quadratic form of performance index. The solutions of the optimal control problem are calculated by using the Pontryagin’s minimum principle (PMP), which provides the necessary condition for optimality. For obtaining the solution for the PMP, we apply the artificial neural networks. The PNN is stated to obtain the solution of the problem.
Comparative study on biodiesel production from Jatropha Curcas oil by supercritical and chemical catalytic method: a mathematical approach
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Jahangir Chowdhury, Priti Kumar Roy, Siddhartha Datta
Proof. Pontryagin minimum principle provides necessary conditions for an optimal control problem. This principle converts optimality system into a problem of minimizing hamiltonian. Hamiltonian equation (9) can be written as,