Multi-objective optimization - Wikipedia
Solving optimal control problems by means of direct collocation implies that the differential equation is approximated by a discrete time counterpart. The accuracy of the solution is dependent on the method of collocation and the number of elements. In order to assess the accuracy of the optimization result, we may simulate the system using a DAE solver using the optimal control profile as input. With this approach, the state profiles are computed with high accuracy and the result may then be compared with the profiles resulting from optimization. The procedure for setting up and executing this simulation is similar to above:
MAE Courses - University of California San Diego
This extensive work, aside from its focus on the mainstream dynamicprogramming and optimal controltopics, relates to our (Athena Scientific, 2013),a synthesis of classical research on the foundations of dynamic programming with modern approximate dynamic programming theory, and the new class of semicontractive models, (Athena Scientific, 1996),which deals with the mathematical foundations of the subject, (Athena Scientific,1996), which develops the fundamental theory for approximation methods in dynamic programming,and (2nd Edition, Athena Scientific,2008), which provides the prerequisite probabilistic background.
The leading and most up-to-date textbook on the far-rangingalgorithmic methododogy of Dynamic Programming, which can be used for optimal control,Markovian decision problems, planning and sequential decision making under uncertainty, anddiscrete/combinatorial optimization. The treatment focuses on basic unifyingthemes, andconceptual foundations. Itillustrates the versatility, power, and generality of the method withmany examples and applicationsfrom engineering, operations research, and other fields. It alsoaddresses extensively the practicalapplication of the methodology, possibly through the use of approximations, andprovides an extensive treatment of the far-reaching methodology ofNeuro-Dynamic Programming/Reinforcement Learning.