Galerkin Optimal Control

Abstract

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Convergence Results of Galerkin Optimal Control with Legendre Test Function∗∗The work and views expressed in this paper are those of the authors and do not reflect the oficial policy or position of the U.S. Department of the Army, the U.S. Department of the Navy, the U.S. Department of Defense or the U.S. Government.

“…The Galerkin formulation with weak imposition of endpoint conditions may also allow for problem discretizations with other than Legendre-Gauss-Lobatto (LGL) nodes, such as Legendre-Gauss (LG) and LegendreGauss-Radau (LGR) points. This is discussed in some detail in Boucher (2015).…”

“…For the reason of space, the feasibility of the computational strategy is not proved in this paper. However, some similar proofs are provided in Boucher (2015) as reference.…”

Adaptively Receding Galerkin Optimal Control for a Nonlinear Boiler-Turbine Unit

“…where y p = y + d is the practical output and y m is the output of an independent model. Here, the independent model is simply defined as the same as models (18), (19), (20), (21), (22), and (23). To this end, the estimated disturbancesd are fed back instead of d in (33) to implement the receding Galerkin method.…”

“…In this way, the estimate error e will just approach zero. (27) do in fact exist by selecting appropriate feasibility tolerance δ N and the order of approximation N, as remarked in [21,23]. Precise bounds for δ N can be found experimentally using a recursive refinement process through increasing the order of approximation N until all the constraints in a nonlinear programming problem like (27) are satisfied.…”

“…The main difficulty arises in seeking a closed-form solution to the Hamilton-Jacobi equation or in solving the canonical Hamiltonian equations resulting from an application of the minimum principle [21]. Alternatively, a Galerkin pseudospectral method [22,23] is one of the most efficient computational approaches, intending to solve the optimal state and control sequences through transforming the state-and controlconstrained nonlinear optimal control problems into a nonlinear programming problem [18,24]. There are some obstacles on the path to design a Galerkin optimal controller to make the unit track large-scale load demand/reference.…”