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- W2069789015 abstract "The linear quadratic cost control problem dot{x}(t) = A(t)x(t) + B(t)u(t) x(0) = x_{0} with a cost functional J[u] = frac{1}{2} intmin{0}max{T} [langlex, Q(t)xrangle + langleu, R(t)urangle] dt is considered, supposing S is a suitable space of piecewise cubic polynominals on a mesh of norm h on the interval [0, T] . Then a Ritz type algorithm is developed for minimizing J [cdotp] over S . The authors have previously discussed [3] certain convergence properties of the algorithm. Here the algorithm is discussed in a form suitable for real-time implementation and additional convergence criteria are presented. In [3] it was shown that the Ritz-Treffiz suboptimal control bar{u} converges to the optimal control uast with order 0(h^{3}) . If x_{bar{u}} is the trajectory generated by bar{u} , then it is shown that x_{bar{u}} approximates the optimal trajectory xast to 0(h^{3}) . Finally, it is shown that J[bar{u}] approximates J[uast] to order 0(h^{6}) . The numerical properties of the algorithm, including speed and accuracy comparisons with the conventional numerical approach, are presented in a forthcoming paper." @default.
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- W2069789015 date "1970-12-01" @default.
- W2069789015 modified "2023-09-27" @default.
- W2069789015 title "Direct method approximation to the state regulator control problem using a Ritz-Trefftz suboptimal control" @default.
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- W2069789015 doi "https://doi.org/10.1109/tac.1970.1099594" @default.
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