Abstract
A quadratic regulator problem for a class of nonlinear systems is considered in which the control cost is multiplied by a small parameter, which becomes a so-called cheap control problem. Conditions are found under which the minimum cost becomes zero (perfect regulation) and the linear part in the optimal control law becomes dominant as the small parameter goes to zero. Near optimality of control laws truncated from the optimal control law in series form is also found.
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Communicated by G. Leitmann
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Lee, J.T., Bien, Z.N. A quadratic regulator with cheap control for a class of nonlinear systems. J Optim Theory Appl 55, 289–302 (1987). https://doi.org/10.1007/BF00939086
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DOI: https://doi.org/10.1007/BF00939086