Abstract
This paper is a sequel to a previous article by the author, concerned with a certain canonical problem in optimal control involving constraints of the typeψ α(t, x)⩽0, α=1,...,m. In that article, a set of second-order conditions necessary for a solution arc was obtained. In this paper, those results are extended to a general control problem involving the above type of constraints.
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References
Russak, I. B.,Second-Order Conditions for Problems with State Inequality Constraints, SIAM Journal on Control (to appear).
Russak, I. B.,On Problems with Bounded State Variables, Journal of Optimization Theory and Applications, Vol. 5, No. 2, 1970.
Russak, I. B.,On General Problems with Bounded State Variables, Journal of Optimization Theory and Applications, Vol. 6, No. 6, 1970.
Hestenes, M. R.,Calculus of Variations and Optimal Control Theory, John Wiley and Sons, New York, New York, 1966.
Pennisi, L. L.,An Indirect Sufficiency Proof for the Problem of Lagrange with Differential Inequalities as Added Side Conditions, University of Chicago, Ph.D. Thesis, 1952.
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Communicated by M. R. Hestenes
This task was supported by an NPS Foundation Grant.
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Russak, I.B. Second-order necessary conditions for general problems with state inequality constraints. J Optim Theory Appl 17, 43–92 (1975). https://doi.org/10.1007/BF00933916
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DOI: https://doi.org/10.1007/BF00933916