Necessary conditions for optimal control problems: conjugate points
In this paper we introduce a definition of “normality” and of “conjugate points” for a general
optimal control problem. Using these concepts we obtain new second-order necessary
conditions for optimality. In the special case when the control set U is the whole space or in
the classical setting of calculus of variations, our conditions reduce to known results, namely,
the Jacobi condition and the existence of a solution to a certain Riccati equation.
optimal control problem. Using these concepts we obtain new second-order necessary
conditions for optimality. In the special case when the control set U is the whole space or in
the classical setting of calculus of variations, our conditions reduce to known results, namely,
the Jacobi condition and the existence of a solution to a certain Riccati equation.
In this paper we introduce a definition of “normality” and of “conjugate points” for a general optimal control problem. Using these concepts we obtain new second-order necessary conditions for optimality. In the special case when the control set U is the whole space or in the classical setting of calculus of variations, our conditions reduce to known results, namely, the Jacobi condition and the existence of a solution to a certain Riccati equation.
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