Conjugate points and optimal control: counterexamples

The authors provide three counterexamples. One shows that the accessory problem proposed in P. Bernhard (Advance in Hamiltonian Systems, 1983, pp.109-142) is not complete, and the others illustrate that one-sided controllability assumptions are not enough to derive the necessary conditions involving the conjugate point theory in optimal control. Hence, it is concluded that the corresponding theorems by Bernhard and by J. V. Breakwell and Y.C. Ho (1965) are incorrect.<
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