i am solving Pontryagin's Maximum Principle (PMP) but in my case x(t0) are fixed instead of x(tf), it is x(t1) is fixed where as t1 is some point which lies between t0 and tf. How can i solve such a problem..should i first solve from to to t1 and then t1 to tf?but i want to solve it as single intersection? plz guide me
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You'll get a jump condition on the co-state variable at $t_1$, see Maximum principle for optimal control problems with intermediate constraints by Dmitruk-Kaganovich, Theorem 4. – Conifold Apr 09 '19 at 09:38