Why the discontinuous trajectories are not desirable ? I mean if we know that the optimal trajectory is the one having jumps then would we implement the corresponding optimal control law or shall we restrain form implementing it to avoid trajectory having jumps?
Hi, in the calssical formulation of an optimal control problem, the state is assumed to be continuous and differentiable almost everywhere. This assumption together with the differentiability of the functions that appear in the problem (dynamics, cost function, terminal conditions) is necessary to apply Pontryagin's Maximum Principle. In case you know that your state is discuntinuous and you also know the number of discontinuities I think you can add the jumps as additional unknowns and formulate this as n optimal control problems linked together.
Dear Avinash,
Always is it we can found a solution for discontinuous trajectories in optimal control, for this i suggest you to see links and attached files in subject.
-Optimal control problems with unbounded constraint sets: Optimization ...
https://www.tandfonline.com/doi/abs/10.../02331930008844501
-Optimal trajectory tracking
https://arxiv.org › math
-Optimal Control With Discontinuous Running Cost - CiteSeerX
citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.26...
-OPTIMAL CONTROL OF SYSTEMS WITH DISCONTINUOUS ...
www.mcs.anl.gov/papers/P1258.pdf
-Pontryagin's Maximum Principle for Optimal Impulsive Control Problems
https://www.researchgate.net/.../243092421_Pontryagin's_Maximu...
Best regards
There are Jump Function concept, you must know it.
Sergienko and Deinka 2004 make a lot of papers and books.
Sergienko, I.V., Deineka, V.S., Optimal control of an elliptic system with conjugation
conditions and Neumann boundary conditions, Cybernetic and Systems Analysis, 40,
6,(2004).@
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