Abstract
We consider a deterministic impulsive control problem. We discretize the Hamilton-Jacobi-Bellman equation satisfied by the optimal cost function and we obtain discrete solutions of the problem. We give an explicit rate of convergence of the approximate solutions to the solution of the original problem. We consider the optimal switching problem as a special case of impulsive control problem and we apply the same structure of discretization to obtain also a rate of convergence in this case. We present a numerical example.
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Tidball, M. (1997). Rate of convergence of a numerical procedure for impulsive control problems. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_130
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DOI: https://doi.org/10.1007/3-540-62598-4_130
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