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Probabilistic solution to a two-dimensional LQG homing problem

Makasu C., Lefebvre M.

Control and Cybernetics

2012

Vol. 41, no. 1

5-12

Let xt be an arbitrary one-dimensional diffusion process and yt be a one-dimensional controlled diffusion process starting from y0 = y ∈ (a, b). The process is controlled until yt crosses either y = a or y = b for the first time. Our aim is to find the control ut that minimizes an expected cost functional with both quadratic control and boundary crossing costs. An explicit form for the optimal control is obtained under certain conditions.