Mathematics of Operations Research
Convex Approximations of Chance Constrained Programs
SIAM Journal on Optimization
Dynamic Programming and Optimal Control, Vol. II
Dynamic Programming and Optimal Control, Vol. II
The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs
SIAM Journal on Optimization
Hi-index | 22.14 |
Here we consider a state-constrained stochastic linear-quadratic control problem. This problem has linear dynamics and a quadratic cost, and states are required to satisfy a probabilistic constraint. In this paper, the joint probabilistic constraint in the model is converted to a conservative deterministic constraint using a multi-dimensional Chebyshev bound. A maximum volume inscribed ellipsoid problem is solved to obtain this probability bound. Using the probability bound, we develop a recursive state feedback control algorithm for a special class of state-constrained stochastic linear-quadratic regulator (LQR). The performance of this approach is explored in a numerical example.