Optimal bang-bang control of linear stochastic systems with a small noise parameter
- 1 December 1967
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 12 (6) , 682-690
- https://doi.org/10.1109/TAC.1967.1098731
Abstract
This study considers the problem of determining optimal feedback control laws for linear stochastic systems with amplitude-constrained control inputs. Two basic performance indices are considered, average time and average integral quadratic form. The optimization interval is random and defined as the first time a trajectory reaches the terminal regionR. The plant is modeled as a stochastic differential equation with an additive Wiener noise disturbance. The variance parameter of the Wiener noise process is assumed to be suitably small. A singular perturbation technique is presented for the solution of the stochastic optimization equations (second-order partial differential equation). A method for generating switching curves for the resulting optimal bang-bang control system is then developed. The results are applied to various problems associated with a second-order purely inertial system with additive noise at the control input. This problem is typical of satellite attitude control problems.Keywords
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