Abstract
Control of stochastic linear systems with quadratic objective function is considered under the assumption that control variables are constrained. Production-inventory control in a stochastic environment is a typical example of such systems. To control stochastic linear systems, a suboptimal closed-loop control law is derived by using Lagrange multipliers in a dynamic fashion. In terms of ease of implementation, the derived suboptimal algorithm is comparable with that of the well-known unconstrained Linear-Quadratic-Gaussian (LQG) control law. The problem of inventory balancing in distribution systems is used to evaluate the performance of the proposed algorithm. The test results indicate that, under control constraints, the new algorithm significantly reduces the loss compared with that of the simple saturated LQG algorithm. It is proven that the proposed algorithm outperforms the saturated control.
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