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In this paper we show that the solution to a dynamic optimization problem: optimize an integral quadratic performance criterion along trajectories of a linear dynamic system over an infinite time period (steady-state linear-quadratic optimal controller) can be solved using elementary mathematics as a static optimization problem. The derivations require only a basic (undergraduate) usage of linear...
The paper deals with a state observer design for linear systems with disturbances that lie in the control space. We propose a pseudo output, Σ(t), to be included in the observer. It is found that this pseudo output can be related to the measurable output, y(t), by a dynamic mapping which is invariant of the disturbances. Using the inverse method, Σ(t) can be retrieved by y(t) such that the inaccessible...
This note considers the long-run aver- age cost control problem for a class of discrete-time stochastic systems. The stochastic system is assumed to be linear with respect to the state but the controls possess a general structure, possibly a nonlinear one. The main contribution of this paper is to show that the existence of a minimal second moment system state implies the existence of an optimal stationary...
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