Abstract
The linear estimation (or optimal control) problem in the emerging area of time-delay systems, multiplicative noise systems, and Markov jump linear systems has been taken into consideration by the control engineers. The purpose of this survey is to provide a review of duality between linear estimation and optimal control in the above-mentioned area. The mentioned subjects are studied to indicate the essential connection between control and estimation problems and to investigate the major cause that the classical duality still holds (not holds) for the broader systems, such as time-delay systems, multiplicative noise systems, Markov jump linear systems, and the like.
Highlights
According to the duality principle, the linear quadratic regulation (LQR) problem for deterministic systems and the optimal estimation problem for additive noise including systems are dual [1]
The duality principle between the linear minimum mean square error (LMMSE) estimation problem for continuous systems containing multiple time delays appearing in a single observation channel and the LQR problem for continuous systems containing multiple input delays appearing in a single input channel has been established in [2]
After comparing the LMMSE estimator and the LQR controller results, we find that the duality between the LMMSE estimate problem for general timedelay discrete systems with additive noise and the LQR problem for general time-delay deterministic discrete systems with a quadratic criterion in the inverse time still holds, (2019) 2019:90
Summary
According to the duality principle, the linear quadratic regulation (LQR) problem for deterministic systems and the optimal estimation problem for additive noise including systems are dual [1]. According to this principle, the optimal estimation problem with the linear minimum mean square error (LMMSE) criterion could be converted to an optimal control problem with a quadratic performance index in the inverse time, and vice versa. The duality principle between the LMMSE estimation problem for continuous systems containing multiple time delays appearing in a single observation channel and the LQR problem for continuous systems containing multiple input delays appearing in a single input channel has been established in [2]. Song et al Advances in Difference Equations (2019) 2019:90 jump system, the multiplicative noise system, and the time-delay system? In the following we will give a survey of duality between the LQR and the linear estimation problem for discrete-time systems
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