Output Regulation of Linear Stochastic Systems

Mellone, Alberto; Scarciotti, Giordano

doi:10.1109/tac.2021.3064829

“…, is well-defined almost surely. The following Lemma extends the results in [33] to systems with nonlinear drift and diffusion terms. Lemma 3.…”

Section: A Estimation Of the Brownian Motionsupporting

confidence: 61%

“…The estimation of the Brownian variations is performed by periodically sampling the state. This method was first introduced in [33] in order to practically solve the problem of output regulation of linear stochastic systems. We now extend it to the present context of nonlinear stochastic systems.…”

Section: A Estimation Of the Brownian Motionmentioning

confidence: 99%

Stochastic Relative Degree and Path-Wise Control of Nonlinear Stochastic Systems

Mellone

¹

,

Scarciotti

²

2023

IEEE Trans. Automat. Contr.

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0

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We address the path-wise control of systems described by a set of nonlinear stochastic differential equations. For this class of systems, we introduce a notion of stochastic relative degree and a change of coordinates which transforms the dynamics to a stochastic normal form. The normal form is instrumental for the design of a state-feedback control which linearises and makes the dynamics deterministic. We observe that this control is idealistic, i.e. it is not practically implementable because it employs a feedback of the Brownian motion (which is never available) to cancel the noise. Using the idealistic control as a starting point, we introduce a hybrid control architecture which achieves practical path-wise control. This hybrid controller uses measurements of the state to perform periodic compensations for the noise contribution to the dynamics. We prove that the hybrid controller retrieves the idealistic performances in the limit as the compensating period approaches zero. We address the problem of asymptotic output tracking, solving it in the idealistic and in the practical framework. We finally validate the theory by means of a numerical example.

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“…Definition 8. Consider the autonomous system (33). A smooth function V : U × R ≥0 → R, where U is a bounded domain, is said to be a strict Lyapunov function for system (33) if…”

Section: Appendixmentioning

confidence: 99%

“…• ∂V ∂xi (x, t) and ∂ 2 V ∂xi∂xj (x, t) are bounded for all x ∈ U and t ≥ 0, • L ps V (x, t) = 0 for all x ∈ U and t ≥ 0, then system (33) has an almost surely totally stable equilibrium at x = 0.…”

Section: Appendixmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic Relative Degree and Path-wise Control of Nonlinear Stochastic Systems

Mellone¹,

Scarciotti²

2022

Preprint

Self Cite

0

View full text Add to dashboard Cite

We address the path-wise control of systems described by a set of nonlinear stochastic differential equations. For this class of systems, we introduce a notion of stochastic relative degree and a change of coordinates which transforms the dynamics to a stochastic normal form. The normal form is instrumental for the design of a state-feedback control which linearises and makes the dynamics deterministic. We observe that this control is idealistic, i.e. it is not practically implementable because it employs a feedback of the Brownian motion (which is never available) to cancel the noise. Using the idealistic control as a starting point, we introduce a hybrid control architecture which achieves practical path-wise control. This hybrid controller uses measurements of the state to perform periodic compensations for the noise contribution to the dynamics. We prove that the hybrid controller retrieves the idealistic performances in the limit as the compensating period approaches zero. We address the problem of asymptotic output tracking, solving it in the idealistic and in the practical framework. We finally validate the theory by means of a numerical example.

show abstract

Mean-Square Output Consensus of Heterogeneous Multi-Agent Systems with Multiplicative Noises in Dynamics and Measurements

Lin,

Luo,

Jiang

2023

J Syst Sci Complex

1

0

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Output Regulation of Linear Stochastic Systems

Cited by 10 publications

References 36 publications

Stochastic Relative Degree and Path-Wise Control of Nonlinear Stochastic Systems

Stochastic Relative Degree and Path-Wise Control of Nonlinear Stochastic Systems

Stochastic Relative Degree and Path-wise Control of Nonlinear Stochastic Systems

Mean-Square Output Consensus of Heterogeneous Multi-Agent Systems with Multiplicative Noises in Dynamics and Measurements

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