Prescribing Transient and Asymptotic Behavior to Deterministic Systems with Stochastic Initial Conditions

Martijn Dresscher*, Bayu Jayawardhana

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

We study a containment control problem (CCP) and a shape control problem (SCP) for systems whose initial condition is a random variable with known distribution. The two control problems both require exponential convergence to a desired trajectory, which is complemented by either; i) a required cumulative distribution over a prescribed containment set at a specific transient time for the CCP, or; ii) a maximum distance between an attained and a desired probability density function of the state for the SCP. For the CCP, we obtain solutions for both linear and nonlinear systems by designing the closed-loop such that the initial pdf shrinks or contracts to a desired trajectory. For the SCP, we obtain solutions for linear systems and an admissible desired pdf, by designing the closed-loop such that the evolution of the pdf at the transient time is similar to the target pdf.
Original languageEnglish
Number of pages27
JournalInternational Journal of Control
Early online date25-May-2020
DOIs
Publication statusE-pub ahead of print - 25-May-2020

Keywords

  • CONTRACTION ANALYSIS
  • TRACKING
  • SYNCHRONIZATION
  • DIVERGENCE

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