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Reachable Set Estimation and Synthesis for Periodic Positive Systems.

Yong Chen, James Lam, Yukang Cui

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    |April 26, 2019
    PubMed
    Summary

    This study estimates reachable sets for periodic positive systems facing disturbances. It develops methods to bound these sets and design controllers, ensuring system stability within defined limits.

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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Systems Analysis
    • Optimization Theory

    Background:

    • Periodic positive systems are crucial in various applications, but their analysis is complicated by exogenous disturbances.
    • Estimating the reachable set is vital for guaranteeing system performance and safety under uncertainty.
    • Existing methods often struggle with the complexity of periodic dynamics and multiple disturbance types.

    Purpose of the Study:

    • To develop novel methods for reachable set estimation in periodic positive systems with dual exogenous disturbances.
    • To synthesize state-feedback controllers that constrain the closed-loop system's reachable set within specified bounds.
    • To provide computationally efficient optimization techniques for minimizing reachable set estimations.

    Main Methods:

    • Application of the lifting method and pseudoperiodic Lyapunov function for reachable set estimation.
    • Derivation of reachable set bounding conditions using Lyapunov-based inequalities and the S-procedure.
    • Implementation of two optimization algorithms to minimize hyper-pyramid bounds of the reachable set.
    • Formulation of state-feedback controller design conditions based on reachable set constraints.

    Main Results:

    • Established conditions for bounding the reachable set of periodic positive systems with two distinct exogenous disturbances.
    • Successfully minimized the size of bounding hyper-pyramids using proposed optimization methods.
    • Derived verifiable conditions for designing state-feedback controllers to ensure closed-loop system containment.
    • Validated the effectiveness of the theoretical results through numerical examples.

    Conclusions:

    • The proposed methods effectively address reachable set estimation and controller synthesis for disturbed periodic positive systems.
    • The employed Lyapunov-based inequalities and optimization techniques offer a robust framework for stability analysis and control design.
    • The results provide practical tools for ensuring the safety and performance of complex dynamical systems.