Passivity and are key concepts in adaptive control, ensuring systems consume more energy than they produce and maintain . These principles are crucial for designing robust controllers that can handle parameter variations and uncertainties in various applications.
using hyperstability techniques employ , implement , and satisfy . These methods are applied in diverse fields like robotics, , and , enhancing stability and performance in complex, uncertain environments.
Passivity and Hyperstability in Adaptive Systems
Passivity and hyperstability concepts
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Top images from around the web for Passivity and hyperstability concepts
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On the Alternatives of Lyapunov’s Direct Method in Adaptive Control Design View original
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Passivity energy-based concept in control theory relates of a system consumes more energy than it produces (electrical circuits, mechanical systems)
Hyperstability generalizes absolute stability applies to wider class of nonlinear systems ensures bounded input-output behavior (robot control, aircraft stabilization)
Relevance to adaptive systems provides robust stability guarantees allows for parameter variations and uncertainties facilitates design of adaptive controllers (, )
Conditions for passive systems
Input-output relationship: ∫0TyT(t)u(t)dt≥−β where β is finite constant u(t) is input y(t) is output
State-space representation uses for defines conditions on system matrices (A, B, C, D)
Physical interpretation system dissipates or stores energy cannot generate energy (RC circuits, mass-spring-damper systems)
Stability analysis with passivity theory
analysis constructs appropriate Lyapunov function proves negative definiteness of its derivative
Passivity-based stability analysis:
Decompose system into feedforward and
Show passivity of individual components
Apply
Hyperstability-based analysis uses Popov criterion or (IQC) verifies conditions for bounded input-output behavior
investigates stability margins assesses performance under parameter variations (, )