Delay‐adaptive control of first‐order hyperbolic partial integro‐differential equations
Shanshan Wang, Jie Qi, Miroslav Krstić
Abstract
Abstract We develop a delay‐adaptive controller for a class of first‐order hyperbolic partial integro‐differential equations with an unknown input delay. By employing a transport PDE to represent delayed actuator states, the system is transformed into a transport partial differential equation with unknown propagation speed cascaded with a PIDE. A parameter update law is designed using a Lyapunov argument and the infinite‐dimensional backstepping technique to establish global stability results. Subsequently, the effectiveness of the proposed approach was validated through numerical simulations.
Topics & Concepts
BacksteppingHyperbolic partial differential equationControl theory (sociology)MathematicsPartial differential equationController (irrigation)Stability (learning theory)Applied mathematicsFirst-order partial differential equationLyapunov functionMathematical analysisComputer scienceAdaptive controlNonlinear systemControl (management)PhysicsQuantum mechanicsArtificial intelligenceBiologyMachine learningAgronomyStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Dynamics and Pattern Formation