Cho, NamhoonShin, Hyo-Sang2025-03-052025-03-052024-12-16Cho N, Shin H-S. (2024) A passivity-based method for accelerated convex optimisation. In: Proceeding of the 2024 IEEE 63rd Conference on Decision and Control (CDC), 16-19 Dec 2024, Milan, Italy, pp. 5503-5508https://doi.org/10.1109/cdc56724.2024.10886267https://dspace.lib.cranfield.ac.uk/handle/1826/23575This study presents a constructive methodology for designing accelerated convex optimisation algorithms in continuous-time domain. The two key enablers are the classical concept of passivity in control theory and the time-dependent change of variables that maps the output of the internal dynamic system to the optimisation variables. The Lyapunov function associated with the optimisation dynamics is obtained as a natural consequence of specifying the internal dynamics that drives the state evolution as a passive linear time-invariant system. The passivity-based methodology provides a general framework that has the flexibility to generate convex optimisation algorithms with the guarantee of different convergence rate bounds on the objective function value. The same principle applies to the design of online parameter update algorithms for adaptive control by re-defining the output of internal dynamics to allow for the feedback interconnection with tracking error dynamics.pp. 5503-5508enAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/4901 Applied Mathematics49 Mathematical Sciences4007 Control Engineering, Mechatronics and Robotics40 EngineeringSystematicsHeuristic algorithmsOrdinary differential equationsLinear programmingGeneratorsMathematical modelsControl theoryOptimizationConvergenceLyapunov methodsConference paper979-8-3503-1633-92576-2370565660