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Distributed Robust Continuous-Time Optimization Algorithms for Time-Varying Constrained Cost
Published 9 Sep 2024 in eess.SY and cs.SY | (2409.05293v1)
Abstract: This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances. By incorporating tools such as log-barrier penalty functions to address inequality constraints, an integral sliding mode control for disturbance mitigation is proposed. The algorithm ensures asymptotic tracking of the optimal solution, achieving a tracking error of zero. The convergence of the introduced algorithms is demonstrated through Lyapunov analysis and nonsmooth techniques. Furthermore, the framework's effectiveness is validated through numerical simulations considering two scenarios for the communication networks.
- A. Cherukuri and J. Cortes, “Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment,” Automatica, vol. 74, pp. 183–193, 2016.
- X. Yi, S. Zhang, T. Yang, T. Chai, and K. H. Johansson, “A primal-dual sgd algorithm for distributed nonconvex optimization,” IEEE/CAA Journal of Automatica Sinica, vol. 9, no. 5, pp. 812–833, 2022.
- C. Li, X. Yu, X. Zhou, and W. Ren, “A fixed time distributed optimization: A sliding mode perspective,” in IECON 2017-43rd Annual Conference of the IEEE Industrial Electronics Society. IEEE, 2017, pp. 8201–8207.
- P. Lin, W. Ren, and J. A. Farrell, “Distributed continuous-time optimization: nonuniform gradient gains, finite-time convergence, and convex constraint set,” IEEE Transactions on Automatic Control, vol. 62, no. 5, pp. 2239–2253, 2016.
- Z. Feng, G. Hu, and C. G. Cassandras, “Finite-time distributed convex optimization for continuous-time multiagent systems with disturbance rejection,” IEEE Transactions on Control of Network Systems, vol. 7, no. 2, pp. 686–698, 2019.
- B. Huang, Y. Zou, Z. Meng, and W. Ren, “Distributed time-varying convex optimization for a class of nonlinear multiagent systems,” IEEE Transactions on Automatic control, vol. 65, no. 2, pp. 801–808, 2019.
- B. Wang, S. Sun, and W. Ren, “Distributed continuous-time algorithms for optimal resource allocation with time-varying quadratic cost functions,” IEEE Transactions on Control of Network Systems, vol. 7, no. 4, pp. 1974–1984, 2020.
- S. G. Lee, Y. Diaz-Mercado, and M. Egerstedt, “Multirobot control using time-varying density functions,” IEEE Transactions on robotics, vol. 31, no. 2, pp. 489–493, 2015.
- A. Jadbabaie, A. Rakhlin, S. Shahrampour, and K. Sridharan, “Online optimization: Competing with dynamic comparators,” in Artificial Intelligence and Statistics. PMLR, 2015, pp. 398–406.
- S. Rahili and W. Ren, “Distributed continuous-time convex optimization with time-varying cost functions,” IEEE Transactions on Automatic Control, vol. 62, no. 4, pp. 1590–1605, 2016.
- S. He, X. He, and T. Huang, “A continuous-time consensus algorithm using neurodynamic system for distributed time-varying optimization with inequality constraints,” Journal of the Franklin Institute, vol. 358, no. 13, pp. 6741–6758, 2021.
- Q. Wang, Z. Duan, Y. Lv, Q. Wang, and G. Chen, “Distributed model predictive control for linear–quadratic performance and consensus state optimization of multiagent systems,” IEEE Transactions on Cybernetics, vol. 51, no. 6, pp. 2905–2915, 2020.
- S. Sun and W. Ren, “Distributed continuous-time optimization with time-varying objective functions and inequality constraints,” in 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020, pp. 5622–5627.
- R. Zhang and G. Guo, “Continuous distributed robust optimization of multi-agent systems with time-varying cost,” IEEE Transactions on Control of Network Systems, 2023.
- S. Sun, J. Xu, and W. Ren, “Distributed continuous-time algorithms for time-varying constrained convex optimization,” IEEE Transactions on Automatic Control, 2022.
- C. Edmonds, “Undirected graph theory,” Archive of Formal Proofs, 2022.
- D. Shevitz and B. Paden, “Lyapunov stability theory of nonsmooth systems,” IEEE Transactions on automatic control, vol. 39, no. 9, pp. 1910–1914, 1994.
- A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE transactions on Automatic Control, vol. 57, no. 8, pp. 2106–2110, 2011.
- V. Andrieu, L. Praly, and A. Astolfi, “Homogeneous approximation, recursive observer design, and output feedback,” SIAM Journal on control and optimization, vol. 47, no. 4, pp. 1814–1850, 2008.
- Z. Zuo and L. Tie, “A new class of finite-time nonlinear consensus protocols for multi-agent systems,” International Journal of Control, vol. 87, no. 2, pp. 363–370, 2014.
- M. Fazlyab, S. Paternain, V. M. Preciado, and A. Ribeiro, “Prediction-correction interior-point method for time-varying convex optimization,” IEEE Transactions on Automatic Control, vol. 63, no. 7, pp. 1973–1986, 2017.
- Y. Ding, W. Ren, and Z. Meng, “Distributed continuous-time resource allocation algorithm for networked double-integrator systems with time-varying non-identical hessians and resources,” in 2023 American Control Conference (ACC). IEEE, 2023, pp. 1159–1164.
- D. Verscheure, B. Demeulenaere, J. Swevers, J. De Schutter, and M. Diehl, “Time-optimal path tracking for robots: A convex optimization approach,” IEEE Transactions on Automatic Control, vol. 54, no. 10, pp. 2318–2327, 2009.
- J. Cortes, “Discontinuous dynamical systems,” IEEE Control systems magazine, vol. 28, no. 3, pp. 36–73, 2008.
- H. Khalil, “Nonlinear systems,” Prentice Hall, 2002.
- S. Ko, “Mathematical analysis,” 2006.
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