Distributed constrained optimization for multi-agent systems over a directed graph with piecewise stepsize. (English) Zbl 1437.93007
Summary: In this paper, the distributed constrained optimization problem over a directed graph is considered. We assume that the digraph has a row-stochastic adjacency matrix, which corresponds to the case when agents assign weights to the received information individually. We present an algorithm that converges to the optimal solution even with a time-varying stepsize which is not attenuated to zero. The choice of stepsizes is relatively easy. The usable type of stepsizes is added. The diminishing or constant stepsizes can be used in our algorithm. Equality constraints and set constraints are also considered in this paper. Convergence analysis of the proposed algorithm relies on a conversion theorem between column-stochastic and row-stochastic matrices. Finally, the results of the numerical simulation are provided to verify the effectiveness of the proposed algorithm.
References:
| [1] | Wu, Z.-G.; Shi, P.; Su, H.; Chu, J., Stochastic synchronization of markovian jump neural networks with time-varying delay using sampled data, IEEE Trans. Cybern., 43, 6, 1796-1806 (2013) |
| [2] | Mu, C.; Zhao, Q.; Gao, Z.; Sun, C., Q-learning solution for optimal consensus control of discrete-time multiagent systems using reinforcement learning, J. Frankl. Inst., 356, 13, 6946-6967 (2019) · Zbl 1418.93250 |
| [3] | Ren, W.; Beard, R. W.; Atkins, E. M., Information consensus in multivehicle cooperative control, IEEE Control Syst., 27, 2, 71-82 (2007) |
| [4] | Liu, B.; Hill, D. J.; Yao, J., Global uniform synchronization with estimated error under transmission channel noise, IEEE Trans. Circuits Syst. I: Regul. Pap., 56, 12, 2689-2702 (2009) · Zbl 1468.34102 |
| [5] | Yi, H.; Liu, M.; Li, M., Event-triggered fault tolerant control for spacecraft formation attitude synchronization with limited data communication, Eur. J. Control, 48, 97-103 (2019) · Zbl 1415.93241 |
| [6] | Zhang, Y.; Li, F.; Chen, Y., Leader-following-based distributed kalman filtering in sensor networks with communication delay, J. Frankl. Inst., 354, 16, 7504-7520 (2017) · Zbl 1373.93355 |
| [7] | Peng, C.; Tian, Y.-C.; Tade, M. O., State feedback controller design of networked control systems with interval time-varying delay and nonlinearity, Int. J. Robust Nonlinear Control, 18, 12, 1285-1301 (2008) · Zbl 1284.93111 |
| [8] | Dong, H.; Wang, Z.; Gao, H., Distributed h_∞ filtering for a class of markovian jump nonlinear time-delay systems over lossy sensor networks, IEEE Trans. Ind. Electron., 60, 10, 4665-4672 (2013) |
| [9] | Hua, Y.; Dong, X.; Wang, J.; Li, Q.; Ren, Z., Time-varying output formation tracking of heterogeneous linear multi-agent systems with multiple leaders and switching topologies, J. Frankl. Inst., 356, 1, 539-560 (2019) · Zbl 1405.93015 |
| [10] | Ho, C. Y.-F.; Ling, B. W.-K.; Benmesbah, L.; Kok, T. C.-W.; Siu, W.-C.; Teo, K.-L., Two-channel linear phase fir qmf bank minimax design via global nonconvex optimization programming, IEEE Trans. Signal Process., 58, 8, 4436-4441 (2010) · Zbl 1392.94819 |
| [11] | Yang, H.; Xu, Y.; Xia, Y.; Zhang, J., Networked predictive control for nonlinear systems with arbitrary region quantizers, IEEE Trans. Cybernet., 47, 8, 2244-2255 (2017) |
| [12] | Zeng, X.; Yi, P.; Hong, Y., Distributed algorithm for robust resource allocation with polyhedral uncertain allocation parameters, J. Syst. Sci. Complex., 31, 1, 103-119 (2018) · Zbl 1390.93309 |
| [13] | Wei, Q.; Liu, D.; Shi, G.; Liu, Y., Multibattery optimal coordination control for home energy management systems via distributed iterative adaptive dynamic programming, IEEE Trans. Ind. Electron., 62, 7, 4203-4214 (2015) |
| [14] | Yi, P.; Hong, Y.; Liu, F., Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems, Automatica, 74, 259-269 (2016) · Zbl 1348.93024 |
| [15] | Yang, S.; Liu, Q.; Wang, J., A multi-agent system with a proportional-integral protocol for distributed constrained optimization, IEEE Trans. Autom. Control, 62, 7, 3461-3467 (2017) · Zbl 1370.90259 |
| [16] | He, Y.; Liu, G.; Rees, D.; Wu, M., Improved stabilisation method for networked control systems, IET Control Theory Appl., 1, 6, 1580-1585 (2007) |
| [17] | Ye, M.; Hu, G., Distributed extremum seeking for constrained networked optimization and its application to energy consumption control in smart grid, IEEE Trans. Control Syst. Technol., 24, 6, 2048-2058 (2016) |
| [18] | Wen, S.; Zeng, Z.; Huang, T., Robust probabilistic sampling h_∞ output tracking control for a class of nonlinear networked systems with multiplicative noises, J. Frankl. Inst., 350, 5, 1093-1111 (2013) · Zbl 1293.93513 |
| [19] | Dong, S.; Ren, W.; Wu, Z.-G., Observer-based distributed mean-square consensus design for leader-following multiagent markov jump systems, IEEE Trans. Cybernet. (2019) |
| [20] | Wu, Z.-G.; Xu, Y.; Pan, Y.-J.; Su, H.; Tang, Y., Event-triggered control for consensus problem in multi-agent systems with quantized relative state measurements and external disturbance, IEEE Trans. Circuits Syst. I: Regul. Pap., 65, 7, 2232-2242 (2018) · Zbl 1468.93039 |
| [21] | Nedic, A.; Ozdaglar, A., Distributed subgradient methods for multi-agent optimization, IEEE Trans. Autom. Control, 54, 1, 48-61 (2009) · Zbl 1367.90086 |
| [22] | Yuan, K.; Ling, Q.; Yin, W., On the convergence of decentralized gradient descent, SIAM J. Opt., 26, 3, 1835-1854 (2016) · Zbl 1345.90068 |
| [23] | Mokhtari, A.; Ling, Q.; Ribeiro, A., Network newton distributed optimization methods, IEEE Trans. Signal Process., 65, 1, 146-161 (2017) · Zbl 1414.90080 |
| [24] | Chen, I.-A., Fast Distributed First-order Methods (2012), Massachusetts Institute of Technology, Ph.D. thesis |
| [25] | Duchi, J. C.; Agarwal, A.; Wainwright, M. J., Dual averaging for distributed optimization: convergence analysis and network scaling, IEEE Trans. Autom. Control, 57, 3, 592-606 (2012) · Zbl 1369.90156 |
| [26] | Nedić, A.; Olshevsky, A., Distributed optimization over time-varying directed graphs, IEEE Trans. Autom. Control, 60, 3, 601-615 (2015) · Zbl 1360.90262 |
| [27] | Shi, W.; Ling, Q.; Wu, G.; Yin, W., Extra: an exact first-order algorithm for decentralized consensus optimization, SIAM J. Opt., 25, 2, 944-966 (2015) · Zbl 1328.90107 |
| [28] | Su, H.-S.; Zhang, W., Second-order consensus of multiple agents with coupling delay, Commun. Theoret. Phys., 51, 1, 101 (2009) · Zbl 1172.93305 |
| [29] | Liu, Q.; Yang, S.; Hong, Y., Constrained consensus algorithms with fixed step size for distributed convex optimization over multiagent networks, IEEE Trans. Autom. Control, 62, 8, 4259-4265 (2017) · Zbl 1373.90106 |
| [30] | Xin, R.; Khan, U. A., A linear algorithm for optimization over directed graphs with geometric convergence, IEEE Control Syst. Lett., 2, 3, 315-320 (2018) |
| [31] | Pu, S.; Shi, W.; Xu, J.; Nedić, A., A push-pull gradient method for distributed optimization in networks, 2018 IEEE Conference on Decision and Control (CDC), 3385-3390 (2018) |
| [32] | Xin, R.; Xi, C.; Khan, U. A., Frostfast row-stochastic optimization with uncoordinated step-sizes, EURASIP J. Adv. Signal Process., 2019, 1, 1 (2019) |
| [33] | Xi, C.; Khan, U. A., On the linear convergence of distributed optimization over directed graphs, Mathematics, 60, 3, 601-615 (2015) · Zbl 1360.90262 |
| [34] | Chung, F., Laplacians and the cheeger inequality for directed graphs, Ann. Combinat., 9, 1, 1-19 (2005) · Zbl 1059.05070 |
| [35] | Mai, V. S.; Abed, E. H., Distributed optimization over weighted directed graphs using row stochastic matrix, 2016 American Control Conference (ACC), 7165-7170 (2016) |
| [36] | Kinderlehrer, D.; Stampacchia, G., An Introduction to Variational Inequalities and their Applications, 31 (1980), SIAM · Zbl 0457.35001 |
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