This paper proposes a singularity-free prescribed-time distributed optimization algorithm for nonlinear multi-agent systems with time-varying cost functions and dynamic communication topologies. The proposed algorithm avoids singularity, and it does not require the local cost functions to have identical Hessian matrices. First, a novel time-varying scaling function based on time-space deformation theory is designed to address the singularity issue in the proposed distributed optimization algorithm. Second, a distributed prescribed-time optimization estimator by introducing an intermediate driving variable to counteract the inconsistency disturbances is designed to track the average of the global gradients, global Hessian matrices, and the global partial derivatives of gradients, respectively. Furthermore, under this estimator, all local cost functions need not have identical Hessians. Third, refined theoretical analysis demonstrates that our algorithm converges to the globally optimal trajectory. Meanwhile it is also shown to avoid the singularity problem and achieve prescribed-time estimation. Finally, a UAV formation experiment verifies the effectiveness of our proposed algorithm, including its singularity-free property, prescribed-time convergence, and optimality.
- Open Access
- Article
Singularity-Free Prescribed-Time Distributed Optimization for Nonlinear Multi-Agent Systems with Time-Varying Cost Functions
- Huan Wang 1,
- Tao Dong 2,
- Yihan Yang 1,
- Tiancheng Liu 1,
- Aijuan Wang 1,*
Author Information
Received: 25 Dec 2025 | Revised: 12 Mar 2026 | Accepted: 24 Mar 2026 | Published: 27 Mar 2026
Abstract
Keywords
nonlinear multi-agent systems | distributed optimization | singularity-free | prescribed-time convergence | time-varying cost functions
References
- 1.
Lu, Q.; Liao, X.; Li, H.; et al. Achieving Acceleration for Distributed Economic Dispatch in Smart Grids over Directed Networks. IEEE Trans. Netw. Sci. Eng. 2020, 7, 1988–1999.
- 2.
Wang, A.; Liu, W.; Dong, T.; et al. DisEHPPC: Enabling Heterogeneous Privacy-Preserving Consensus-Based Scheme for Economic Dispatch in Smart Grids. IEEE Trans. Cybern. 2020, 52, 5124–5135.
- 3.
Liu, S.; Wang, Z.; Wei, G.; et al. Distributed Set-Membership Filtering for Multirate Systems under the Round-Robin Scheduling over Sensor Networks. IEEE Trans. Cybern. 2019, 50, 1910–1920.
- 4.
Huang, J.; Zhou, S.; Tu, H.; et al. Distributed Optimization Algorithm for Multi-Robot Formation with Virtual Reference Center. IEEE CAA J. Autom. Sin. 2022, 9, 732–734.
- 5.
Lin, P.; Ren, W.; Song, Y. Distributed Multi-Agent Optimization Subject to Nonidentical Constraints and Communication Delays. Automatica 2016, 65, 120–131.
- 6.
Nedic, A.; Olshevsky, A.; Shi, W. Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs. SIAM Journal on Optimization 2017, 27, 2597–2633.
- 7.
Liu, H.; Zheng,W.X.; Yu,W. Distributed Discrete-Time Algorithms for Convex Optimization with General Local Constraints on Weight-Unbalanced Digraph. IEEE Trans. Control Netw. Syst. 2020, 8, 51–64.
- 8.
Li, H.; Zheng, L.; Wang, Z.; et al. S-DIGing: A Stochastic Gradient Tracking Algorithm for Distributed Optimization. IEEE Trans. Emerg. Top. Comput. Intell. 2020, 6, 53–65.
- 9.
Xin, R.; Khan, U.A. Distributed Heavy-Ball: A Generalization and Acceleration of First-Order Methods with Gradient Tracking. IEEE Trans. Autom. Control 2019, 65, 2627–2633.
- 10.
Shi, X.; Wen, G.; Cao, J.; et al. Finite-Time Distributed Average Tracking for Multiagent Optimization with Bounded Inputs. IEEE Trans. Autom. Control 2022, 68, 4948–4955.
- 11.
Qiu, Z.; Liu, S.; Xie, L. Distributed Constrained Optimal Consensus of Multi-Agent Systems. Automatica 2016, 68, 209–215.
- 12.
Lu, K.; Jing, G.; Wang, L. Distributed Algorithm for Solving Convex Inequalities. IEEE Trans. Autom. Control 2017, 63, 2670–2677.
- 13.
Carnevale, G.; Notarnicola, I.; Marconi, L.; et al. Triggered Gradient Tracking for Asynchronous Distributed Optimization. Automatica 2023, 147, 110726.
- 14.
Wang, X.; Mou, S.; Anderson, B.D. Consensus-Based Distributed Optimization Enhanced by Integral Feedback. IEEE Trans. Autom. Control 2022, 68, 1894–1901.
- 15.
Wu, Z.; Li, Z.; Yu, J. Designing Zero-Gradient-Sum Protocols for Finite-Time Distributed Optimization Problem. IEEE Trans. Syst. Man Cybern. Syst. 2021, 52, 4569–4577.
- 16.
Yuquan, C.; Fumian, W.; Songsong, C.; et al. A Novel Protocol for Fixed-Time Distributed Optimization over Networks Based on Zero-Gradient-Sum Strategy. In Proceedings of the International Symposium on Autonomous Systems, Nanjing, China, 23–25 June 2023.
- 17.
Zhang, R.; Guo, G. Continuous Distributed Robust Optimization of Multiagent Systems with Time-Varying Cost. IEEE Trans. Control Netw. Syst. 2023, 11, 586–598.
- 18.
Ju, X.; Yuan, S.; Yang, X.; et al. Fixed-Time Neurodynamic Optimization Algorithms and Application to Circuits Design. IEEE Trans. Circuits Syst. I Regul. Pap. 2024, 71, 2171–2181.
- 19.
Dai, H.; Fang, X.; Jia, J. Consensus-Based Distributed Fixed-Time Optimization for a Class of Resource Allocation Problems. J. Frankl. Inst. 2022, 359, 11135–11154.
- 20.
Wang, Y.; Song, Y.; Hill, D.J.; et al. Prescribed-Time Consensus and Containment Control of Networked Multiagent Systems. IEEE Trans. Cybern. 2018, 49, 1138–1147.
- 21.
Chen, S.; Jiang, H.; Yu, Z. Distributed Predefined-Time Optimization Algorithm: Dynamic Event-Triggered Control. IEEE Trans. Control Netw. Syst. 2023, 11, 486–497.
- 22.
De Villeros, P.; Aldana-L´opez, R.; S´anchez-Torres, J.; et al. Robust Fixed-Time Distributed Optimization with Predefined Convergence-Time Bound. J. Frankl. Inst. 2024, 361, 106988.
- 23.
Zhou, S.; Wei, Y.; Cao, J.; et al. Multi/Single-Stage Sliding Manifold Approaches for Prescribed-Time Distributed Optimization. IEEE Trans. Autom. Control 2024, 70, 2794–2801.
- 24.
Ding, C.; Wei, R.; Liu, F. Prescribed-Time Distributed Optimization for Time-Varying Objective Functions: A Perspective from Time-Domain Transformation. J. Frankl. Inst. 2022, 359, 10267–10280.
- 25.
Gong, X.; Cui, Y.; Shen, J.; et al. Distributed Optimization in Prescribed-Time: Theory and Experiment. IEEE Trans. Netw. Sci. Eng. 2021, 9, 564–576.
- 26.
Deng, Z. Distributed Online Path-Length-Independent Algorithm for Noncooperative Games over Unbalanced Digraphs. Automatica 2025, 175, 112200.
- 27.
Rahili, S.; Ren, W. Distributed Continuous-Time Convex Optimization with Time-Varying Cost Functions. IEEE Trans. Autom. Control 2016, 62, 1590–1605.
- 28.
Sun, S.; Xu, J.; Ren, W. Distributed Continuous-Time Algorithms for Time-Varying Constrained Convex Optimization. IEEE Trans. Autom. Control 2022, 68, 3931–3946.
- 29.
Shi, X.; Wen, G.; Yu, X. Finite-Time Convergent Algorithms for Time-Varying Distributed Optimization. IEEE Control Syst. Lett. 2023, 7, 3223–3228.
- 30.
Zhang, R.; Guo, G.; Zhou, Z.D. Balance of Communication and Convergence: Predefined-Time Distributed Optimization Based on Zero-Gradient-Sum. IEEE Trans. Cybern. 2025, 55, 661–671.
- 31.
Cui, Q.; Song, Y.; Wen, C. Prescribed Time Consensus Control of Multiagent Systems with Minimized Time-Varying Cost Function. IEEE Trans. Autom. Control 2023, 69, 3381–3388.
- 32.
Chen, Y.; Yang, J.; Zhong, W.; et al. Distributed Time-Varying Optimization with Prescribed-Time Approach. J. Franklin Inst. 2024, 361, 107270.
- 33.
Ye, H.;Wen, C.; Song, Y. Decentralized Prescribed-Time Control for Interconnected Nonlinear Systems via Output-Feedback. Automatica 2024, 163, 111571.
- 34.
Ding, Y.; Zhou, B.; Zhang, K.K.; et al. Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback. IEEE Trans. Autom. Control 2023, 69, 4072–4079.
- 35.
Orlov, Y. Time Space Deformation Approach to Prescribed-Time Stabilization: Synergy of Time-Varying and Non-Lipschitz Feedback Designs. Automatica 2022, 144, 110485.
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