Robust Control of Nonlinear Dynamic Systems

(2015.10 - 2020.09, HRC and HR-Recycler projects)

Research Focus

This research investigates how unknown external influences—such as disturbances, collisions, and faults—can be reconstructed from partially observed nonlinear systems and incorporated into robust control design.

The central idea is to treat external uncertainties as latent dynamical signals that can be estimated through system structure and exploited for control.

The main research question is:

How can unknown external influences be accurately reconstructed from system dynamics, and how can such reconstructed signals be integrated into robust control to improve safety and responsiveness?

This work is motivated by safety-critical human–robot collaboration, where external forces and unexpected interactions cannot be directly measured but must be detected and handled in real time.

Rather than relying purely on conservative robust control design, this research explores how state reconstruction techniques can reduce conservatism by explicitly estimating uncertainty signals.

Technical Challenges

Robotic systems operating in collaborative environments face several fundamental limitations:

• External disturbances and interaction forces are typically not directly measurable.

• High-bandwidth collisions require rapid signal reconstruction.

• Conventional robust control methods prioritize steady-state robustness over fast disturbance response.

• Fault diagnosis approaches are often decoupled from real-time control synthesis.

As a result, robotic systems may struggle to distinguish between:

• Accidental collisions

• Intentional human interaction

• Unknown external disturbances

and therefore respond either too conservatively or too slowly.

Methodological Contributions

This research establishes a framework combining state reconstruction and robust nonlinear control for safety-critical robotic systems.

1. High-Bandwidth Disturbance Reconstruction

Observer-based methods were developed to estimate unknown external inputs in nonlinear mechanical systems.

Key results include:

• Integral sliding-mode observers for disturbance estimation [8].

• Super-twisting observers for high-bandwidth unknown input reconstruction [5].

• Sensorless collision perception through observer-based torque estimation.

These techniques enable real-time estimation of unknown forces in high-DoF Euler–Lagrangian systems without external force sensors.

2. Robust Safety Control with Reconstructed Signals

The reconstructed disturbance signals are integrated into control design to improve safety and responsiveness.

Contributions include:

• Adaptive sliding-mode control for robotic manipulators [6].

• Second-order sliding-mode tracking under uncertainty.

• Compliance-aware safe tracking for human–robot interaction.

By incorporating reconstructed disturbance signals into the control loop, the resulting controllers achieve:

• Faster disturbance rejection.

• Improved safety during physical interaction.

• Reduced conservatism compared to classical robust control.

Outcomes and Implications

This research demonstrates that state reconstruction can fundamentally enhance robust control design.

Key insights include:

• High-bandwidth disturbance observers enable rapid detection of external interactions.

• Unknown external forces can be reconstructed from system dynamics without dedicated force sensors.

• Integrating reconstructed signals into control loops significantly improves safety responsiveness.

Overall, the framework bridges several classical areas of control theory:

• Robust nonlinear control

• Unknown input observation

• Disturbance estimation

• Fault-tolerant control

and provides a systematic foundation for safe human–robot collaboration systems.

Exploration Studies

Beyond the main research thread, several exploratory studies extended the state reconstruction perspective to other domains.

These projects were conducted through collaborations and focus on applying reconstruction and estimation techniques to different system classes.

1. Statistical Signal Inference for Collision Identification

While observer-based methods reconstruct external signals from system dynamics, certain uncertainties cannot be fully inferred from internal models alone.

This study explored whether data-driven statistical inference could complement reconstruction methods for fault identification.

Contributions include:

• Supervised learning–based collision classification [7].

• Bayesian decision frameworks for distinguishing accidental and intentional contacts.

• Dataset construction for robot torque measurements during physical interaction.

These results demonstrate how statistical inference can transform reconstructed signals into interpretable safety decisions.

2. Robust Filtering and Control of Networked Systems

The reconstruction-based perspective was extended to networked dynamical systems with stochastic uncertainties.

In collaboration with colleagues working on network epidemic dynamics, this work contributed to:

• Optimal filtering for stochastic network processes [3].

• Robust control of information epidemic models with uncertain transition dynamics [4].

My primary contribution focused on observer and filtering design for uncertain networked systems.

3. Adaptive Identification of Nonlinear Dynamic Systems

The reconstruction framework was further extended to adaptive state and parameter identification in switched systems.

This work developed:

• Adaptive observers for systems with switched unknown parameters [1].

• Identification schemes that avoid classical persistent excitation requirements [2].

These results highlight how state reconstruction principles can be generalized to adaptive identification problems.

Publications

1. T. Liu, Z. Zhang, F. Liu, M. Buss, "Adaptive Observer for a Class of Systems with Switched Unknown Parameters Using DREM", in IEEE Transactions on Automatic Control, Vol. 69, no. 4, Apr 2024, DOI: 10.1109/TAC.2023.3309228. [IEEEXplore] [ResearchGate]

2. Z. Zhang, F. Liu, T. Liu, J. Qiu, and M. Buss, "A Persistent-Excitation-Free Method for System Disturbance Estimation Using Concurrent Learning", in IEEE Transactions on Circuits and Systems I: Regular Papers,  vol. 70, no. 8, pp. 3305-3315, Aug 2023, DOI: 10.1109/TCSI.2023.3274558. [IEEEXplore][arXiv]

3. F. Liu, Z. Zhang, and M. Buss. "Optimal filtering and control of network information epidemics", in at - Automatisierungstechnik, vol. 69, no. 2, pp. 122-130, 2021, DOI: 10.1515/auto-2020-0096. [De Gruyter] [ResearchGate]

4. F. Liu, Z. Zhang, and Martin Buss. "Robust optimal control of deterministic information epidemics with noisy transition rates", in Physica A: Statistical Mechanics and its Applications, vol. 517, no. 4955, pp. 577-587, Mar 2019, DOI: 10.1016/j.physa.2018.11.025. [ScienceDirect] [ResearchGate]

5. Z. Zhang, D. Wollherr, and H. Najjaran*,  "Disturbance estimation for robotic systems using continuous integral sliding mode observer", in International Journal of Robust and Nonlinear Control, Vol. 32, no. 14, pp. 7946-7966, Sept. 2022, doi: 10.1002/rnc.6252. [Wiley]

6. Y. Wang, Z. Zhang*, C. Li, and M. Buss, Adaptive incremental sliding mode control for a robot manipulator, in Mechatronics, vol. 82, no. 2022, pp. 102717, 2022, doi: 10.1016/j.mechatronics.2021.102717. [ScienceDirect]

7. Z. Zhang, K. Qian*, B. W. Schuller, and D. Wollherr, "An Online Robot Collision Detection and Identification Scheme by Supervised Learning and Bayesian Decision Theory," in IEEE Transactions on Automation Science and Engineering, vol. 18, no. 3, pp. 1144-1156, July. 2021, doi: 10.1109/TASE.2020.2997094. [IEEEXplore]

8. Z. Zhang*, M. Leibold, and D. Wollherr, "Integral Sliding-Mode Observer-Based Disturbance Estimation for Euler–Lagrangian Systems," in IEEE Transactions on Control Systems Technology, vol. 28, no. 6, pp. 2377-2389, Nov. 2020, doi: 10.1109/TCST.2019.2945904. [IEEEXplore]

9. Y. Sun*, Z. Zhang, M. Leibold, R. Hayat, D. Wollherr, and M. Buss. "Protective Control For Robot Manipulator By Sliding Mode Based Disturbance Reconstruction Approach." 2017 IEEE International Conference on Advanced Intelligent Mechatronics (AIM). Munich, Germany, 03-07 July 2017.

Datasets

• The Robot Joint Torque Measurements for Accidental Collisions and Intentional Contacts [Zenodo]