Invariant set based vehicle handling improvement at tire saturation using fuzzy output feedback
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Summary
This paper addresses the challenge of maintaining vehicle stability and handling during extreme lateral dynamics, specifically when tires approach saturation. The authors aim to improve vehicle control by ensuring that the system’s trajectories remain within a defined invariant set, thereby preventing loss of control even under disturbances. The work is motivated by the limitations of current Electronic Stability Control (ESC) systems and the potential of future x-by-wire technologies that allow for independent wheel braking and active steering. The methodology begins with a nonlinear bicycle model of vehicle lateral dynamics, incorporating Pacejka’s magic formula to accurately represent tire-road interaction forces across linear, decreasing, and saturated regions. To handle this nonlinearity, the authors employ the exact linear sectors procedure to derive a four-rule Takagi-Sugeno (TS) fuzzy model. This model captures the behavior of lateral tire forces based on front and rear sideslip angles. A dynamic fuzzy output feedback controller is then designed using Parallel Distributed Compensation (PDC). This controller utilizes steering angle rate and differential braking torque as control inputs, relying only on yaw rate and steering angle as measured variables. The design leverages quadratic boundedness theory and Lyapunov stability to guarantee that vehicle trajectories starting within a calculated invariant set will not exceed it, effectively bounding the system’s response to disturbances. The study presents bifurcation analysis results quantifying the vehicle’s stability region in the front sideslip angle and rate phase plane. These results demonstrate that the stability margin decreases with increased steering angles and significantly shrinks under low road adhesion conditions. Simulation tests validate the proposed controller using standard maneuvers, including the ISO3888-2 transient maneuver and roundabout maneuvers. The results indicate that the controlled vehicle satisfactorily tracks the desired yaw rate and maintains stability within the invariant set, even when operating near tire saturation limits. The significance of this work lies in its robust approach to vehicle handling improvement at the limits of adhesion. By combining TS fuzzy modeling with invariant set theory, the proposed controller offers a mathematically guaranteed bound on vehicle behavior, enhancing safety during extreme maneuvers. The use of output feedback with limited measured variables makes the solution practical for implementation, while the integration of differential braking and steering provides the necessary control authority to manage nonlinear tire dynamics effectively.
Provenance
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| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | Crossref | — | — | 1 | 2026-06-25 |
| archive | success | unpaywall | — | — | 2 | 2026-06-26 |
| extract | success | cached | — | — | 2 | 2026-06-26 |
| clean | success | clean | — | — | 1 | 2026-06-26 |
| chunk | success | chunk | — | — | 1 | 2026-06-26 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-26 |
| enrich | success | openalex | — | — | 1 | 2026-06-26 |
| promote | success | — | — | — | 1 | 2026-06-25 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 1 | 2026-06-26 |
| tag | success | vector_similarity | — | — | 6 | 2026-06-26 |
| verify | success | — | — | — | 1 | 2026-06-26 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.
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