[Paper Review] First and High Order Sliding Mode-Multimodel Stabilizing Control Synthesis using Single and Several Sliding Surfaces for Nonlinear Systems: Simulation on an Autonomous Underwater Vehicles (AUV)

Ahmed Rhif, Zohra Kardous+1 more|arXiv (Cornell University)|Apr 1, 2013

Adaptive Control of Nonlinear Systems14 references3 citations

TL;DR

This paper proposes a first- and high-order sliding mode-multimodel control synthesis using single and multiple sliding surfaces to stabilize nonlinear systems, specifically applied to autonomous underwater vehicles (AUVs). By replacing discontinuous switching with smooth fusion of control laws via Lyapunov-type functions, the method achieves finite-time convergence to the sliding set and ultimate stability with minimal chattering and low control effort, validated through AUV immersion control simulations.

ABSTRACT

This paper provides new analytic tools for a rigorous control formulation and stability analysis of sliding mode-multimodel controller (SM-MMC). In this way to minimise the chattering effect we will adopt as a starting point the multimodel approach to change the commutation of the sliding mode control (SMC) into fusion using a first order then a high order sliding mode control with single sliding surface and, then, with several sliding surfaces. For that the stability conditions invoke the existence of two Lyapunov-type functions, the first associated to the passage to the sliding set in finite time, and the second with convergence to the desired state. The approaches presented in this work are simulated on the immersion control of a submarine mobile which presents a problem for the actuators because of the high level of system non linearity and because of the external disturbances. Simulation results show that this control strategy can attain excellent performances with no chattering problem and low control level.

Motivation & Objective

• To address chattering and control saturation in sliding mode control for highly nonlinear systems.
• To develop a stabilizing control synthesis using first- and high-order sliding modes in conjunction with multimodel frameworks.
• To investigate the use of single and multiple sliding surfaces to improve robustness and convergence performance.
• To ensure finite-time convergence to the sliding set and ultimate stability using Lyapunov-based analysis.
• To validate the approach on an AUV with strong nonlinearities and external disturbances.

Proposed method

• The control strategy employs a multimodel approach to replace abrupt switching in sliding mode control with smooth fusion of control laws.
• First-order sliding mode control is used initially, followed by high-order sliding mode control to reduce chattering.
• Stability is analyzed using two Lyapunov-type functions: one ensuring finite-time reachability of the sliding set, the other guaranteeing convergence to the desired state.
• Multiple sliding surfaces are introduced to enhance system robustness and control performance in high-dimensional nonlinear systems.
• The control synthesis integrates both control laws through a blending mechanism that ensures continuity and reduces control effort.
• The approach is applied to an AUV’s immersion control system, simulating high nonlinearity and external disturbances.

Experimental results

Research questions

• RQ1 How can chattering be minimized in sliding mode control of nonlinear systems using multimodel fusion?
• RQ2 What is the role of first- and high-order sliding modes in improving convergence and stability in multimodel control frameworks?
• RQ3 How do single versus multiple sliding surfaces affect control performance and robustness in nonlinear systems?
• RQ4 Can finite-time convergence to the sliding set and ultimate stability be guaranteed using two Lyapunov-type functions?
• RQ5 What performance improvements are achieved in AUV immersion control using this multimodel sliding mode approach?

Key findings

• The proposed control strategy achieves finite-time convergence to the sliding set, ensuring rapid system response.
• The use of high-order sliding modes significantly reduces chattering compared to conventional sliding mode control.
• Control effort is minimized due to smooth fusion of control laws instead of discontinuous switching.
• The multimodel approach enhances robustness against external disturbances and system nonlinearities in AUV simulations.
• Simulation results demonstrate excellent performance in AUV immersion control with no observable chattering and stable convergence.
• The dual Lyapunov function approach successfully guarantees both finite-time reachability and asymptotic stability.