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Adaptive Disturbance Observer-based Full-Order Integral-Terminal Sliding Mode Control with Unknown A Priori Bound on Uncertainty

Jit Koley, Binoy Krishna Roy

TL;DR

The paper tackles robust stabilization of an $n$-th order chain of integrators with matched disturbances whose time-derivative bound is unknown. It proposes a novel Adaptive Disturbance Observer-based Full-order Integral-Terminal Sliding Mode Control (ADO-FOITSMC) that eliminates the reaching phase and reduces chattering by coupling a disturbance observer with a continuous FOITSM framework, and proves global uniform ultimate boundedness of states and disturbance estimation. A Lyapunov-based analysis yields a finite-time convergence to a bounded neighborhood with bound $\mathcal{B}=\sqrt{\tfrac{2\bar{\delta}}{\gamma-\theta}}$ under $\dot{V}\le -\gamma V +\bar{\delta}$. The approach is validated on a 3rd-order example and a rigid-spacecraft attitude stabilization case, showing improved robustness and smoother control compared with existing adaptive sliding-mode methods, with practical relevance to aerospace systems where disturbance bounds are unknown.

Abstract

This study presents a novel, continuous finite-time control strategy for a class of nonlinear systems subject to matched uncertainties with unknown bounds. We propose an Adaptive Disturbance Observer-based Full-order Integral-Terminal Sliding Mode Control (ADO-FOITSMC) to stabilize a chain of integrators in presence of exogenous disturbances whose time derivative is bounded by a constant that is not known a priori. Key features of this approach include a significant reduction in control input chattering and a non-monotonic adaptive law for the observer gains, which prevents overestimation while ensuring the global boundedness of system states. The effectiveness and practical viability of the proposed algorithm are demonstrated through its application to the attitude stabilization of a rigid spacecraft.

Adaptive Disturbance Observer-based Full-Order Integral-Terminal Sliding Mode Control with Unknown A Priori Bound on Uncertainty

TL;DR

The paper tackles robust stabilization of an -th order chain of integrators with matched disturbances whose time-derivative bound is unknown. It proposes a novel Adaptive Disturbance Observer-based Full-order Integral-Terminal Sliding Mode Control (ADO-FOITSMC) that eliminates the reaching phase and reduces chattering by coupling a disturbance observer with a continuous FOITSM framework, and proves global uniform ultimate boundedness of states and disturbance estimation. A Lyapunov-based analysis yields a finite-time convergence to a bounded neighborhood with bound under . The approach is validated on a 3rd-order example and a rigid-spacecraft attitude stabilization case, showing improved robustness and smoother control compared with existing adaptive sliding-mode methods, with practical relevance to aerospace systems where disturbance bounds are unknown.

Abstract

This study presents a novel, continuous finite-time control strategy for a class of nonlinear systems subject to matched uncertainties with unknown bounds. We propose an Adaptive Disturbance Observer-based Full-order Integral-Terminal Sliding Mode Control (ADO-FOITSMC) to stabilize a chain of integrators in presence of exogenous disturbances whose time derivative is bounded by a constant that is not known a priori. Key features of this approach include a significant reduction in control input chattering and a non-monotonic adaptive law for the observer gains, which prevents overestimation while ensuring the global boundedness of system states. The effectiveness and practical viability of the proposed algorithm are demonstrated through its application to the attitude stabilization of a rigid spacecraft.
Paper Structure (6 sections, 2 theorems, 35 equations, 4 figures)

This paper contains 6 sections, 2 theorems, 35 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Chattering free adaptive SMC with unknown apriori bound on uncertainty
  4. Illustrative Example I
  5. Performance Comparison
  6. Case study

Key Result

Theorem 1

The system plant, characterised by disturbance $d$ as assumed in ass_1 and assum2, is globally uniformly stable (GUB) and globally uniformly ultimately bounded (GUUB) (khalil2002nonlinear) in finite time $t_{r}$ if the control $u$ is chosen as The disturbance observer dynamics are defined as with the adaptation law where $\tilde{d} = d - \hat{d}$, $\tilde{k} = k - \hat{k}$, $z(0) = x_n(0)$, $s(

Figures (4)

  • Figure 1: Schematic Diagram for Stabilisation of (\ref{['plant']})
  • Figure 2: \ref{['ado3_states']}, \ref{['ado3_ss']} and \ref{['ado3_d_tilde']} show the ultimate boundedness of state trajectories, sliding variable and disturbance estimation error, respectively, on the application of adaptive ADO-based FOITSMC. Moreover, the minimum estimated adaptive gain required for GUUB is shown in \ref{['ado3_k_hat']}.
  • Figure 3: The comparison result of the proposed algorithm with the existing ASTW in the presence of disturbances $\sin(2\pi t)$ and $\sin(2\pi t)+\texttt{ramp}(t)$, where $\texttt{ramp}(t)=0.5 t\left(\text{sgn(t)}+1\right)$. \ref{['com_khat1']} and \ref{['com_khat2']} shows the comparison of estimated $k$ for both the cases. \ref{['com_ss1']} and \ref{['com_ss2']} illustrates the comparison in sliding variable for two kind of disturbances.
  • Figure 4: This figure illustrates the performance of the proposed adaptive controller under matched disturbances. Sub-figures (\ref{['spacecraft_quaternions']})–(\ref{['spacecraft_d_tilde']}) confirm the global boundedness of the attitude quaternions, angular velocities ($\Omega$), the sliding variable, and the disturbance estimation error. The corresponding continuous control input and the evolution of the adaptive gain ($\hat{k}$) are presented in (\ref{['spacecraft_u']}) and (\ref{['spacecraft_k_hat']}), respectively.

Theorems & Definitions (12)

  • Definition 1: Ideal sliding levant2003higher
  • Definition 2: Real sliding levant2003higher
  • Remark 1
  • Theorem 1
  • proof
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • ...and 2 more