[Paper Review] Output Feedback Tracking Control for a Class of Uncertain Systems subject to Unmodeled Dynamics and Delay at Input

Quan Quan, Hai Lin+1 more|arXiv (Cornell University)|Nov 1, 2011

Adaptive Control of Nonlinear Systems27 references3 citations

TL;DR

This paper proposes an output feedback tracking control scheme for uncertain nonlinear SISO systems with unmodeled dynamics, input delay, mismatched uncertainties, and disturbances. By using additive state decomposition, the system is transformed into an uncertainty-free form where all uncertainties are lumped into a new output disturbance, enabling observer-based control design that ensures stable, accurate tracking without parameter estimation.

ABSTRACT

Besides parametric uncertainties and disturbances, the unmodeled dynamics and time delay at the input are often present in practical systems, which cannot be ignored in some cases. This paper aims to solve output feedback tracking control problem for a class of nonlinear uncertain systems subject to unmodeled high-frequency gains and time delay at the input. By the additive decomposition, the uncertain system is transformed to an uncertainty-free system, where the uncertainties, disturbance and effect of unmodeled dynamics plus time delay are lumped into a new disturbance at the output. Sequently, additive decomposition is used to decompose the transformed system, which simplifies the tracking controller design. To demonstrate the effectiveness, the proposed control scheme is applied to three benchmark examples.

Motivation & Objective

• Address the challenge of output feedback tracking control in nonlinear systems with mismatched parametric uncertainties, disturbances, unmodeled high-frequency gains, and input time delay.
• Overcome limitations of traditional adaptive control and high-gain feedback methods that fail under unmodeled dynamics or input delays.
• Develop a control framework that ensures stability and accurate tracking despite the absence of exact parameter knowledge or direct estimation of uncertainties.
• Demonstrate the effectiveness of the proposed scheme on benchmark nonlinear systems under various uncertainty conditions.

Proposed method

• Apply additive state decomposition to transform the original uncertain system into an uncertainty-free system where all mismatched uncertainties, disturbances, and input delay effects are lumped into a single output disturbance.
• Redesign the input to ensure smoothness and boundedness, thereby containing the impact of unmodeled high-frequency gains and time delays.
• Design a state observer for the transformed system to estimate both the new state and the lumped disturbance using output feedback.
• Decompose the transformed system into two independent subsystems: one for tracking (including disturbance rejection) and one for input realization, enabling modular controller design.
• Use a low-pass filter to ensure physical realizability of the compensator, and derive the control input via inverse Laplace transform of a filtered transfer function to achieve desired reference tracking.
• Combine the observer-based state estimation with the filtered control input to form a complete output feedback controller that does not require online parameter adaptation.

Experimental results

Research questions

• RQ1 Can a robust output feedback tracking controller be designed for nonlinear systems with unmodeled dynamics and input delay without relying on parameter estimation?
• RQ2 How can mismatched uncertainties and disturbances be effectively handled in the absence of full state information?
• RQ3 To what extent can additive state decomposition simplify the control design for systems with complex uncertainties?
• RQ4 How does the proposed controller perform under parameter mismatch or time delay, compared to standard adaptive or high-gain feedback methods?
• RQ5 Can the controller achieve stable and accurate tracking even when the true system parameters differ from the estimated ones?

Key findings

• The proposed controller achieves accurate output tracking across all three benchmark examples, including cases with unknown or mismatched parameters.
• Simulation results show that tracking performance in Case 2 (unknown parameters) is a trade-off between Case 1 (known parameters) and Case 3 (parameter change), indicating robustness to parameter uncertainty.
• The controller maintains stability and good transient response even when unmodeled dynamics and input delays are present, avoiding the instability issues common in conventional adaptive schemes.
• The response in Case 2 is faster than in Case 1, suggesting that the controller adapts effectively to parameter mismatch without explicit estimation.
• The controller's performance is similar to model reference adaptive control, but without requiring online parameter estimation or persistent excitation.
• The use of a fifth-order low-pass filter ensures physical realizability of the compensator while maintaining tracking accuracy.