State estimation for a class of nonlinear time-varying uncertain system under multiharmonic disturbance (2407.18987v1)

Abstract: The paper considers the observer synthesis for nonlinear, time-varying plants with uncertain parameters under multiharmonic disturbance. It is assumed that the relative degree of the plant is known, the regressor linearly depends on the state vector and may have a nonlinear relationship with the output signal. The proposed solution consists of three steps. Initially, an unknown input state observer is synthesized. This observer, however, necessitates the measurement of output derivatives equal to the plant's relative degree. To relax this limitation, an alternative representation of the observer is introduced. Further, based on this observer, the unknown parameters and disturbances are reconstructed using an autoregression model and the dynamic regressor extension and mixing (DREM) approach. This approach allows the estimates to be obtained in a finite time. Finally, based on these estimates, an observer has been constructed that does not require measurements of the output derivatives. The effectiveness and efficiency of this solution are demonstrated through a computer simulation.

• The paper proposes a novel observer synthesis that achieves finite-time state estimation without relying on output derivatives.
• It relaxes traditional sensor constraints by employing unknown input observers and DREM methods to manage parameter uncertainties.
• Simulation results confirm rapid observer convergence and robustness against multiharmonic disturbances in nonlinear time-varying systems.

State Estimation in Nonlinear Time-Varying Systems under Multiharmonic Disturbance

This paper presents a novel approach to state estimation in nonlinear time-varying systems characterized by uncertain parameters and multiharmonic disturbances. The research targets systems where sensor installation for direct state measurement is either costly or technologically infeasible. It discusses synthesizing an observer for nonlinear, time-varying plants with such parameter uncertainties, leveraging methodologies like unknown input observers (UIOs) and dynamic regressor extension and mixing (DREM) approaches.

Summary of Key Contributions

The authors propose a systematic method consisting of three main steps:

1. Unknown Input State Observer Synthesis: The paper begins with a UIO that requires measuring output derivatives equal to the system's relative degree—an obstacle in practical applications.
2. Relaxation of Output Derivatives Requirement: To mitigate the dependency on output derivatives, an alternative observer representation is developed. This reformulation provides a finite-time estimation of the state vector, sidestepping the need for these derivatives.
3. Estimation of Unknown Parameters and Disturbances: Using the DREM method, the unknown input parameters and disturbances are reconstructed without the output derivatives. The approach is validated through computer simulations, which highlight its efficacy and efficiency.

Methodological Insights

The technique's backbone is an adaptive observer that combines UIO principles for estimating state variables in systems with unknown inputs. It introduces a novel synthesis approach by making use of autoregressive models and the dynamic regressor extension, greatly enhancing traditional observer methods, which often rely on linear transformations and approximations for nonlinearity management.

Numerical Results and Simulation

The effectiveness of this approach is demonstrated through simulations that exhibit the observer's rapid convergence to actual states. The results underline the methodology's robustness against measurement noise, offering a promising direction for future implementations in real-world dynamic systems.

Theoretical Implications

Theoretically, this method expands the class of nonlinear systems that can be addressed by UIO techniques, usually restricted by the requirement of relative degree one. The provision for arbitrary relative degrees signifies a considerable theoretical advancement, tackling challenges that most traditional observer designs encounter in non-linear, time-variant contexts.

Practical Implications and Future Prospects

Practically, the paper positions itself as a stepping stone for future state estimation in applications such as autonomous vehicles and aerospace engineering, where systems frequently encounter nonlinear and time-varying disturbances. The finite-time estimation capability is particularly beneficial for systems that necessitate rapid state adaptation and precise control.

Future research directions could focus on refining the observer design to handle systems with even more complex nonlinearities and disturbances. Additionally, exploring applications in more diversified fields where such disturbances are prevalent will help validate and enhance the generalizability of the proposed approach.

In conclusion, this paper presents a comprehensive solution for state estimation in complex, nonlinear time-varying systems affected by multiharmonic disturbances. It not only addresses theoretical gaps in the observer design for arbitrary relative degrees but also proposes a robust practical framework adaptable to various real-world applications.