Lara JABER will defend her doctoral thesis on Wednesday, December 10, 2025: “Design of Observers for Uncertain Systems: Artificial-Delays based Derivative Approximation and Neural-Network Modeling”

The estimation of signal derivatives from noisy measurements is a classical ill-posed problem. In control and observer design, knowledge of derivatives is often essential. This task is usually performed using differentiators. However, each type of differentiator has inherent limitations and relies on specific assumptions about the system.

The first contribution of this thesis is the development of a new model-free and prescribed-time method for approximating output derivatives. The main idea is to compute derivatives through a weighted combination of past system measurements. This approach eliminates the need for a separate dynamic differentiator whenever derivative information is required.

By exploiting the Taylor approximation of past measurements, the concept of artificial delays can be employed to determine the required weighting coefficients.

The necessary conditions on the system output, which guarantee the applicability and validity of this approach, are clearly defined. These conditions ensure that the desired derivatives can be accurately approximated from the available measurements and that the estimation precision remains guaranteed under mild smoothness assumptions.

The proposed method acts as a general operator that can be integrated into any linear or nonlinear controller or observer requiring the knowledge of a linear combination of output derivatives. A systematic procedure is introduced to determine the optimal weighting coefficients in the presence and absence of measurement noise. It makes use of available information about derivative bounds or measurement noise to achieve an optimal trade-off between accuracy, convergence speed, and robustness to noise. The influence of each parameter on these properties is analyzed, leading to practical tuning guidelines.

The second part of the thesis focuses on integrating this method into the design of observers for systems with uncertain dynamics or unknown inputs.

The method is first combined with a High-Gain Observer, where it is shown that, under suitable conditions, it improves estimation accuracy and reduces the peaking phenomenon and the amplification of measurement noise.

The proposed method is then applied to an Unknown Input Observer for systems with arbitrary relative degree. It removes the need for external differentiators and simplifies the observer structure.

The concept of artificial delays is further extended to estimate the derivatives of unknown inputs. This extension relaxes the classical assumption of a zero derivative for the unknown input, which is typically imposed in standard Extended State Observers.

Finally, motivated by the growing popularity of neural networks, the thesis proposes a new Unknown Input Observer in which the unknown input is modeled by a neural network. The network parameters are estimated online as part of an extended state that also includes the system state. This approach removes the usual zero-derivative assumption on the unknown input that constrains conventional extended state designs.