A registration for this workshop is required via the ECC conference web page before the 12th of April, see the following link: https://ecc26.euca-ecc.org/workshops/ 

Cyber-physical systems are characterized by a strong interplay between hardware and software and only obtain their specific properties concerning (energy) efficiency, robustness, fault tolerance and resilience against disturbances and adversarial attacks by state estimation and control approaches which are robust against uncertainty. In recent years, cyber-physical systems have significantly grown in their complexity concerning the number of components. Moreover, their importance increases in many domains of critical infrastructure, for example, in transportation and energy supply. Due to the high safety levels required for these kinds of systems, it is indispensable to guarantee functional properties such as trajectory tracking capabilities, stability despite omnipresent uncertainty and environmental influences, and robustness against an imperfect knowledge of the exact system dynamics. To ensure these properties, set-based representations, i.e., worst-case bounds, for uncertain parameters, disturbances, and the influence of measurement noise can be used to develop estimation and control procedures so that desired performance indicators are met with certainty. Although this is extremely appealing from a methodological and application point of view, the use of set-based approaches is still underrepresented in the literature and in industry. Within this workshop, we aim at presenting fundamentals and most recent developments concerning set-based identification, state and disturbance estimation, fault detection, and control methods. The applicability of the presented methods is highlighted by a collection of real-life use cases, ranging from estimation within the energy domain, over reliable control of thermal systems, the detection of faults and cyber attacks to localization and navigation in maritime robotics.

Morning session: 8:30-12:00

Opening:

Andreas Rauh and Marit Lahme (Carl von Ossietzky Universität Oldenburg, Germany) – Introduction to the Workshop: An Overview of Applications of Set-Based Methods from the Perspectives of Modeling, Identification, State Estimation and Control”

Estimation and Identification:

Daniel Silvestre (Universidade NOVA de Lisboa, Portugal)

Title: Explicit Set-based Estimation: Optimal Accuracy without Order Reduction Methods

Abstract: The key trade-off in set-based estimation for linear systems is between accuracy and the complexity of the data structures associated with the set representation. On one extreme, solutions using Interval or Ellipsoids have constant complexity but suffer from the wrapping effect where the conservatism added because the set operations are not exact gets propagated to future estimates, thus degrading the accuracy. On the other extreme, solutions based on Constrained Zonotopes (CZs) or Constrained Convex Generators (CCGs) have exact operations and optimal accuracy at the expense of a linear increase in the size of the data structures. In this presentation, we will highlight this problem and showcase a new type of observer that has constant size of data structures and an accuracy close to the optimal, removing the need for expensive order reductions methods. We will also cover applications in the domain of Robust Model Predictive Control and Safe Navigation that can leverage this explicit observer to provide theoretical guarantees.

Tarek Raissi (CNAM, Paris, France)

Title: Functional Interval Observers Design for Linear Systems

Abstract: This lecture presents recent advances in functional interval estimation for continuous-time systems subject to both time-varying and time-invariant bounded uncertainties. In particular, it highlights an important technique based on peak-to-peak functional observer design and interval analysis, recently published. Two main approaches are discussed. First, a splitting-based method is introduced, where the estimation error dynamics are decomposed into two subsystems to effectively handle time-invariant disturbances and improve estimation accuracy. Then, an augmentation-based method is presented, further enhancing performance by explicitly incorporating time-invariant properties into both the observer design and the interval estimation process. A theoretical comparison of the different methods, including state-of-the-art approaches, is carried out, and simulation results highlight their respective performance and effectiveness.

Marit Lahme (Carl von Ossietzky Universität Oldenburg, Germany)

Title: Interval-Based Identification of Characteristic Curves

Abstract: Characteristic curves describe the relationship between different physical quantities of a system. The knowledge about these relationships is essential for various applications, such as monitoring its current state, predicting its future behavior, and designing appropriate controllers. This presentation focuses on the interval-based identification of characteristic curves. In state-space systems, the relationships to be identified can appear within the state equations or the output equation. In certain applications, it is not feasible to directly obtain the characteristic curves of interest by measuring the corresponding physical quantities, because sometimes they cannot be measured directly. A common approach to obtain a characteristic curve is to use a parameter identification to fit the parameters of a function representing the characteristic curve to measured or estimated data. This approach requires that the structure of the function is known beforehand and permits the identification of the characteristic during system operation only under special circumstances. In this presentation, we investigate a possible approach to identify characteristic curves during system operation without a-priori knowledge about the structure of the function. 

Andreas Rauh (Carl von Ossietzky Universität Oldenburg, Germany)

Title: Set-Based Methods for Secure State Estimation under Consideration of Cyber-Attack Scenarios

Abstract: In this talk, we focus on set-based algorithms for the estimation of states in the presence of bounded uncertainty, external disturbances, and a-priori unknown effects of cyber-attacks. Here, a distinction between attack-based sensor anomalies and sensor malfunctioning is made. The presented algorithm basically is an extension of a former predictor-corrector set-valued state estimator to the case where the feasible domains of the bounded uncertainties are time-varying. Moreover, the introduced algorithm comprises several set-membership tests that allow detecting the occurrence of sensor faults or output malicious attacks and then discarding them from the estimation process. Moreover, to defeat the attacker’s strategy, only a sub-set of the available sensors is selected randomly at each time instant, to improve the efficiency of the estimation algorithm.

Afternoon session: 13:30-17:30

Methods for Control and Verification:

Vicenç Puig (Universitat Politècnica de Catalunya, Spain)

Title: Set-Based Approaches for Diagnosis and Fault-Tolerant Control 

Abstract: This talk reviews the use of set-based methods in fault diagnosis (FD) and tolerant control (FTC). Set-based methods use a deterministic unknown-but-bounded description of noise and parametric uncertainty. These methods aim to check the consistency between observed and predicted behavior by using simple sets to approximate the exact set of possible behaviors (in parameter or state space). When an inconsistency is detected between the measured and predicted behavior obtained using a faultless model of the systems, a fault can be indicated. Otherwise, nothing can be stated. The same principle can be used to identify interval models for fault detection and to develop methods for fault tolerance evaluation. Finally, some real applications will be used to illustrate the usefulness and performance of set- methods for FDI and FTC.
 

Julien Alexandre dit Sandretto (ENSTA, Paris, France)

Title: Confidence-Based Signal Temporal Logic and Application to Uncertain Cyber-Physical Systems

Abstract: Verifying that cyber-physical systems satisfy temporal specifications under uncertainty is a fundamental challenge in control engineering. Stochastic approaches offer probabilistic assessments but often lack formal guarantees, while reachability-based methods provide soundness, at the cost of some conservatism. We present a framework that bridges these two paradigms by combining reachability analysis with the Potential Cloud formalism. Signal Temporal Logic (STL) semantics are extended to sets of trajectories through a three-valued interpretation that explicitly distinguishes guaranteed satisfaction, guaranteed violation, and uncertainty. By propagating confidence intervals through reachable tubes, we derive certified lower bounds on the probability of STL satisfaction without requiring knowledge of the future state distribution. The approach is demonstrated on a nonlinear multi-parameter system and a neural network–controlled vehicle, yielding guaranteed probabilistic safety bounds with practical computation times, significantly outperforming individual-clause approximations.

Control Applications:

Quentin Brateau (ENSTA, Brest, France)

Title: Capture Basin Characterization for Frugal Extremum Seeking Cyclic Navigation using Set Methods

Abstract: This presentation focuses on the formal characterization of the capture basin for a frugal, localization-free extremum seeking strategy applied to Unmanned Surface Vehicles (USVs). The control method utilizes a cyclic navigation approach to navigate toward the extremum of a scalar field, such as the deepest point of a lake. A key feature of this strategy is its extreme computational frugality, requiring only a single memory state to store the previous sensor measurement, and a simple control law. While local stability can be demonstrated using discrete-time linear analysis, determining the capture basin of this hybrid system is challenging. We propose the use of set methods, specifically interval analysis, to provide a guaranteed characterization of this basin. This approach allows us to rigorously define the set of initial configurations from which the USV is guaranteed to converge to the target orbit, even under bounded measurement noise and sparse sampling conditions.

Title: Characterization of the secure zone using Interval Analysis and graphs

Abstract: This presentation addresses the problem of securing zones against intruders using a fleet of mobile robots. Guaranteed detection is achieved by forming a continuous barrier of "secure zones," defined as the union of past visibility regions eroded by the intruder’s maximum speed. Mathematically, this involves projecting a time-evolving set from the space-time manifold onto R2. Standard interval-based paving methods often suffer from significant over-approximation and the loss of topological information during projection. We propose a novel certified projection method that focuses on boundary detection rather than volumetric enclosure. By combining centered-form evaluations with a directed graph approach based on boundary detection contractors, our method faithfully recovers the topology of the secure area. Numerical experiments demonstrate that this approach significantly reduces the wrapping effect and provides higher geometric precision and scalability compared to traditional paving techniques.