Fuzzy systems

Most nonlinear systems contain nonlinearities that are bounded in a bounded region of the state space. Based on this fact, “fuzzy” rules, originally used as smooth interpolators between several behaviours acquired a new meaning and modern fuzzy control, together with LPV control arose in the late 90’s as a successful approach to control nonlinear systems. Takagi-Sugeno (TS) fuzzy models can be regarded as a blending of linear models via non-linear functions. Stability and observer or controller design conditions for these models are usually developed via Lyapunov's direct method.

For the sake of simplicity, classically a quadratic Lyapunov function has been used. Lately, nonquadratic Lyapunov functions gained more interest, with significant results mainly in the discrete-time case, while in the continuous-time their use led to the development of local results.

This research direction focuses on the development of methods for TS models and their practical application in mechanical systems. Specifically, we investigate analysis and design for systems that have a switching nature or that can be described using descriptor models.

Our open and ongoing projects in this area are listed below, together with a selection of completed projects where relevant.

Assistive autonomous UAVs

Robots that assist elderly or disabled persons in their day-to-day tasks can lead to a huge improvement in quality of life. This project employs UAVs to monitor at-risk persons, and research challenges range from real-time observation and observation to high-level vision and control for person monitoring. The project is appropriate for a team of students, each of them working on a well-defined subtask, such as:

Real-time control using a polynomial representation

Fuzzy-polynomial approaches have gained considerable interest in the last years for control of nonlinear systems. The stability and design conditions for such models are derived in the form of sum-of-squares, which can be solved using available tools.

This project aims at the testing and validation of the SOS approach on an available laboratory setup. Options include the Quanser rotational inverted pendulum, controlling an Inteco3D crane to move the load along a designated trajectory, a Cyton Gamma robot arm, etc.

Observer and controller design for laboratory experimental setups

This project will develop observers and controllers for one of the experimental setups in our group. Options include the Quanser rotational inverted pendulum, controlling an Inteco3D crane to move the load along a designated trajectory, etc. We will start by classical parallel distributed compensation-type control and estimation for the fuzzy model, and continue with more complex, non-PDC approaches. Preliminary results will be validated in simulation, after which real-time implementation and validation is performed.

Young Teams grant: Handling non-smooth effects in control of real robotic systems

Robotics has a growing impact on our everyday life. Traditional applications are complemented by the integration of robots in the human environment. With the availability of low cost sensors, aerial robotics also became an active area of research. However, many of the practical challenges associated to the real time control of robotic systems are not yet resolved.

Young Teams grant: Observer design for structured distributed dynamic systems

Power systems, traffic and communication networks, irrigation systems, hydropower valleys, or smart grids are composed of structured interconnections of lower-dimensional subsystems. To monitor such systems, one has to know the values of the variables in the system. Since in general not all these variables can be measured, they must be estimated, based on the system model and available measurements. However, there is no general method to design estimators for nonlinear systems. The challenge of designing an estimator becomes even more difficult if the system is distributed.

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