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.

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.

Controller design for a robot arm

This project concerns controller design for the Cyton Gamma 7DOF robot arm available in our group. This being a mechanical system, modeling will commence from the Euler-Lagrange equations, leading to a TS model in descriptor form. For the sake of simplicity of the controller implementation, this form will be maintained for the design. We will start by testing existing results and continue with incorporating in the design further algebraic constraints. Preliminary results will be validated in simulation, after which real-time implementation and validation is performed.

Observer for the estimation of the force at the shoulder of a person in a wheelchair

In the context of the development of a new strategy for helping persons with limited mobiliy in wheelchair, we wish to estimate the forces at the shoulder of a person during his moving in wheelchair. To achieve this goal, an observer has to be designed from a mechanical model of the upper body of the person and from experimentations on a wheelchair.

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.

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.

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