Leonardo Amaral Mozelli

Stability analysis of linear time-varying systems: Improving conditions by adding more information about parameter variation

Abstract In this paper a new Lyapunov function is proposed for stability analysis of linear time-varying systems. This new function carries more information regarding parameter variation leading to less conservative conditions. Using Finsler’s lemma and a suitable form to describe the high-order time-derivatives of the parameters, finite sets of LMIs are obtained which are progressively less conservative as a pair of parameters grow. Previous results can be seen as a special case and numerical examples are carried out for the sake of illustration.

Less conservative fuzzy control for discrete-time Takagi-Sugeno systems.

New analysis and control design conditions of discrete-time fuzzy systems are proposed. Using fuzzy Lyapunovs functions and introducing slack variables, less conservative conditions are obtained. The controller guarantees system stabilization and ℋ∞ performance. Numerical tests and a practical experiment in Chuas circuit are presented to show the effectiveness.

New Lyapunov function and extra information on membership functions for improving stability conditions of TS systems

Abstract This paper presents an improved stability condition for Takagi-Sugeno (TS) fuzzy systems based on a new fuzzy Lyapunov function. This new fuzzy Lyapunov function aggregates more information with respect to the membership function variation (time-derivative) via an augmented state vector. This new fuzzy Lyapunov function is not just parametrized by the membership functions variations but it is also based on a polynomial combination of them. To derive LMI based stability condition using the proposed new fuzzy Lyapunov function two ideas are invoked: i ) the inclusion of the membership function time-derivative information using a finite number of vectors and, ii ) the use of the so-called null term. Two numerical examples are presented to illustrate the improvements.

SOFC for TS fuzzy systems: Less conservative and local stabilization conditions

The static output feedback control (SOFC) for Takagi-Sugeno (TS) fuzzy systems is addressed in this paper. Based on Lyapunov theory the proposed methods are formulated as Linear Matrix Inequalities (LMIs). To obtain less conservative conditions the properties of membership functions time-derivative are explored. Wiht this new methodology SOFC with higher H∞ attenuation level can be designed. Moreover, the method is extended to local stabilization using the concepts of invariant ellipsoids and regions of stability. These local conditions overcome some difficulties associated with estimating bounds for the timederivative of the membership functions. Examples are given to illustrate the merits of the proposed approaches.

STABILITY ANALYSIS OF TAKAGI-SUGENO FUZZY SYSTEMS VIA LMI: METHODOLOGIES BASED ON A NEW FUZZY LYAPUNOV FUNCTION

Stability analysis of TS fuzzy systems can be much improved by resorting to fuzzy Lyapunov functions, since they are parameterized by membership functions and can better characterize the time-varying feature of these systems by means of the information regarding the rst time-derivative of the membership functions. In this paper an enhanced fuzzy Lyapunov function is used to develop stability conditions that evaluate also the second time-derivative of membership functions, improving the time-varying characterization of TS systems. By using dieren t strategies to consider the information regarding such derivatives and employing some numerical tools that decouple system from Lyapunov function matrices new LMI tests are developed. Numerical examples illustrate the eectiv eness of those methodologies.

LMI designmethod for networked-based PID control

ABSTRACT In this paper, we propose a methodology for the design of networked PID controllers for second-order delayed processes using linear matrix inequalities. The proposed procedure takes into account time-varying delay on the plant, time-varying delays induced by the network and packed dropouts. The design is carried on entirely using a continuous-time model of the closed-loop system where time-varying delays are used to represent sampling and holding occurring in a discrete-time digital PID controller.

Attitude control for an Hybrid Unmanned Aerial Underwater Vehicle: A robust switched strategy with global stability

This paper presents a method for stabilizing the attitude of a Hybrid Unmanned Aerial Underwater Vehicle. Firstly, we present aerodynamic and hydrodynamic models for the angular motion of our robot, discussing effects like buoyancy force and added inertia. Next, we apply robust control techniques for both environment, aerial and underwater, based on linear uncertain models with only four vertices and well-defined stability criteria, such as D-stability and ℋ2 performance. Gain matrices Kair and Kwat are computed and the attitude of the vehicle at the hovering operation point for each environment is controlled, respectively. Finally, a procedure is proposed to check the global stability for the switching control case, when the robot changes from air to water (or vice-versa). Numerical simulations with disturbances and switching control are presented to show the stability at different initial conditions.

Attitude of quadrotor-like vehicles: Fuzzy modeling and control with prescribed rate of convergence

This paper addresses a method for stabilizing the attitude of a quadrotor-like Unmanned Aerial Vehicle (UAV). Towards this end, a new fuzzy control technique based on Linear Matrix Inequalities (LMIs) is proposed, relying on a simple Takagi-Sugeno (TS) fuzzy model when compared to others found in the Literature. This strategy guarantees prescribed performance criteria, such as exponential decay rate, allowing stability under aggressive disturbances. The designed local gains are combined through membership functions of the model and are used to regulate the attitude of the vehicle on the hovering operating point, an important flight mode for this kind of robot. Numerical analysis reveal how the transient response can be tuned and tests with disturbances show the stability of the vehicle starting from different initial conditions, illustrating the merits of the proposed approach.

PID tuning under uncertain conditions: robust LMI design for second-order plus time-delay transfer functions*

Abstract This paper proposes a systematic method for design of PID controllers for continuous time systems subjected to time-delay. An appropriate Lyapunov-Krasovskii functional is proposed yielding delay dependent conditions that guarantee a prescribed H ∞ performance for the closed-loop system. The controller design is carried out by means of convex optimization problems written in the form of linear matrix inequalities. The innovative aspect is that robustness issues associated with time-delay are investigated by assuming that it can vary within prescribed bounds. Numerical experiments are provided to illustrate the advantages.

Fiducial Markers Applied for Pose Tracking of a Robotic Manipulator: Application in Visual Servoing Control

This paper presents the implementation of visual servo control for a robotic manipulator bereft of proprioceptive sensors, employing for such purpose computer vision techniques to infer the joint angles and position coordinates of the system in real-time. Fiducial markers were attached to the links of the manipulator, so that, through a simple camera physically arranged in monocular topology and steady configuration (eye to hand), and a processing and data extraction interface, it is possible to compute the complete spatial configuration of the manipulator and therefore, calculate control laws for it. Regarding this aspect, the manipulator dynamics was disregarded, and a resolved-rate control method was applied, based on the differential kinematics of the robot.