Finite-Time Stability for Discrete-Time Systems with Time-Varying Delays and Nonlinear Perturbations Using Relaxed Summation Inequality

Producción CientíficaThis article deals with the problem of delay-dependent finite-time stability (FTS) for delayed discrete-time systems with nonlinear perturbations. First, based on a Lyapunov–Krasovskii Functional, delay-dependent FTS conditions are provided by introducing some free-weighting matrices. Then, a new reduced free-matrix-based inequality is established to estimate the single summation term. The dimensions of these free matrices integral in our results are less than those obtained in the literature. This reduction in the number of variables does not mean that our method is a particular case but simply that our approach is completely different from the others and therefore our method is more effective. Thus, less conservative design conditions are obtained in this paper in terms of linear matrix inequalities (LMIs) and solved using MATLAB’s LMI toolbox to achieve the desired performance. The purpose of this paper is to derive sufficient conditions that ensure the finite-time stability of the discrete-time system. Finally, numerical examples are examined to show the advantage and effectiveness of the proposed results.MICInn, PID2021-123654OB-C31MICInn, PID2020-112871RB-C2

Robust H∞ Control of Takagi–Sugeno Systems with Actuator Saturation

Producción CientíficaThe robust static output feedback control for continuous-time Takagi–Sugeno systems subject to actuator saturation is solved here, including H∞ performance guarantees. Based on a polytopic model of the saturation, sufficient conditions are proposed for designing these controllers in terms of Linear Matrix Inequalities. With the aid of some special derivations, bilinear matrix inequalities are converted into a set of linear matrix inequalities which can be solved easily without requiring iterative algorithms or equality constraints, moreover, the output matrix of the considered system does not require to be full row rank. Finally, some examples are presented to show the validity of the proposed methodology

Improving Leader-Follower Formation Control Performance for Quadrotors

This thesis aims to improve the leader-follower team formation flight performance of Unmanned Aerial Vehicles (UAVs) by applying nonlinear robust and optimal techniques, in particular the nonlinear H_infinity and the iterative Linear Quadratic Regulator (iLQR), to stabilisation, path tracking and leader-follower team formation control problems. Existing solutions for stabilisation, path tracking and leader-follower team formation control have addressed a linear or nonlinear control technique for a linearised system with limited disturbance consideration, or for a nonlinear system with an obstacle-free environment. To cover part of this area of research, in this thesis, some nonlinear terms were included in the quadrotors' dynamic model, and external disturbance and model parameter uncertainties were considered. Five different controllers were developed. The first and the second controllers, the nonlinear suboptimal H_infinity control technique and the Integral Backstepping (IBS) controller, were based on Lyapunov theory. The H_infinity controller was developed with consideration of external disturbance and model parameter uncertainties. These two controllers were compared for path tracking and leader-follower team formation control. The third controller was the Proportional Derivative square (PD2), which was applied for attitude control and compared with the H_infinity controller. The fourth and the fifth controllers were the Linear Quadratic Regulator (LQR) control technique and the optimal iLQR, which was developed based on the LQR control technique. These were applied for attitude, path tracking and team formation control and there results were compared. Two features regarding the choice of the control technique were addressed: stability and robustness on the one hand, which were guaranteed using the H_infinity control technique as the disturbance is inherent in its mathematical model, and the improvement in the performance optimisation on the other, which was achieved using the iLQR technique as it is based on the optimal LQR control technique. Moreover, one loop control scheme was used to control each vehicle when these controllers were implemented and a distributed control scheme was proposed for the leader-follower team formation problem. Each of the above mentioned controllers was tested and verified in simulation for different predefined paths. Then only the nonlinear H_infinity controller was tested in both simulation and real vehicles experiments

A Human Driver Model for Autonomous Lane Changing in Highways: Predictive Fuzzy Markov Game Driving Strategy

This study presents an integrated hybrid solution to mandatory lane changing problem to deal with accident avoidance by choosing a safe gap in highway driving. To manage this, a comprehensive treatment to a lane change active safety design is proposed from dynamics, control, and decision making aspects. My effort first goes on driver behaviors and relating human reasoning of threat in driving for modeling a decision making strategy. It consists of two main parts; threat assessment in traffic participants, (TV s) states, and decision making. The first part utilizes an complementary threat assessment of TV s, relative to the subject vehicle, SV , by evaluating the traffic quantities. Then I propose a decision strategy, which is based on Markov decision processes (MDPs) that abstract the traffic environment with a set of actions, transition probabilities, and corresponding utility rewards. Further, the interactions of the TV s are employed to set up a real traffic condition by using game theoretic approach. The question to be addressed here is that how an autonomous vehicle optimally interacts with the surrounding vehicles for a gap selection so that more effective performance of the overall traffic flow can be captured. Finding a safe gap is performed via maximizing an objective function among several candidates. A future prediction engine thus is embedded in the design, which simulates and seeks for a solution such that the objective function is maximized at each time step over a horizon. The combined system therefore forms a predictive fuzzy Markov game (FMG) since it is to perform a predictive interactive driving strategy to avoid accidents for a given traffic environment. I show the effect of interactions in decision making process by proposing both cooperative and non-cooperative Markov game strategies for enhanced traffic safety and mobility. This level is called the higher level controller. I further focus on generating a driver controller to complement the automated car’s safe driving. To compute this, model predictive controller (MPC) is utilized. The success of the combined decision process and trajectory generation is evaluated with a set of different traffic scenarios in dSPACE virtual driving environment. Next, I consider designing an active front steering (AFS) and direct yaw moment control (DYC) as the lower level controller that performs a lane change task with enhanced handling performance in the presence of varying front and rear cornering stiffnesses. I propose a new control scheme that integrates active front steering and the direct yaw moment control to enhance the vehicle handling and stability. I obtain the nonlinear tire forces with Pacejka model, and convert the nonlinear tire stiffnesses to parameter space to design a linear parameter varying controller (LPV) for combined AFS and DYC to perform a commanded lane change task. Further, the nonlinear vehicle lateral dynamics is modeled with Takagi-Sugeno (T-S) framework. A state-feedback fuzzy H∞ controller is designed for both stability and tracking reference. Simulation study confirms that the performance of the proposed methods is quite satisfactory

Robust stabilization and observation of positive Takagi-Sugeno systems

Esta tesis propone metodologías para diseñar controladores robustos y observadores para los sistemas positivos descritos por modelos de Takagi-Sugeno (TS), lineal, inciertos, y tal vez con retraso. Las condiciones de síntesis se expresan como LMIs (desigualdades matriciales lineales). En la primera parte, se establecen las condiciones para garantizar la estabilización asintótica y la α-estabilización de los sistemas T-S lineales positivas y, tal vez afectados por incertidumbres de intervalo, usando controladores de retroalimentación de estado descompuestos. En la segunda parte, se dan las condiciones necesarias y suficientes para la estabilización de los sistemas de T-S positivos con retraso, en dos casos: cuando las variables de premisa del sistema son medibles o no. Además, el problema de diseño de control basado en observador es considerado, por las leyes de retroalimentación del estado que se pueden elegir con o sin memoria. Para mostrar la eficacia de los métodos propuestos, se proporcionan ejemplos numéricos y prácticos, dando resultados satisfactorios.Departamento de Ingeniería de Sistemas y Proceso