Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems

This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Sampled-data fuzzy controller for continuous nonlinear systems

The sampled-data fuzzy control of nonlinear systems is presented. The consequents of the fuzzy controller rules are linear sampled-data sub-controllers. As a result, the fuzzy controller is a weighted sum of some linear sampled-data sub-controllers that can be implemented by a microcontroller or a digital computer to lower the implementation cost. Consequently, a hybrid fuzzy controller consisting of continuous-time grades of memberships and discrete-time sub-controller is obtained. The system stability of the fuzzy control system is investigated on the basis of Lyapunov-based approach. The sampling activity introduces discontinuity to complicate the system dynamics and make the stability analysis difficult. The proposed fuzzy controller exhibits a favourable property to alleviate the conservativeness of the stability analysis. Furthermore, linear matrix inequality-based performance conditions are derived to guarantee the system performance of the fuzzy control system. An application example is given to illustrate the merits of the proposed approac

Integrated fault estimation and accommodation design for discrete-time Takagi-Sugeno fuzzy systems with actuator faults

This paper addresses the problem of integrated robust fault estimation (FE) and accommodation for discrete-time Takagi–Sugeno (T–S) fuzzy systems. First, a multiconstrained reduced-order FE observer (RFEO) is proposed to achieve FE for discrete-time T–S fuzzy models with actuator faults. Based on the RFEO, a new fault estimator is constructed. Then, using the information of online FE, a new approach for fault accommodation based on fuzzy-dynamic output feedback is designed to compensate for the effect of faults by stabilizing the closed-loop systems. Moreover, the RFEO and the dynamic output feedback fault-tolerant controller are designed separately, such that their design parameters can be calculated readily. Simulation results are presented to illustrate our contributions

Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults

The goal of this paper is to describe a novel fault tolerant tracking control (FTTC) strategy based on robust fault estimation and compensation of simultaneous actuator and sensor faults. Within the framework of fault tolerant control (FTC) the challenge is to develop an FTTC design strategy for nonlinear systems to tolerate simultaneous actuator and sensor faults that have bounded first time derivatives. The main contribution of this paper is the proposal of a new architecture based on a combination of actuator and sensor Takagi-Sugeno (T-S) proportional state estimators augmented with proportional and integral feedback (PPI) fault estimators together with a T-S dynamic output feedback control (TSDOFC) capable of time-varying reference tracking. Within this architecture the design freedom for each of the T-S estimators and the control system are available separately with an important consequence on robust L₂ norm fault estimation and robust L₂ norm closed-loop tracking performance. The FTTC strategy is illustrated using a nonlinear inverted pendulum example with time-varying tracking of a moving linear position reference. Keyword

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228

T-S Fuzzy Bibo Stabilisation of Non-Linear Systems Under Persistent Perturbations Using Fuzzy Lyapunov Functions and Non-PDC Control Laws

[EN] This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi-Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded output stabilisation in closed-loop throughout the computation of generalised inescapable ellipsoids. These controllers are computed with linear matrix inequalities using fuzzy Lyapunov functions and integral delayed Lyapunov functions. LMI conditions developed in this paper provide non-PDC controllers with a minimum *-norm (upper bound of the 1-norm) for the T-S fuzzy system under persistent perturbations. The results presented in this paper can be classified into two categories: local methods based on fuzzy Lyapunov functions with guaranteed bounds on the first derivatives of membership functions and global methods based on integral-delayed Lyapunov functions which are independent of the first derivatives of membership functions. The benefits of the proposed results are shown through some illustrative examples.This work has been funded by Ministerio de Economia y Competitividad, Spain (research project RTI2018-096904-B-I00) and Conselleria de Educacion, Cultura y Deporte-Generalitat Valenciana, Spain (research project AICO/2019/055).Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2020). T-S Fuzzy Bibo Stabilisation of Non-Linear Systems Under Persistent Perturbations Using Fuzzy Lyapunov Functions and Non-PDC Control Laws. International Journal of Applied Mathematics and Computer Science (Online). 30(3):529-550. https://doi.org/10.34768/amcs-2020-0039S52955030

A New Sum-of-Squares Design Framework for Robust Control of Polynomial Fuzzy Systems With Uncertainties

This paper presents a new sum-of-squares (SOS, for brevity) design framework for robust control of polynomial fuzzy systems with uncertainties. Two kinds of robust stabilization conditions are derived in terms of SOS. One is global SOS robust stabilization conditions that guarantee the global and asymptotical stability of polynomial fuzzy control systems. The other is semiglobal SOS robust stabilization conditions. The latter is available for very complicated systems that are difficult to guarantee the global and asymptotical stability of polynomial fuzzy control systems. The main feature of all the SOS robust stabilization conditions derived in this paper are to be expressed as nonconvex formulations with respect to polynomial Lyapunov function parameters and polynomial feedback gains. Since a typical transformation from nonconvex SOS design conditions to convex SOS design conditions often results in some conservative issues, the new design framework presented in this paper gives key ideas to avoid the conservative issues. The first key idea is that we directly solve nonconvex SOS design conditions without applying the typical transformation. The second key idea is that we bring a so-called copositivity concept. These ideas provide some advantages in addition to relaxations. To solve our SOS robust stabilization conditions efficiently, we introduce a gradient algorithm formulated as a minimizing optimization problem of the upper bound of the time derivative of an SOS polynomial that can be regarded as a candidate of polynomial Lyapunov functions. Three design examples are provided to illustrate the validity and applicability of the proposed design framework. The examples demonstrate advantages of our new SOS design framework for the existing linear matrix inequality approaches and the existing convex SOS approach

BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation

[EN] This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi¿Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.The authors wish to thank the Editor-in-Chief and the anonymous reviewers for their valuable comments and suggestions. This work has been funded by Ministerio de Economia y Competitividad (Spain) through the research project DPI2015-71443-R and by Generalitat Valenciana (Valencia, Spain) through the research project GV/2017/029.Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2018). BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation. International Journal of Applied Mathematics and Computer Science (Online). 28(3):457-472. https://doi.org/10.2478/amcs-2018-0035S45747228