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

Robust Stabilisation of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes

This paper addresses the robust stabilisation problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a non-parallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for T-S fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analysed and the sliding mode controller is parameterised in terms of the solutions of a set of linear matrix inequalities (LMIs) which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented

Decentralised control for complex systems - An invited survey

© 2014 Inderscience Enterprises Ltd. With the advancement of science and technology, practical systems are becoming more complex. Decentralised control has been recognised as a practical, feasible and powerful tool for application to large scale interconnected systems. In this paper, past and recent results relating to decentralised control of complex large scale interconnected systems are reviewed. Decentralised control based on modern control approaches such as variable structure techniques, adaptive control and backstepping approaches are discussed. It is well known that system structure can be employed to reduce conservatism in the control design and decentralised control for interconnected systems with similar and symmetric structure is explored. Decentralised control of singular large scale systems is also reviewed in this paper

Non-fragile H∞ control with randomly occurring gain variations, distributed delays and channel fadings

This study is concerned with the non-fragile H∞ control problem for a class of discrete-time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite-distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time-delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non-fragile H∞ outputfeedback controller such that the closed-loop control system is stochastically stable with a prescribed H∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H∞ disturbance attenuation, and the addressed non-fragile control problem is then recast as a convex optimisation problem solvable via the semidefinite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method

Performance Guarantee of a Class of Continuous LPV System with Restricted-Model-Based Control

This paper considers the problem of the robust stabilisation of a class of continuous Linear Parameter Varying (LPV) systems under specifications. In order to guarantee the stabilisation of the plant with very large parameter uncertainties or variations, an output derivative estimation controller is considered. The design of such controller that guarantee desired  induced gain performance is examined. Furthermore, a simple procedure for achieving the  norm performance is proved for any all-poles single-input/single-output second order plant. The proof of stability is based on the polytopic representation of the closed loop under Lyapunov conditions and system transformations. Finally, the effectiveness of the proposed method is verified via a numerical example

An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both 'slow' and 'fast' dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable

Delay-Dependent Finite-Time H

Delay-dependent finite-time H∞ controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-time H∞ controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds the H∞ performance to a prescribed disturbance attenuation level γ. The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI). Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve a H∞ performance level

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

Dynamic output feedback sliding mode control for uncertain linear systems

In this paper, a class of uncertain linear systems with unmatched disturbances is considered, where the nominal system representation is allowed to be non-minimum phase. A sliding surface is designed which is dependent on the system output, observed state, and estimated uncertain parameters. A linear coordinate transformation is introduced so that the stability analysis of the reduced-order sliding mode dynamics can be conveniently performed. A robust output feedback sliding mode control (OFSMC) is then designed to drive the considered system state to reach the sliding surface in finite time and maintain a sliding motion thereafter. A simulation example for a high incidence research model (HIRM) aircraft is used to demonstrate the effectiveness of the proposed method

Robust model-based fault estimation and fault-tolerant control : towards an integration

To maintain robustly acceptable system performance, fault estimation (FE) is adopted to reconstruct fault signals and a fault-tolerant control (FTC) controller is employed to compensate for the fault effects. The inevitably existing system and estimation uncertainties result in the so-called bi-directional robustness interactions defined in this work between the FE and FTC functions, which gives rise to an important and challenging yet open integrated FE/FTC design problem concerned in this thesis. An example of fault-tolerant wind turbine pitch control is provided as a practical motivation for integrated FE/FTC design.To achieve the integrated FE/FTC design for linear systems, two strategies are proposed. A H∞ optimization based approach is first proposed for linear systems with differentiable matched faults, using augmented state unknown input observer FE and adaptive sliding mode FTC. The integrated design is converted into an observer-based robust control problem solved via a single-step linear matrix inequality formulation.With the purpose of an integrated design with more freedom and also applicable for a range of general fault scenarios, a decoupling approach is further proposed. This approach can estimate and compensate unmatched non-differentiable faults and perturbations by combined adaptive sliding mode augmented state unknown input observer and backstepping FTC controller. The observer structure renders a recovery of the Separation Principle and allows great freedom for the FE/FTC designs.Integrated FE/FTC design strategies are also developed for Takagi-Sugeno fuzzy modelling nonlinear systems, Lipschitz nonlinear systems, and large-scale interconnected systems, based on extensions of the H∞ optimization approach for linear systems.Tutorial examples are used to illustrate the design strategies for each approach. Physical systems, a 3-DOF (degree-of-freedom) helicopter and a 3-machine power system, are used to provide further evaluation of the proposed integrated FE/FTC strategies. Future research on this subject is also outlined