Antonio Sala

Perspectives of fuzzy systems and control

Although fuzzy control was initially introduced as a model-free control design method based on the knowledge of a human operator, current research is almost exclusively devoted to model-based fuzzy control methods that can guarantee stability and robustness of the closed-loop system. State-of-the-art techniques for identifying fuzzy models and designing model-based controllers are reviewed in this article. Attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy, such as expert control, supervision and diagnostic systems. Open issues are highlighted and an attempt is made to give some directions for future research.

Computer control under time-varying sampling period: An LMI gridding approach

This paper addresses computer control under time-varying sampling period and delayed actuation. The proposed approach uses time-varying observers and state-feedback controllers designed by means of linear matrix inequalities (LMI) and quadratic Lyapunov functions. The use of non-stationary Kalman filters is also discussed. A separation principle applies in some cases. A DC motor control setup shows the applicability of the approach in a real implementation.

Polynomial Fuzzy Models for Nonlinear Control: A Taylor Series Approach

Classical Takagi-Sugeno (T-S) fuzzy models are formed by convex combinations of linear consequent local models. Such fuzzy models can be obtained from nonlinear first-principle equations by the well-known sector-nonlinearity modeling technique. This paper extends the sector-nonlinearity approach to the polynomial case. This way, generalized polynomial fuzzy models are obtained. The new class of models is polynomial, both in the membership functions and in the consequent models. Importantly, T-S models become a particular case of the proposed technique. Recent possibilities for stability analysis and controller synthesis are also discussed. A set of examples shows that polynomial modeling is able to reduce conservativeness with respect to standard T-S approaches as the degrees of the involved polynomials increase.

Relaxed Stability and Performance LMI Conditions for Takagi--Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes

Most linear matrix inequality (LMI) fuzzy control results in literature are valid for any membership function, i.e., independent of the actual membership shape. Hence, they are conservative (with respect to other nonlinear control approaches) when specific knowledge of the shapes is available. This paper presents relaxed LMI conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints, generalizing previous works by the authors. Interesting particular cases are overlap (product) bounds and ellipsoidal regions. Numerical examples illustrate the achieved improvements, as well as the possibilities of solving some multiobjective problems. The results also apply to polynomial-in-membership Takagi-Sugeno fuzzy systems.

On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems

A fairly general class of nonlinear plants can be modeled as fuzzy systems, i.e., as a time-varying convex combination of “vertex” linear systems. As many linear LMI control results naturally generalize to such fuzzy systems, LMI formulations for fuzzy control became the tool of choice in the 1990s. Important results have since been obtained in the fuzzy arena, although significant sources of conservativeness remain. This paper reviews some of the sources of conservativeness of fuzzy control designs based on the linear vertex models instead of the original nonlinear equations. Then, ideas that may overcome some of the conservativeness issues (but increasing computational requirements) are discussed. Recently, the sum of squares paradigm extended some linear results to polynomial systems; this idea can be used for the so-called fuzzy polynomial systems that are also discussed in this work.

Technical communique: Extensions to virtual reference feedback tuning: A direct method for the design of feedback controllers

The papers [Campi, Lecchini & Savaresi (2002). Automatica, 38(8), 1337-1346; (2003). European Journal of Control, 9(1), 66-76] present a direct controller synthesis procedure that uses identification algorithms applied to filtered input-output plant data. This contribution discusses variations that, in some cases, may alleviate noise-induced correlation (in the open-loop case) and allow the applicability of the approach to unstable plants. Importantly, it also introduces an invalidation test step based on the available data (i.e., prior to experimental controller testing), to check if the flexibility of the controller parameterisation and the approximations involved are suitable for the design objectives or, on the contrary, the resulting closed loop may be unstable.

Iterative Identification and Control

In this chapter, we first review the changing role of the model in control system design over the last fifty years. We then focus on the development over the last ten years of the intense research activity and on the important progress that has taken place in the interplay between modelling, identification and robust control design. The major players of this interplay are presented; some key technical difficulties are highlighted, as well as the solutions that have been obtained to conquer them. We end the chapter by presenting the main insights that have been gained by a decade of research on this challenging topic. 1.1 A not-so-brief Historical Perspective There are many ways of describing the evolution of a field of science and engineering over a period of half a century, and each such description is necessarily biased, oversimplified and sketchy. But I have always learned some new insight from such sketchy descriptions, whoever the author. Thus, let me attempt to start with my own modest perspective on the evolution of modelling, identification and control from the post-war period until the present day. Until about 1960, most of control design was based on model-free methods. This was the golden era of Bode and Nyquist plots, of Ziegler-Nichols charts and lead/lag compensators, of root-locus techniques and other graphical design methods. From model-free to model-based control design The introduction of the parametric state-space models by Kalman in 1960, together with the solution of optimal control and optimal filtering problems in a Linear Quadratic Gaussian (LQG) framework [90,91] gave birth to a tremendous development of model-based control design methods. Successful applications abounded, particularly in aerospace, where accurate models were readily available. From modelling to identification The year 1965 can be seen as the founding year for parametric identification with the publication of two milestone papers. The paper [80] set the stage for state-space realisation theory which, twenty-five years later, became the major stepping stone towards what is now called subspace identification. The paper [12] proposed a Maximum Likelihood (ML) framework for the identification of input-output (i. e., ARMAX) models that gave rise to the celebrated

Extensions to “Stability Analysis of Fuzzy Control Systems Subject to Uncertain Grades of Membership”

In the December 2005 issue of this journal, Lam and Leung proposed stability results for fuzzy control systems where the membership functions in the controller were not the same as those from the process one, but some multiplicative bounds were known. The main practical context where that situation arises is the uncertain knowledge of the memberships of a Takagi-Sugeno model. This correspondence presents further extensions of those results, allowing for a richer description of the membership uncertainty, in terms of affine inequalities.

A Triangulation Approach to Asymptotically Exact Conditions for Fuzzy Summations

Many Takagi-Sugeno (T-S) fuzzy control-synthesis problems in the literature are expressed as the problem of finding decision variables in a double convex sum (fuzzy summation) of positive definite matrices. Matricespsila coefficients in the summation take values in the standard simplex. This paper presents a triangulation approach to the problem of generating simplicial partitions of the standard simplex in order to set up a family of sufficient conditions and, in parallel, another family of necessary ones for fuzzy summations. The conditions proposed in this paper are asymptotically exact as the size of the involved simplices decreases; its conservativeness vanishes for a sufficiently fine partition (sufficiently dense mesh of vertex points). The set of conditions is in the form of linear matrix inequalities (LMIs), for which efficient software is available.

A Delay-Dependent Dual-Rate PID Controller Over an Ethernet Network

In this paper, a methodology to design controllers able to cope with different load conditions on an Ethernet network is introduced. Load conditions induce time-varying delays between measurements and control. To face these variations an interpolated, delay-dependent gain scheduling law is used. The lack of synchronization is solved by adopting an event-based control approach. The dual-rate control action computation is carried out at a remote controller, whereas control actions and measurements are taken out locally at the controlled process site. Stability is proved in terms of probabilistic linear matrix inequalities. TrueTime simulations in an Ethernet case show the benefit of the proposal, which is later validated on an experimental test-bed Ethernet environment.