Kiriakos Kiriakidis

Fuzzy model-based control of complex plants

In the field of fuzzy modeling, the Takagi-Sugeno fuzzy model has been used to approximate accurately the dynamics of complex plants. The paper addresses two control design problems associated with state-space realizations of such fuzzy models. First, we treat the stability robustness of fuzzy model-based controllers against modeling uncertainty. Second, we develop observer-based control schemes and further investigate the behavior of estimated-state feedback. In both cases, we provide sufficient conditions that guarantee stability of the closed loop. The results are demonstrated on the fuzzy model of a gas furnace process.

Robust stabilization of the Takagi-Sugeno fuzzy model via bilinear matrix inequalities

Quadratic stability has enabled, mainly via the linear matrix inequality framework, the analysis and design of a nonlinear control system from the local matrices of the systems Takagi-Sugeno (T-S) fuzzy model. It is well known, however, that there exist stable differential inclusions, hence T-S fuzzy models whose stability is unprovable by a globally quadratic Lyapunov function. At present, literature in the broader area of stability analysis suggests piecewise-quadratic stability as a means to avoid such conservatism. This paper generalizes the idea and proposes a framework that supports less conservative sufficient conditions for the stability of the T-S model by using piecewise-quadratic generalized Lyapunov functions. The advocated approach results in the formulation of the controller synthesis, which, herein, aims for robust stabilization, as a problem of bilinear rather than linear matrix inequalities. Simulation studies, which include an algorithm for solution of bilinear matrix inequalities, demonstrate the proposed method.

Quadratic stability analysis of the Takagi-Sugeno fuzzy model

The nonlinear dynamic Takagi-Sugeno fuzzy model with offset terms is analyzed as a perturbed linear system. A sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model. The criterion accepts a convex programming formulation of reduced computational cost compared to the common Lyapunov matrix approach. Parametric robust control techniques suggest synthesis tools for stabilization of the fuzzy system. Application examples on fuzzy models of nonlinear plants advocate the efficiency of the method. The examples demonstrate reduced conservatism compared to norm-based criteria.

Reconfigurable robot teams: modeling and supervisory control

Teams of land-based, airborne, or submerged robots constitute a new breed of robotic systems for which the issue of controlled behavior arises naturally. In this brief, we model the dynamics of the robot team in the discrete-event system (DES) framework and design a reconfigurable system that can handle situations in which robot units may switch offline. In particular, we exploit the dichotomy between controllable and uncontrollable behavior to synthesize a supervisor using only controllable events, but also one whose structure adapts to uncontrollable events. This brief presents a novel method based on learning and verification for restoring supervision as well as behavioral assurance of the team.

Nonlinear modeling by interpolation between linear dynamics and its application in control

This paper proposes a finite series expansion to approximate general nonlinear dynamics models to arbitrary accuracy. The method produces an approximation of nonlinear dynamics in the form of an aggregate of linear models, weighted by unimodal basis functions, and results in a linear growth bound on the approximation error. Furthermore, this paper demonstrates that the proposed approximation satisfies the modeling assumptions for analysis based on linear matrix inequalities and hence widens the applicability of these techniques to the area of nonlinear control.

Single-snapshot robust direction finding

The paper presents a novel approach for recursively estimating the directions of arrival of incident signals as measurements are received along a sensor array. Using a single snapshot and without any statistical assumptions, the proposed method employs a robust performance criterion, which is based on worst-case gain minimization. The criterion aims to reduce the estimation error induced by worst-case amplitude and phase perturbations as well as additive noise in the array model. An algorithm that guarantees the criterion-within a first-order approximation-is developed and shown to converge. Moreover, instead of using a trial-and-error method to find a constant, minimum worst-case gain, the minimum worst-case gain is updated as each sensor measurement is processed. A step-by-step implementation of the algorithm is presented, and its computational complexity is analyzed. The performance of the new approach is evaluated by simulating the estimation algorithm for a linear array and comparing its performance with that of an existing single-snapshot algorithm.

Supervision of multiple-robot systems

Teams of miniature robots (land-based, airborne, or submerged) constitute a new breed of robotic systems where the issue of controlled behavior arises naturally. At the highest level, the dynamics of such systems are event-driven. Herein, we consider multiple-robot systems whose robot units go off-line upon the occurrence of certain events. To supervise such event-varying structure, we propose an adaptive supervisory control method.

Adaptive control of time-varying systems based on parameter set estimation

Adaptive control of time-varying plants, in the presence of unmodeled dynamics and bounded disturbances, via parameter set estimation is proposed. The set estimator uses normalization and maps the uniformly bounded equation error on parametric error, which characterizes the modeled part of the plant. Based on the information from the set estimator, a switching control criterion selects the parametric vector from a set of nominal model parameters and tunes in the adaptive controller. At the same time, through stabilization against the parametric error, the policy renders the closed-loop modeled dynamics robust with respect to the equation error mechanisms.

Dynamic output feedback control of gas furnaces via fuzzy modeling

The paper addresses the control problem of complex plants, using state space realizations derived from Takagi-Sugeno fuzzy models. In particular, a state feedback controller, based on the estimated state information, is proposed for the regulation of gas furnaces. The method described comprises procedures to design a converging state estimator and a stabilizing controller respectively. It is shown that if the estimator and controller gains satisfy an additional sufficient condition then the observer-based closed loop is stable. Simulation studies on the fuzzy model of the gas furnace process verify the result.

Optimal Estimation of Blood Insulin From Blood Glucose

Plasma insulin estimation from plasma glucose has been proposed in order to avoid hyperinsulinemia in the control of diabetes. This paper presents an estimator with error feedback based on measured and predicted plasma glucose designed to tolerate measurement noise as well as discretization error by means of the H∞ criterion. The proposed estimator is tested and evaluated using synthetic patient data.Copyright