This paper addresses the optimization in fuzzy model predictive control. When the prediction model is a nonlinear fuzzy model, nonconvex, time-consuming optimization is necessary, with no guarantee of finding an optimal solution. A possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control (i.e., quadratic programming). For long-range predictive control, however, the influence of the linearization error may significantly deteriorate the performance. In our approach, this is remedied by linearizing the fuzzy model along the predicted input and output trajectories. One can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories. Four different methods for the construction of the optimization problem are proposed, making difference between the cases when a single linear model or a set of linear models are used. By choosing an appropriate method, the user can achieve a desired tradeoff between the control performance and the computational load. The proposed techniques have been tested and evaluated using two simulated industrial benchmarks: pH control in a continuous stirred tank reactor and a high-purity distillation column.

Addresses model-based fuzzy control. A constructive and automated method for the design of a gain-scheduling controller is presented. Based on a given Takagi-Sugeno fuzzy model of the plant, the controller is designed such that stability and prescribed performance of the closed loop are guaranteed. These properties are valid in a wide working range around an equilibrium without restrictions to slowly varying trajectories. The synthesis is based on linear matrix inequalities and convex optimization techniques. If required, a fuzzy state estimator and an extended controller can be included, providing a zero steady-state error in the presence of disturbances and modeling errors. The proposed method has been applied to a control of a laboratory liquid-level process. Hence, the performance has been evaluated in simulations as well as in real-time control.

A sensor management system based on soft computing techniques has been developed and implemented in the flight control system of a small commercial aircraft. Unlike in the conventional sensor management system, the signals from sensors are assigned weights based on fuzzy membership functions and the consolidated signal is computed as a weighted average. This approach improves the quality of the consolidated signal and reduces transients due to sensor failures. This soft voting is extended to soft flight control law reconfiguration. In addition, a virtual sensor has been introduced as an arbitrator which enables the isolation of the failed sensor in the duplex operation and the detection of a sensor failure in the simplex operation. The effectiveness of the proposed methods is demonstrated by using an extensive simulation model of a small commercial aircraft, developed by airframe and control system manufacturers on the basis of an existing business jet. Furthermore, the system has been successfully evaluated and compared to standard techniques by means of pilot-in-the-loop simulations on the Research Flight Simulator of the National Aerospace Laboratory in The Netherlands. This application, developed within a Brite/EuRam research project, is characterized by the effective combination of novel soft computing techniques with standard, well proven methods of the aircraft industry. The properties of the conventional sensor management system have been retained, with the additional advantage that the quality of the consolidated signal is improved, the failure-induced transients are reduced, and the consolidated signal remains available up to the last valid sensor.

Input-output interactions in the inherently nonlinear Takagi-Sugeno (TS) MIMO fuzzy models can not be analyzed by using standard methods such as the relative gain array (RGA). Two methods are proposed that exploit the specific TS structure. The first one is based on a number of RGAs which can indicate sufficiently well the interactions in the model. Another tool to analyze input-output interactions is the output sensitivity, computed as a partial derivative of the output with respect to the considered input. The use of these techniques is illustrated with the help of a TS fuzzy model of a high-purity distillation column.

A decoupling strategy for affine discrete-time nonlinear systems is proposed. The idea is to invert a nonlinear model and to use the inverted model to compensate for the coupling. Linear model based predictive controller is employed to provide the reference to be followed. The control system comprises: 1) a feedback decoupling scheme, 2) a linear model-based predictive controller (MBPC), and 3) a constraints mapping that transforms the actual input constraints into constraints on the linear system. The nonlinear system to be decoupled is expressed by a Takagi-Sugeno type fuzzy model.

The attitude control of a satellite is often characterized by a limit cycle, caused by measurement inaccuracies and noise in the sensor output. In order to reduce the limit cycle, a nonlinear fuzzy controller was applied. The controller was tuned by means of reinforcement learning without using any model of the sensors or the satellite. The reinforcement signal is computed as a fuzzy performance measure using a noncompensatory aggregation of two control subgoals. Convergence of the reinforcement learning scheme is improved by computing the temporal difference error over several time steps and adapting the critic and the controller at a lower sampling rate. The results show that an adaptive fuzzy controller can better cope with the sensor noise and nonlinearities than a standard linear controller.

This article is a reaction to recent publications on rule-based modeling using fuzzy set theory and fuzzy logic. The interest in fuzzy systems has recently shifted from the seminal ideas about complexity reduction toward data-driven construction of fuzzy systems. Many algorithms have been introduced that aim at numerical approximation of functions by rules, but pay little attention to the interpretability of the resulting rule base. We show that fuzzy rule-based models acquired from measurements can be both accurate and transparent by using a low number of rules. The rules are generated by product-space clustering and describe the system in terms of the characteristic local behavior of the system in regions identified by the clustering algorithm. The fuzzy transition between rules makes it possible to achieve precision along with a good qualitative description in linguistic terms. The latter is useful for expert evaluation, rule-base maintenance, operator training, control systems design, user interfacing, etc. We demonstrate the approach on a modeling problem from a recently published article.