In this paper, we investigate the indirect adaptive regulation problem of unknown affine in the control nonlinear systems. The proposed approach consists of choosing an appropriate system approximation model and a proper control law, which will regulate the system under the certainty equivalence principle. The main difference from other relevant works of the literature lies in the proposal of a potent approximation model that is bilinear with respect to the tunable parameters. To deploy the bilinear model, the components of the nonlinear plant are initially approximated by Fuzzy subsystems. Then, using appropriately defined fuzzy rule indicator functions, the initial dynamical fuzzy system is translated to a dynamical neuro-fuzzy model, where the indicator functions are replaced by High Order Neural Networks (HONNS), trained by sampled system data. The fuzzy output partitions of the initial fuzzy components are also estimated based on sampled data. This way, the parameters to be estimated are the weights of the HONNs and the centers of the output partitions, both arranged in matrices of appropriate dimensions and leading to a matrix to matrix bilinear parametric model. Based on the bilinear parametric model and the design of appropriate control law we use a Lyapunov stability analysis to obtain parameter adaptation laws and to regulate the states of the system. The weight updating laws guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. Moreover, introducing a method of "concurrent" parameter hopping, the updating laws are modified so that the existence of the control signal is always assured. The main characteristic of the proposed approach is that the a priori experts information required by the identification scheme is extremely low, limited to the knowledge of the signs of the centers of the fuzzy output partitions. Therefore, the proposed scheme is not vulnerable to initial design assumptions. Simulations on selected examples of well-known benchmarks illustrate the potency of the method.

In this paper we analyze the identification problem which consists of choosing an appropriate identification model and adjusting its parameters according to some adaptive law, such that the response of the model to an input signal (or a class of input signals), approximates the response of the real system for the same input. For identification models we use fuzzy-recurrent high order neural networks. High order networks are expansions of the first-order Hopfield and Cohen-Grossberg models that allow higher order interactions between neurons. The underlying fuzzy model is of Mamdani type assuming a standard defuzzification procedure such as the weighted average. Learning laws are proposed which ensure that the identification error converges to zero exponentially fast or to a residual set when a modeling error is applied. There are two core ideas in the proposed method: (1) Several high order neural networks are specialized to work around fuzzy centers, separating in this way the system into neuro-fuzzy subsystems, and (2) the use of a novel method called switching parameter hopping against the commonly used projection in order to restrict the weights and avoid drifting to infinity.

A new method for the direct adaptive regulation of unknown nonlinear dynamical systems is proposed in this paper, paying special attention to the analysis of the model order problem. The method uses a neurofuzzy (NF) modeling of the unknown system, which combines fuzzy systems (FSs) with high order neural networks (HONNs). We propose the approximation of the unknown system by a special form of an NF-dynamical system (NFDS), which, however, may assume a smaller number of states than the original unknown model. The omission of states, referred to as a model order problem, is modeled by introducing a disturbance term in the approximating equations. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. An adaptive modification method, termed ‘parameter hopping’, is incorporated into the weight estimation algorithm so that the existence and boundedness of the control signal are always assured. The applicability and potency of the method are tested by simulations on well known benchmarks such as ‘DC motor’ and ‘Lorenz system’, where it is shown that it performs quite well under a reduced model order assumption. Moreover, the proposed NF approach is shown to outperform simple recurrent high order neural networks (RHONNs).

The indirect adaptive regulation of unknown nonlinear dynamical systems with multiple inputs and states (MIMS) under the presence of dynamic and parameter uncertainties, is considered in this paper. The method is based on a new neuro-fuzzy dynamical systems description, which uses the fuzzy partitioning of an underlying fuzzy systems outputs and high order neural networks (HONN's) associated with the centers of these partitions. Every high order neural network approximates a group of fuzzy rules associated with each center. The indirect regulation is achieved by first identifying the system around the current operation point, and then using its parameters to device the control law. Weight updating laws for the involved HONN's are provided, which guarantee that, under the presence of both parameter and dynamic uncertainties, both the identification error and the system states reach zero, while keeping all signals in the closed loop bounded. The control signal is constructed to be valid for both square and non square systems by using a pseudoinverse, in Moore-Penrose sense. The existence of the control signal is always assured by employing a novel method of parameter hopping instead of the conventional projection method. The applicability is tested on well known benchmarks.

The direct adaptive regulation of unknown nonlinear dynamical systems in Brunovsky form with modeling error effects, is considered in this paper. Since the plant is considered unknown, we propose its approximation by a special form of a Brunovsky type neuro-fuzzy dynamical system (NFDS) assuming also the existence of disturbance expressed as modeling error terms depending on both input and system states plus a not-necessarily-known constant value. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. The existence and boundness of the control signal is always assured by introducing a novel method of parameter hopping and incorporating it in weight updating laws. Simulations illustrate the potency of the method and its applicability is tested on well known benchmarks, as well as in a bioreactor application. It is shown that the proposed approach is superior to the case of simple recurrent high order neural networks (HONN's).

Fuzzy cognitive maps (FCMs) have been introduced by Kosko to model complex behavioral systems in various scientific areas. One issue that has not been adequately studied so far is the conditions under which they reach a certain equilibrium point after an initial perturbation. This is equivalent to studying the existence and uniqueness of solutions for their concept values. In this paper, we study the existence of solutions of FCMs equipped with continuous differentiable sigmoid functions having contractive or, at least, nonexpansive properties. This is done by using an appropriately defined contraction mapping theorem and the nonexpansive mapping theorem. It is proved that when the weight interconnections fulfill certain conditions, the concept values will converge to a unique solution, regardless of the exact values of the initial concept values perturbations, or in some cases, a solution exists that may not necessarily be unique; otherwise, the existence or the uniqueness of equilibrium cannot be assured. Based on these results, an adaptive weight-estimation algorithm is proposed that employs appropriate weight projection criteria to assure that the uniqueness of FCM solution is not compromised. In view of these results, recently proposed extensions of FCM, which are the fuzzy cognitive networks (FCN), are invoked.

The indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper. The method is based on a new neuro-fuzzy dynamical system (neuro-FDS) definition, which uses the concept of adaptive fuzzy systems (AFSs) operating in conjunction with high-order neural network functions (FHONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of an FDS and then the fuzzy rules are approximated by appropriate HONNFs. Thus, the identification scheme leads up to a recurrent high-order neural network (RHONN), which however takes into account the fuzzy output partitions of the initial FDS. The proposed scheme does not require a priori experts' information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. Once the system is identified around an operation point, it is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The existence of the control signal is always assured by introducing a novel method of parameter hopping, which is incorporated in the weight updating law. Simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given. Also, the applicability of the method is tested on a direct current (dc) motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation.

In recent years there has been a great effort to convert the existing Air Traffic Control system into a novel system known as Free Flight. Free Flight is based on the concept that increasing international airspace capacity will grant more freedom to individual pilots during the enroute flight phase, thereby giving them the opportunity to alter flight paths in real time. Under the current system, pilots must request, then receive permission from air traffic controllers to alter flight paths. Understandably the new system allows pilots to gain the upper hand in air traffic. At the same time, however, this freedom increase pilot responsibility. Pilots face a new challenge in avoiding the traffic shares congested air space. In order to ensure safety, an accurate system, able to predict and prevent conflict among aircraft is essential. There are certain flight maneuvers that exist in order to prevent flight disturbances or collision and these are graded in the following categories: vertical, lateral and airspeed. This work focuses on airspeed maneuvers and tries to introduce a new idea for the control of Free Flight, in three dimensions, using neural networks trained with examples prepared through non-linear programming.

In this paper, optimal resolution of air-traffic (AT) conflicts were considered. Aircraft are assumed to cruise within a free altitude layer and are modeled in three dimensions with variable velocity and proximity bounds. Aircraft cannot get closer to each other than a predefined safety distance. The problem of solving conflicts arising among several aircraft that are assumed to move in a shared airspace were considered. For such systems of multiple aircraft, the total flight time by avoiding all possible conflicts were minimized. This paper proposes a formulation of the conflict avoidance problem as a mixed-integer nonlinear-programming problem. In the author's case, only velocity changes are admissible as maneuvers. Nevertheless, in subsequent work, simultaneous velocity and heading angle changes will be checked too. Simulation results for realistic aircraft conflict scenarios are provided.

Present multimedia services are provided through a heterogeneous set of networks. Because of the heterogeneity of the networks, long-term resource availability guarantees are difficult to obtain. Consequently, even if the resource requirements throughout the service could be accurately mapped, it would not be feasible to provide overall performance guarantees. Application adaptation arises as an appropriate solution for quality-of-service assurance in such dynamic service infrastructures. Application adaptation basically involves adapting application characteristics according to the network resource availability. We formulate the problem of adaptation of multimedia applications to network infrastructure as well as to user- and application-imposed constraints and preferences. We benefit from the good approximation, identification, and control capabilities of recurrent high-order neural networks and we introduce an algorithm that guarantees the resource constraints of the network infrastructure will not be violated while maintaining the user and application requirements.

It is known that the problem of learning the shape parameters of unknown surfaces that are in contact with a robot end-effector can be formulated as a nonlinear parameter estimation problem and an extended Kalman filter can be applied in order to estimate the surface shape parameters. In this paper, we show that the problem of learning the shape parameters of unknown contact surfaces can be formulated as a linear parameter estimation problem and thus globally convergent learning laws can be applied. Moreover, we show that by using appropriate neural network approximators, the unknown surfaces can be learned even if there are no force measurements, i.e., the robot is not provided with any force or tactile sensors.

With this paper we extend our previous work on the subject, by including the case where the number of control inputs is different from the number of states which is frequently faced in control engineering problems. Uniform ultimate boundedness of the state and uniform boundedness of all other signals in the closed loop is guaranteed. Robustness of our algorithm due to the presence of a modeling error term which has linear growth with unknown growth coefficient is also established. Finally, the applicability of our control scheme is highlighted via simulation results.

A mathematical analysis of a class of learning vector quantization (LVQ) algorithms is presented. Using an appropriate time-coordinate transformation, we show that the LVQ algorithms under consideration can be transformed into linear time-varying stochastic difference equations. Using this fact, we apply stochastic Lyapunov stability arguments, and we prove that the LVQ algorithms under consideration do indeed converge, provided that some appropriate conditions hold.

Several continuous-time and discrete-time recurrent neural network models have been developed and applied to various engineering problems. One of the difficulties encountered in the application of recurrent networks is the derivation of efficient learning algorithms that also guarantee the stability of the overall system. This paper studies the approximation and learning properties of one class of recurrent networks, known as high-order neural networks; and applies these architectures to the identification of dynamical systems. In recurrent high-order neural networks, the dynamic components are distributed throughout the network in the form of dynamic neurons. It is shown that if enough high-order connections are allowed then this network is capable of approximating arbitrary dynamical systems. Identification schemes based on high-order network architectures are designed and analyzed.

A direct nonlinear adaptive state regulator, for unknown dynamical systems that are modeled by dynamic neural networks is discussed. In the ideal case of complete model matching, convergence of the state to zero plus boundedness of all signals in the closed loop is ensured. Moreover, the behavior of the closed loop system is analyzed for cases in which the true plant differs from the dynamic neural network model in the sence that it is of higher order, or due to the presence of a modeling error term. In both cases, modifications of the original control and update laws are provided, so that at least uniform ultimate boundedness is guaranteed, even though in some cases the stability results obtained for the ideal case are retained.

The capabilities of recurrent high order neural networks (RHONNs), whose synapses are adjusted according to the learning law proposed in Kosmatopoulos and Christodoulou (1992), and Koostmatopoulos, Christodoulou, and Ioannou (1993) are examined in 1) spatiotemporal pattern learning, recognition, and reproduction and 2) stochastic dynamical system identification problems. The mathematical model describing the stochastic disturbances that affect the spatiotemporal patterns or the system dynamics is quite general, and includes both additive and multiplicative stochastic disturbances. Under an extensive mathematical analysis, the authors show that, for any selection of the neural network's high order terms, the prediction error converges to zero exponentially fast. Extensions are also made to the case where the energy coordinate equivalent (ECE) RHONN's are used.>

In this paper, we are dealing with the problem of controlling an unknown nonlinear dynamical system. The algorithm is divided into two phases. First a dynamical neural network identifier is employed to perform "black box" identification and then a dynamic state feedback is developed to appropriately control the unknown system. We apply the algorithm to control the speed of a nonlinearized DC motor, giving in this way an application insight. In the algorithm, not all the plant states are assumed to be available for measurement.>