Observer Design for Sampled-Data Systems via Deterministic Learning

A unified approach is proposed to design sampled-data observers for a certain type of unknown nonlinear systems undergoing recurrent motions based on deterministic learning in this article. First, a discrete-time implementation of high-gain observer (HGO) is utilized to obtain state trajectory from sampled output measurements. By taking the recurrent estimated trajectory as inputs to a dynamical radial basis function network (RBFN), a partial persistent exciting (PE) condition is satisfied, and a locally accurate approximation of nonlinear dynamics can be realized along the estimated sampled-data trajectory. Second, an RBFN-based observer consisting of the obtained dynamics from the process of deterministic learning is designed. Without resorting to high gains, the RBFN-based observer is shown capable of achieving correct state observation. The novelty of this article lies in that, by incorporating deterministic learning with the discrete-time HGO, the nonlinear dynamics can be accurately approximated along the estimated trajectory, and such obtained knowledge can then be utilized to realize nonhigh-gain state estimation for the same or similar sampled-data systems. Simulation is performed to validate the effectiveness of the proposed approach.

Trajectory Tracking on Uncertain Complex Networks via NN-Based Inverse Optimal Pinning Control

A new approach for trajectory tracking on uncertain complex networks is proposed. To achieve this goal, a neural controller is applied to a small fraction of nodes (pinned ones). Such controller is composed of an on-line identifier based on a recurrent high-order neural network, and an inverse optimal controller to track the desired trajectory; a complete stability analysis is also included. In order to verify the applicability and good performance of the proposed control scheme, a representative example is simulated, which consists of a complex network with each node described by a chaotic Lorenz oscillator.

A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input

In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

INDIRECT ADAPTIVE CONTROL OF NONLINEAR SYSTEMS BASED ON BILINEAR NEURO-FUZZY APPROXIMATION

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.

Discrete-time neural inverse optimal control for nonlinear systems via passivation

This paper presents a discrete-time inverse optimal neural controller, which is constituted by combination of two techniques: 1) inverse optimal control to avoid solving the Hamilton-Jacobi-Bellman equation associated with nonlinear system optimal control and 2) on-line neural identification, using a recurrent neural network trained with an extended Kalman filter, in order to build a model of the assumed unknown nonlinear system. The inverse optimal controller is based on passivity theory. The applicability of the proposed approach is illustrated via simulations for an unstable nonlinear system and a planar robot.

Class of widely linear complex Kalman filters

Recently, a class of widely linear (augmented) complex-valued Kalman filters (KFs), that make use of augmented complex statistics, have been proposed for sequential state space estimation of the generality of complex signals. This was achieved in the context of neural network training, and has allowed for a unified treatment of both second-order circular and noncircular signals, that is, both those with rotation invariant and rotation-dependent distributions. In this paper, we revisit the augmented complex KF, augmented complex extended KF, and augmented complex unscented KF in a more general context, and analyze their performances for different degrees of noncircularity of input and the state and measurement noises. For rigor, a theoretical bound for the performance advantage of widely linear KFs over their strictly linear counterparts is provided. The analysis also addresses the duality with bivariate real-valued KFs, together with several issues of implementation. Simulations using both synthetic and real world proper and improper signals support the analysis.

DYNAMICAL RECURRENT NEURO-FUZZY IDENTIFICATION SCHEMES EMPLOYING SWITCHING PARAMETER HOPPING

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.