The paper addresses the problem of transforming single-output nonlinear state equations affine in disturbance into an extended observer form whose nonlinear injection part depends additionally on the derivatives of the output up to a finite order. Moreover, the considered form is affine in disturbance. Based on the earlier results a detailed algorithm is given and applied to the model of a synchronous machine connected to an infinite bus. For the system in the extended observer form a reduced-order Kalman-filter based observer can be designed such that its error dynamics is exponentially attractive and it is stable in the input-to-state sense with respect to the disturbance.

Compliant fish-like robots are being developed as efficient and dependable underwater observation platforms with low impact on the observed environment. Orientation control is an essential building block to achieve autonomy for those vehicles. So far, the major focus has been on rigid tails or on flexible tails with a high degree of actuation. We present a novel control strategy for an underactuated robotic fish with a flexible tail optimized for cruising. The basis for our approach is the generation of asymmetric velocity profiles of the robot's tail beats. To achieve such velocity profiles, the usual sinusoidal tail actuation is replaced with skewed triangle waves. We provide a simple formulation for such waves, where their skew is dependent on only one variable which we define as skew factor. Furthermore, a nonlinear control law is derived to achieve the desired turning motions. We implement the controller on a compliant fish-like robot with a simple actuation mechanism. The control scheme is experimentally validated, and its robustness is tested in field trials.

A correlation-test-based validation procedure is applied in this study to compare neural networks based nonlinear autoregressive exogenous model class to its subclass of additive nonlinear autoregressive exogenous models.

The paper describes an algebraic construction of the inversive difference field associated with a discrete-time rational nonlinear control system under the assumption that the system is submersive. We prove that a system is submersive iff its associated difference ideal is proper, prime and reflexive. Next, we show that Kähler differentials of the above inversive field define a module over the corresponding ring of Ore operators, and relate its torsion submodule to the vector space of autonomous one-forms, introduced elsewhere. The above results allow us to check accessibility property and simplify transfer functions with computer algebra techniques.

The paper applies the pseudo-linear algebra to unify the study of irreducibility and reduction for continuous-and discrete-time nonlinear control systems. The necessary and sufficient condition for irreducibility of nonlinear input-output equation is presented in terms of the common left factor of two polynomials describing the behaviour of the system. Besides unification, the tools of pseudo-linear algebra allow to extend the results for systems defined by difference, q-shift and q-difference operators.

The paper suggests how to compute the order of the minimal realization of the discrete-time nonlinear control system, described by the set of input-output difference equations, or alternatively, by the two polynomial matrices with the entries in the non-commutative skew polynomial ring. For that purpose the Ore determinant is specified further by including certain additional restrictions and proved that under these additional restrictions the degree of the dieudonne determinant is equal to the degree of the Ore determinant. Finally, the system order is shown to be equal to the degree of the determinant of one polynomial matrix. Only the special case of two output systems is considered in this paper.

The purpose of this paper is to present necessary and sufficient condition for irreducibility of continuous-time nonlinear multi-input multi-output system. The condition is presented in terms of the greatest common left divisor of two polynomial matrices related to the input-output equations of the system. The basic difference is that unlike the linear case the elements of the polynomial matrices belong to a non-commutative polynomial ring. This condition provides a basis for finding the equivalent minimal irreducible representation of the I/O equations which is a suitable starting point for constructing an observable and accessible state space realization

This article is devoted to the training and application of neural networks based additive nonlinear autoregressive exogenous (NN-based ANARX) model. Training of NN-based ANARX model with MATLAB is discussed in detail and illustrated by examples. Dynamic state feedback linearization control algorithm is then applied for control of unknown nonlinear system