Olga G. Andrianova

This study presents a state nonparametric identifier based on neural networks with continuous dynamics, also known as differential neural networks (DNNs). The laws for adjusting their parameters are developed using a control barrier Lyapunov functions (BLFs). The motivation for using the BLF comes from the preliminary information of the system states, which remain in a predefined time-depending set characterized by state or purely time-dependent functions. In this study, time-dependent state constraints are supposed to be known in advance continuous-time functions. The obtained learning laws require solving differential continuous-time Riccati equations and nonlinear differential equations for the learning laws that depend on the identification error and the state restrictions. The developed identifier was evaluated concerning the identifier that does not consider the state restrictions. This comparison included the numerical evaluation of the identifier for a robotic arm intended to reproduce a nonstandard flight simulator. This evaluation confirmed that the identification results were improved using the proposed learning laws and considering that the state limits were not transgressed. The quality indicators based on the mean square error were more minor by 4.2 times.

An axiomatic development of control systems theory can systematize important concepts. The current research article is dedicated to the investigation and comparison of two axiomatic approaches to the analysis of discrete linear time-invariant systems affected by external random disturbances. The main goal of this paper is to explore axiomatics of an anisotropy-based theory in comparison with axiomatics of a spectral entropy approach in detail. It is demonstrated that the use of the spectral entropy approach is mathematically rigorous, which allows one to prove that the minimal disturbance attenuation level in terms of an anisotropy-based control theory provides the desired performance that is not only for ergodic signals. As a result, axiomatics of the spectral entropy approach allows one to rigorously prove that anisotropy-based controllers can be used to guarantee the desired disturbance attenuation level, not only for stationary random sequences, but also for a wider set of input random signals.

This study presents a state non-parametric identifier based on neural networks with continuous dynamics, also known as differential (namely DNNs) whose laws for adjusting their parameters are developed using a control Barrier Lyapunov Functions (BLFs). The motivation for using the BLF comes from the preliminary information of the system states, which remain in a predefined time-depending set characterized by state or purely time-dependent functions. In this study, time-dependent state constraints are supposed to be known in advance of continuous-time functions. The obtained learning laws require solving differential continuous-time Riccati equations and nonlinear differentialequations for the learning laws that depend on the identification error and the state restrictions. The developed identifier was evaluated concerning the identifier that does not consider the state restrictions. This comparison included the numerical evaluation of the identifier considering its application on a robotic arm that is intended to reproduce a non-standard flight simulator. This evaluation confirmed that the identification results were improved using the proposed learning laws considering that the state limits were not transgressed, and the quality indicators based on the mean square error were more minor by 4.2 times.

Purpose: There are common problems in the identification of uncertain nonlinear systems, nonparametric approximation, state estimation, and automatic control. Dynamic neural network (DNN) approximation can simplify the development of all the aforementioned problems in either continuous or discrete systems. A DNN is represented by a system of differential or recurrent equations defined in the space of vector activation functions with weights and offsets that are functionally associated with the input data.Design/methodology/approach: This study describes the version of the toolbox, that can be used to identify the dynamics of the black box and restore the laws underlying the system using known inputs and outputs. Depending on the completeness of the information, the toolbox allows users to change the DNN structure to suit specific tasks.Findings: The toolbox consists of three main components: user layer, network manager, and network instance. The user layer provides high-level control and monitoring of system performance. The network manager serves as an intermediary between the user layer and the network instance, and allows the user layer to start and stop learning, providing an interface to indirectly access the internal data of the DNN.Research limitations/implications: Control capability is limited to adjusting a small number of numerical parameters and selecting functional parameters from a predefined list.Originality/value: The key feature of the toolbox is the possibility of developing an algorithmic semi-automatic selection of activation function parameters based on optimization problem solutions.

Dynamic motion simulators cannot provide the same stimulation of sensory systems as real motion. Hence, only a subset of human senses should be targeted. For simulators providing vestibular stimulus, an automatic bodily function of vestibular–ocular reflex (VOR) can objectively measure how accurate motion simulation is. This requires a model of ocular response to enforced accelerations, an attempt to create which is shown in this paper. The proposed model corresponds to a single-layer spiking differential neural network with its activation functions are based on the dynamic Izhikevich model of neuron dynamics. An experiment is proposed to collect training data corresponding to controlled accelerated motions that produce VOR, measured using an eye-tracking system. The effectiveness of the proposed identification is demonstrated by comparing its performance with a traditional sigmoidal identifier. The proposed model based on dynamic representations of activation functions produces a more accurate approximation of foveal motion as the estimation of mean square error confirms.

The design of a state feedback and robust controller for regulating the tridimensional (3D) movement of autonomous underwater mobile crafts (AUMCs). The controller design is based on the application of Averaged Sub-Gradient Integral Sliding Mode Realisation (ASGISMR). The application of the ASGISMR yields the solution of the closed-loop extreme seeking control for a non-strictly convex functional depending on the tracking error between reference and 3D position of the AUMC. The design of reference trajectories was proposed to enforce the AUMC to follow a continued submersion and ellipsoidal detouring. The mechanical dynamical form of AUMC is well posed for applying the extended version of ASGISMR, considering that integral term represents an ASG associated to the euclidean norm of the tracking error. The time evolution of the functional over the controlled trajectories of the AUMC is compared with the corresponding functional enforced by a traditional state feedback controller with gravity effect compensation. The proposed controller exhibits better tracking and similar control magnitude than the considered reference state feedback realisation. These outcomes justify the potential contributions of the suggested ASGISMR to obtain the local minimisation of the evaluated functional, considering such controller as an extreme seeking realisation for the proposed AUMC.

The design problems of robust static controllers for discrete-time systems with norm-bounded parametric uncertainties and random input disturbances are considered. The controllers under consideration stabilize the plant for all possible values of uncertainty from a given set of parameters and also guarantee a desired suppression level for random exogenous disturbances. A numerical example is given.