Neural Network Modeling and Identification of Dynamical Systems

By Yury Tiumentsev and Mikhail Egorchev

Neural Network Modeling and Identification of Dynamical Systems presents a new approach on how to obtain the adaptive neural network models for complex systems that are typically found in real-world applications. The book introduces the theoretical knowledge available for the modeled system into the purely empirical black box model, thereby converting the model to the gray box category. This approach significantly reduces the dimension of the resulting model and the required size of the training set. This book offers solutions for identifying controlled dynamical systems, as well as identifying characteristics of such systems, in particular, the aerodynamic characteristics of aircraft.

• Covers both types of dynamic neural networks (black box and gray box) including their structure, synthesis and training
• Offers application examples of dynamic neural network technologies, primarily related to aircraft
• Provides an overview of recent achievements and future needs in this area

• Language: English
• Publisher: Academic Press
• Release date: May 17, 2019
• ISBN: 9780128154304

Yury Tiumentsev

Dr. Yury V. Tiumentsev is currently a full professor at Moscow Aviation Institute, teaching in subjects including computer science, computer-aided design, artificial intelligence, artificial neural networks, and soft computing. He is also the Vice President of the Russian Neural Network Society and Vice-Chairman of the Organization and Program Committee of the Annual All-Russia Scientific and Engineering Conference on Neuroinformatics. Dr. Tiumentsev is also a member of the Scientific Committee and a publication reviewer for the International Conference of Artificial Intelligence and Soft Computing (ICAISC), as well as other conference collections such as the International Joint Conference on Neural Networks (IJCNN). His current research subjects include artificial neural networks, adaptive systems, intelligent control, mathematical modeling and computer simulation of complex systems. Dr. Tiumentsev is the author of the Russian-language monograph entitled Neural Network Modeling of Aircraft Motion, and has also written more than 130 articles on his areas of expertise.

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Introduction

Abstract

The introductory chapter of the book is devoted to revealing problems that arise in the development and operation of controlled dynamical systems, as well as the rationale for combining dynamical system technologies and machine learning. We consider this problem with the example of aircraft as one of the most important classes of such systems. Such kind of unification opens up new opportunities for solving the problems of analysis, synthesis, and identification for dynamical systems. However, at the same time, it generates a series of problems that need to be solved. A list of such problems is given, and we outline ways of their solution. We formulate requirements for the models, including accuracy, speed, and adaptability. It is shown that the control problems for dynamical systems under uncertainty conditions generate a need to give the property of adaptability to the dynamical system model. At the same time, we demonstrate the inadequacy of traditional tools of mathematical modeling and computer simulation to solve this task. Overcoming this difficulty is possible by applying techniques of neural network modeling. However, traditional artificial neural network models, which belong to the black box class, do not allow for a complete solution to the task. This circumstance makes it necessary to expand the black box–type neural network models to the gray box class.

The world of controlled dynamical systems is diverse and multifaceted. Among the most important classes of such systems, traditionally difficult to study, are aircraft of various kinds. One of the challenging modern problems of aeronautical engineering is to create highly autonomous robotic unmanned aerial vehicles (UAVs) intended for the accomplishment of civil and military missions under a wide variety of conditions. These missions include patrolling, threat detection, and object protection; monitoring of power lines, pipelines, and forests; aerial photography, monitoring and survey of ice and fishing areas; performing various assembly operations and terrestrial and naval rescue operations; and providing assistance in natural and technogenic disaster recovery, various military operations, and many other scenarios.

Currently, these types of missions are carried out mostly by manned aircraft (airplanes and helicopters). The constantly growing number of applications of UAVs in this field is attractive due to the following reasons:

•  UAVs achieve a significantly higher payload fraction compared to manned aircraft because they require neither flight crew nor life support systems and flight compartments;

•  UAVs are capable of higher maneuverability compared to manned aircraft because of a higher limit g-load level;

•  there is the possibility of creating small UAVs that are significantly less expensive to build and operate;

•  UAVs are capable of accomplishing missions when human presence is undesirable or unacceptable (radioactive hazard, high-risk level, etc.).

Nowadays almost all UAVs are actually remotely piloted vehicles that require a human operator (or even an entire crew) located at the ground control station to manage UAV flight. However, UAVs will be truly effective only when they are capable to accomplish missions with a maximum degree of autonomy, i.e., with minimal human assistance, which is generally reduced to stating the mission goal, monitoring its accomplishment, and, sometimes, adjusting the mission during the flight. This is caused by potential vulnerability of wireless communication channels required for the remotely piloted vehicle. Moreover, the human operator ability to react to complex and rapidly changing situations has certain psychophysiological limitations (attentional capacity, reaction time). High autonomy refers not to the ability to follow a predefined flight schedule, but to a smart autonomous behavior that adapts to highly uncertain, dynamically changing situations. At present, a significant number of researchers from different countries are making an effort to solve the problem of smart autonomy; however there is no satisfactory solution yet for this problem.

Thus, the most important requirement for UAVs is that they must have a high level of independence in solving their tasks. To meet these requirements, a robotic UAV should be able:

•  to achieve its goals in a highly dynamic environment with a significant number of heterogeneous uncertainties in it, taking into account possible counteraction;

•  to adjust the goals, as well as to form new goals and sets of goals, based on the value and regulatory attitudes (motivation) laid down in the UAV behavior control system;

•  to be able to assess the current situation on the basis of a multilateral perception of the external and internal environment, to be able to form a forecast of the development of the situation;

•  to gain new knowledge, accumulate experience in solving various tasks, learn from this experience, and modify its behavior based on the knowledge gained and accumulated experience;

•  to be able to learn how to solve problems not provided for by the original design of the system;

•  to form teams that are able to solve some problem by interactions between their members.

In order for robotic UAVs to be able to accomplish difficult missions on the same efficiency level as a manned aircraft, a radical revision of the current approach to development and management of control algorithms for UAV behavior is needed. In robotics, the totality of all types of processes of functioning of the robot is usually called the behavior of the robot. Accordingly, bearing in mind the ever-increasing trends in the robotization of the UAV, it is accepted to talk about the task of the behavior control for UAVs as the implementation of all types of its functioning necessary to fulfill the abovementioned target tasks. The behavior control of the UAV includes the following elements:

•  planning flight operations, managing its implementation, updating the plan when a situation changes;

•  UAV motion control, including its trajectory motion (including guidance and navigation) and angular motion;

•  management of the solution of target tasks (control of the action of observation and reconnaissance equipment, control of the actions for performing assembly operations, etc.);

•  management of interaction with other aircraft, both unmanned and manned, when the task is accomplished by some team of aircraft, which includes the given UAV.

The control algorithms (formation of control actions, decision making for control) should use information about the mission goals and about the situation characterized by assessments of the current and predicted situation in which it performs the task of the UAV, as input data. This situation is made up of both external components (state of the environment, the state and actions of partners and opponents) and internal components (data on aircraft state, diagnostics data, and performance evaluations of the structure and aircraft systems). Means of obtaining this basic information should also be included in the complex of algorithms that implement the desired behavior of a robotic UAV.

The aforementioned requirements can only be fulfilled if the UAV's behavior control system possesses advanced mechanisms, which allow an adaptation to significantly changing situations with a high degree of uncertainty and also learning and knowledge acquisition based on current UAV activity for future use. Such mechanisms should allow the possibility to solve the following important tasks:

•  obtaining situation awareness which involves current situation assessment and future situation prediction;

•  synthesis and implementation of UAV behavior as an aggregation of purposeful reactions to a current and/or predicted situation.

The implementation of these mechanisms provides the ability to create adaptive and intelligent systems to control the behavior of UAVs. The use of such systems gives an opportunity to implement highly autonomous robotic UAVs, designed to effectively accomplish difficult missions under uncertainty conditions. Another important implication of adaptive and intelligent control of UAV behavior is the possibility to significantly increase survivability of an aircraft in case of severe airframe damage and onboard systems failures.

When implementing the above functions, both in the process of design and in the subsequent operation of various types of aircraft, a significant place is occupied by the analysis of the behavior of dynamical systems, the synthesis of control algorithms for them, and the identification of their unknown or inaccurately known characteristics. A crucial role in solving the problems of these three classes belongs to mathematical and computer models of dynamical systems.

The traditional classes of mathematical models for engineering systems are ordinary differential equations (ODEs) (for systems with lumped parameters) and partial differential equations (PDEs) (for systems with distributed parameters). As applied to controlled dynamical systems, ODEs are most widely used as a modeling tool. These models, in combination with appropriate numerical methods, are widely used in solving problems of synthesis and analysis of controlled motion of aircraft of various classes. Similar tools are also used to simulate the motion of dynamical systems of other types, including surface and underwater vehicles and ground moving vehicles.

Methods of forming and using models of the traditional type are by now sufficiently developed and successfully used to solve a wide range of tasks. However, in relation to modern and advanced engineering systems, a number of problems arise, the solutions of which cannot be provided by traditional methods. These problems are caused by the presence of various and numerous uncertainties in the properties of the corresponding system and in its operational conditions, which can be parried only if the system in question has the property of adaptability, i.e., if there are means of operational adjustment of the system and its model to the changing current situation. In addition, the requirements for the accuracy of models imposed on the basis of the specificity of the applied problem being solved in some cases exceed the capabilities of traditional methods.

As experience shows, the modeling tool that is most appropriate for this situation is the concept of an artificial neural network (ANN). Such an approach can be considered as an alternative to traditional methods of dynamical system modeling, which provides, i.a., the possibility of obtaining adaptive models. At the same time, traditional neural network dynamical system models, in particular, the models of the NARX and NARMAX classes, which are most often used for the simulation of controlled dynamical systems, are purely empirical (black box–type) models, i.e., based solely on experimental data on the behavior of an object. However, in tasks of the complexity level that is typical for aerospace technology, this kind of empirical models is very often not capable of achieving the required level of accuracy. In addition, due to the peculiarities of the structural organization of such models, they do not allow solving the problem of identifying the characteristics of the dynamical system (for example, the aerodynamic characteristics of an aircraft), which is a serious disadvantage of this class of models.

One of the most important reasons for the low efficiency of traditional-type ANN models in problems associated with complex engineering systems is that a purely empirical (black box) model is being formed, which should cover all the peculiarities of the dynamical system behavior. For this, it is necessary to build an ANN model of a sufficiently high dimension (that is, with a large number of adjustable parameters in it). At the same time, it is known from experience of ANN modeling that the larger the dimension of the ANN model, the greater the amount of training data required to configure it. As a result, with the amount of experimental data that can actually be obtained for complex engineering systems, it is not possible to train such models, providing a given level of accuracy.

To overcome this kind of difficulty, which is characteristic of traditional models, both in the form of differential equations and in the form of ANN models, it is proposed to use a combined approach. It is based on ANN modeling, due to the fact that only in this variant it is possible to get adaptive models. Theoretical knowledge about the object of modeling, existing in the form of ODEs (these are, for example, traditional models of aircraft motion), is introduced in a special way into the ANN model of the combined type (semiempirical ANN model). At the same time, a part of the ANN model is formed on the basis of the available theoretical knowledge and does not require further adjustment (training). Only those elements that contain uncertainties, such as the aerodynamic characteristics of the aircraft, are subject to adjustment and/or structural correction in the learning process of the generated ANN model.

The result of this approach is semiempirical ANN models, which allow us to solve problems inaccessible to traditional ANN methods. We can sharply reduce the dimensionality of the ANN model, which allows achieving the required accuracy using training sets that are insufficient in volume for traditional ANN models. Besides, this approach provides the ability to identify the characteristics of the dynamical system, described by nonlinear functions of many variables (for example, the dimensionless coefficients of aerodynamic forces and moments).

In subsequent chapters, we consider an implementation of this approach, as well as examples of its application for simulating the motion of an aircraft and identifying its aerodynamic characteristics.

Chapter 1 is devoted to a statement of the modeling problem for controlled motion of nonlinear dynamical systems. We consider the classes of problems, which arise from the processes of development and operation of dynamical systems (analysis, synthesis, and identification problems) and reveal the role of mathematical modeling and computer simulation in solving these problems. The next set of questions relates to the problem of the adaptability of dynamical systems. In this regard, we analyze the kinds of adaptation, the basic types of adaptive control schemes, and the role of models in the problem of adaptive control. The need for adaptability of the controlled object model is revealed, as well as the need for neural network implementation of adaptive modeling and control algorithms.

Chapter 2 presents the neural network approach to modeling and control of dynamical systems. The classes of ANN models for dynamical systems and their structural organization are considered in this chapter, including static (feedforward) networks and dynamic (recurrent) networks. The next significant problem that arises in the formation of ANN models of dynamical systems is related to the algorithms of their learning. In the second chapter, algorithms for learning dynamic ANN models are considered. The difficulties associated with such learning, as well as ways to overcome them, are analyzed. One of the fundamental requirements for the considered ANN models is giving them the property of adaptability. Methods for satisfying this requirement are considered, including the use of ANN models with interneurons and subnets of interneurons, as well as the incremental formation of ANN models. One of the critical problems when generating ANN models, especially dynamical system models, is an acquisition of training sets. In the second chapter, the specific features of processes needed to generate training sets for the ANN modeling of dynamical systems are analyzed. We consider direct and indirect approaches to the generation of these training sets. Algorithms for generating a set of test maneuvers and test excitation signals for the dynamical system required to obtain a representative set of training data are given.

In Chapter 3, we deal with the neural network black box approach to solving modeling problems associated with dynamical systems. We discuss state space representations and input-output representations for such systems. We attempt to show that using ANN technology we can solve the problem of appropriate representation of a nonlinear model of some dynamical system motion with high efficiency. Using such representation, we synthesize a neural controller that solves the problem of adjusting the dynamic properties of the controlled object (maneuverable aircraft). The next problem we solve in this chapter relates to designing control laws for multimode objects, in particular for airplanes. We consider here the concept of an ensemble of neural controllers (ENC) concerning the control problem for a multimode dynamical system (MDS) as well as the problem of optimal synthesis for the ENC.

Chapter 4 deals with black box neural network modeling of nonlinear dynamical systems for the example of aircraft controlled motion. First of all, we consider the design process for ANN empirical dynamical system models, which belong to the family of black box models. The basic types of such models are described, and approaches to taking into account disturbing actions on the dynamical system are analyzed. Then, we construct the ANN model of the aircraft motion based on a multilayer neural network. As a baseline model, a multilayered neural network with feedbacks and delay lines is considered, in particular, NARX- and NARMAX-type models. The training of such an ANN model in batch mode and in real-time mode is described. Then, the performance of the obtained ANN model of the aircraft motion is evaluated for an example problem of the longitudinal short-period aircraft motion modeling. The performance evaluation of the model is carried out using computational experiments. One of the most important applications of dynamical models is related to the problem of adaptive control for such systems. We consider the solution to the problem of adaptive fault-tolerant control for nonlinear dynamical systems operating under uncertainty conditions to demonstrate the potential capabilities of ANN models in this area. We apply both the model reference adaptive control (MRAC) and model predictive control (MPC) methods using empirical (black box)-type ANN models. Also, synthesis of neurocontrollers is carried