Mutual learning is a machine learning algorithm where multiple machine learning algorithms share knowledge among themselves to improve themselves.The utilization of mutual learning algorithms can effectively enhance the efficiency of machine learning and neural networks within a multiagent system.This approach is particularly useful in scenarios where the system cannot be adequately trained with a large dataset.By exchanging data in a dynamic teacher-student network system, mutual learning can result in efficient learning outcomes.Typically, a large network serves as a static teacher and transfers data to smaller networks, referred to as student networks, to improve their efficiency.In this study, we aim to demonstrate that two small networks can dynamically alternate between the roles of teacher and student to share knowledge, resulting in improved efficiency for both networks.To exemplify this concept, we apply a mutual learning algorithm using convolutional neural networks (CNNs) and Support Vector Machine (SVM) to accurately identify the kidney diseasescyst, tumor and stone using image classification algorithm.

Mutual learning algorithm can be an efficient mechanism for improving the machine learning and neural network efficiency in a multi-agent system. Specifically, in many cases, where the system cannot be trained using a big training dataset, the data exchange in teacher-student network system can lead to efficient learning. Usually, in mutual learning algorithms, a big network plays the role of a static teacher and passes the data to smaller networks, known as student networks, to improve the efficiency of the latter. In this paper, we will show that two small networks can dynamically play the changing roles of teacher and student to share their knowledge and hence, the efficiency of both the networks improve simultaneously. We demonstrate the concept and the proposed mutual learning algorithm using convolutional neural networks (CNNs) to recognize the benchmark Modified National Institute of Standards and Technology (MNIST) hand-writing dataset.

The paper deals with the adaptive control of linear systems whose parameters can vary in a piece-wise constant fashion. The principal aim of the paper is to discuss the questions that arise when dealing with such systems and describe the methods used to identify and control them. These include the use of many models, the choice of their location, and how they are to be activated. Second level adaptation, which incorporates many of these features, is found to be the best method for tracking piece-wise constant systems from the point of view of speed, accuracy, and stability. Simulation results are included to indicate the improvement in performance at every stage.

In two earlier papers presented at the 2019 and 2020 American Control Conferences, the concept of “Mutual Learning” was introduced by the authors and applied to learning in static and dynamic stochastic environments. In this paper, we extend the concept of mutual learning to optimization. Two agents attempting to optimize the same performance index “learn” from each other to reach the solution more efficiently. Since optimization is a well investigated mathematical area in systems theory, it is particularly well suited to the original objective of the authors to study “Mutual Learning” in a systems theoretic framework.The two agents involved in mutual learning can use any of the methods well-known in the literature to optimize the given function. The initial conditions and the period over which the optimization is carried out, may be different for the two agents before they communicate with each other for the first time. The principal conclusion of the paper is that mutual learning should be viewed as a general research area, and not as a specific procedure used in different system theoretic problems.

This paper presents a unified theoretical framework for the identification and control of a nonlinear discrete-time dynamical system, in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a "higher order function." This representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system, and reveals the role played by the linearized system in a more transparent form. Under the assumption that the linearized system is controllable and observable, it is shown that: 1) the nonlinear system is also controllable and observable in a local domain; 2) a feedback law exists to stabilize the nonlinear system locally; and 3) the nonlinear system can exactly track a constant or a periodic sequence locally, if its linearized system can do so. With some additional assumptions, the nonlinear system is shown to have a well-defined relative degree (delay) and zero-dynamics. If the zero-dynamics of the linearized system is asymptotically stable, so is that of the nonlinear one, and in such a case, a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly, in a neighborhood of the equilibrium state. The tracking can be achieved by using the state vector for feedback, or by using only the input and the output, in which case the nonlinear autoregressive moving-average (NARMA) model is established and utilized. These results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete-time dynamical systems.

The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.

The past five years have witnessed a great deal of progress in both the theory and the practice of control using neural net works. After a long period of experimentation and research neural network-based controllers are finally emerging in the marketplace and the benefits of such controllers are now being realized in a wide variety of fields. The practical applications are also calling for a better understanding of the theoretical principles involved. In this paper we review the current status of control practice using neural networks and the theory related to it and attempt to assess the advantages of neurocontrol for technology.

For pt. I see ibid., vol. 4 (1993). This paper considers the problems of regulation and tracking of a dynamical system when the state variables of the dynamical system are not accessible. The existence of the nonlinear maps describing the identifier and controller are first established and the implications for neural network realizations are described. Simulation results are included to complement the theoretical discussions.

The paper presents a novel methodology for the trajectory tracking control of robotic manipulators. The proposed method utilizes multiple models of the manipulator for the identification of its dynamics in an adaptive control frame work. Simulations and experimental test results are also included to demonstrate the improvement in the tracking performance when the proposed methodology is used for different tracking tasks.

This paper is concerned with the identification of an unknown nonlinear dynamic system when only the inputs and outputs are accessible for measurement. Specifically we investigate the use of feedforward neural networks as models for the input-output behavior of such systems. Relying on the approximation capabilities of feedforward neural networks and under mild assumptions regarding the properties of the underlying nonlinear system, it is shown that there exists a feedforward network that for almost all inputs (an open and dense set) will display the input-output behavior of the system.

An attempt is made to indicate how practically viable controllers can be designed using neural networks, based on results in nonlinear control theory. The problem of stabilization of a dynamical system around an equilibrium point when the state of the system is accessible is considered. Simulation results are included to complement the theoretical discussions.

Neural networks with different architectures have been successfully used for the identification and control of a wide class of nonlinear systems. The problem of rejection of input disturbances, when such networks are used in practical problems is considered. A large class of disturbances, which can be modeled as the outputs of unforced linear or nonlinear dynamic systems, is treated. The objective is to determine the identification model and the control law to minimize the effect of the disturbance at the output. In all cases, the method used involves expansion of the state space of the disturbance-free plant in an attempt to eliminate the effect of the disturbance. Several stages of increasing complexity of the problem are discussed in detail. Theoretical justification is provided for the existence of solutions to the problem of complete rejection of the disturbance in special cases. This provides the rationale for using similar techniques in situations where such theoretical analysis is not available.

Associative learning is investigated using neural networks and concepts based on learning automata. The behavior of a single decision-maker containing a neural network is studied in a random environment using reinforcement learning. The objective is to determine the optimal action corresponding to a particular state. Since decisions have to be made throughout the context space based on a countable number of experiments, generalization is inevitable. Many different approaches can be followed to generate the desired discriminant function. Three different methods which use neural networks are discussed and compared. In the most general method, the output of the network determines the probability with which one of the actions is to be chosen. The weights of the network are updated on the basis of the actions and the response of the environment. The extension of similar concepts to decentralized decision-making in a context space is also introduced. Simulation results are included. Modifications in the implementations of the most general method to make it practically viable are also presented. All the methods suggested are feasible and the choice of a specific method depends on the accuracy desired as well as on the available computational power.

An extension of the backpropagation method, termed dynamic backpropagation, which can be applied in a straightforward manner for the optimization of the weights (parameters) of multilayer neural networks is discussed. The method is based on the fact that gradient methods used in linear dynamical systems can be combined with backpropagation methods for neural networks to obtain the gradient of a performance index of nonlinear dynamical systems. The method can be applied to any complex system which can be expressed as the interconnection of linear dynamical systems and multilayer neural networks. To facilitate the practical implementation of the proposed method, emphasis is placed on the diagrammatic representation of the system which generates the gradient of the performance function.

A novel approach to hierarchical multiobjective analysis using the theory of learning automata is introduced. The problem is modeled as several hierarchies of automata involved in stochastic identical payoff games at the various levels. It is shown that if suitable learning algorithms are chosen at all the levels, the overall performance of the system will improve at each stage. The relevance of the model to multilevel optimization problems is illustrated by considering a simple problem of labeling images consistently.>

It is demonstrated that neural networks can be used effectively for the identification and control of nonlinear dynamical systems. The emphasis is on models for both identification and control. Static and dynamic backpropagation methods for the adjustment of parameters are discussed. In the models that are introduced, multilayer and recurrent networks are interconnected in novel configurations, and hence there is a real need to study them in a unified fashion. Simulation results reveal that the identification and adaptive control schemes suggested are practically feasible. Basic concepts and definitions are introduced throughout, and theoretical questions that have to be addressed are also described.

A sequential stochastic game among an arbitrary number of players in which all players' payoffs are identical is analyzed. The players are unaware that they are in a game and hence they have no knowledge of other players' strategies or the payoff structure. At each instant the players use a simple learning algorithm to update their mixed strategy choices based entirely on the response of a random environment. It is shown that the expected change in each player's payoff is nonnegative at every instant, so that the group improves its performance monotonically. This result appears to have important implications in decentralized decision-making in large complex systems.

Two new models of nonstationary random environments whose response characteristics depend on the actios performed on them are intoduced in this paper. The models appear interesting because no one action is optimal and all the actions have to be chosen successively. A preliminary analysis of a linear learning automaton acting in such environments is presented, and certain mathematical questions of convergence which arise are brought to light. The analysis reveals that the automaton tends to equalize the penalty probabilities. Simulation studies of the abstract models as well as the routing of calls in telephone networks appear to reinforce the analytical results and the relevance of such models.

The concept of an automaton operating in a multi-teacher environment is introduced, and several interesting questions that arise in this context are examined. In particular, we concentrate on the consequences of adding a new teacher to an existing n-teacher set as it affects the choice of a switching strategy. The effect of this choice on expediency and speed of convergence is presented for a specific automaton structure.

Application of learning automata theory to telephone traffic routing and control is described. Improved network performance is demonstrated through the comparative simulation of learning automata routing and the existing fixed rule alternate routing in simple telephone networks. Learning automata routing results in significantly lower blocking probability when selected overload conditions prevail and additional capacity exists elsewhere in the network.

General schemes for the adaptive control and identification of multivariable systems whose entire state vectors are accessible for measurement are developed. A model reference approach is used here, and Lyapunov's direct method is employed to ensure the convergence of these schemes. An added feature is the simplicity of the stable adaptive laws, which depend explicitly on the state variables of the plant and a model, and on the plant input. Computer simulation results of several examples are included to illustrate the effectiveness of the proposed schemes.

The extension of some of the results contained in Part I [1] to the case when only the plant outputs rather than all its state variables are accessible for measurement is discussed. A unified approach to the synthesis of an adaptive observer is presented whereby the plant state and parameters are simultaneously estimated. Uniform asymptotic stability of the scheme is proved using Lyapunov's direct method. The information provided by the adaptive observer is used to synthesize an adaptive controller for the plant. While all the principal results obtained here are for the case of a single-input single-output plant, extensions to special classes of multivariable systems is indicated.

Stochastic automata operating in an unknown random environment have been proposed earlier as models of learning. These automata update their action probabilities in accordance with the inputs received from the environment and can improve their own performance during operation. In this context they are referred to as learning automata. A survey of the available results in the area of learning automata has been attempted in this paper. Attention has been focused on the norms of behavior of learning automata, issues in the design of updating schemes, convergence of the action probabilities, and interaction of several automata. Utilization of learning automata in parameter optimization and hypothesis testing is discussed, and potential areas of application are suggested.

The collective behavior of variable-structure stochastic automata in competitive game situations is investigated. It is demonstrated that when the automata use optimal or ε-optimal reinforcement schemes, the Von Neumann value is achieved for games against nature as well as for two-player zero-sum games having a saddle point. Computer simulations of the latter games also indicate that in the absenice of a saddle point the value of the game oscillates about the Von Neunmann value in mixed strategies.

The performance of variable-structure stochastic automata in stationary random environments has been extensively studied for the case when the environment's response is 0 or 1 (P model). A method is suggested for extending the updating schemes known for the P model to the S model, where the environment's output can lie in the interval [0,1], and a class of optimal nonlinear schemes for the S model is derived. Computer simulations reveal the superior performance of the S model in multimodal search even when the bounds on the performance function are unknown.

In the above paper,1 an optimal method of self-optimization of certain system parameters using noisy binary-valued performance feedback is extended, without losing optimality, to situations with many-valued performance feedback. The effect of time-varying feedback mechanisms is briefly considered.