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 analyzes the output feedback control of a class of unknown nonlinear systems in the presence of measurement noise using multiple high-gain observers (MHGOs). It is well known that single high-gain observers (HGOs) are not able to provide satisfactory performance when the system output is contaminated by noise, and in turn, controllers, which utilize such estimations, perform poorly. To address this issue and improve the control performance, a bank of HGOs is employed, and an appropriate combination of their estimations is used for control purposes. The proposed strategy is capable of mitigating destructive effects of measurement noise and improving transient response, and it does that because it introduces an extra design parameter. The performance recovery capabilities of MHGO-based controllers and the stability of the closed-loop system are discussed. The simulations are performed on an underwater vehicle system and a mechanical system to evaluate the performance of the MHGO-based controller. Furthermore, a detailed comparison to controllers based on conventional HGO, HGO with switching gain, and multi-observer approach is provided, which shows the superiority of the MHGO-based controller over the other methods.

This paper presents a tracking control methodology for a class of uncertain nonlinear systems subject to input saturation constraint and external disturbances. Unlike most previous approaches on saturated systems, which assumed affine nonlinear systems, in this paper, tracking control problem is solved for uncertain nonaffine nonlinear systems with input saturation. To deal with the saturation constraint, an auxiliary system is constructed and a modified tracking error is defined. Then, by employing implicit function theorem, mean value theorem, and modified tracking error, updating rules are derived based on the well-known back-propagation (BP) algorithm, which has been proven to be the most relevant updating rule to control problems. However, most of the previous approaches on BP algorithm suffer from lack of stability analysis. By injecting a damping term to the standard BP algorithm, uniformly ultimately boundedness of all the signals of the closed-loop system is ensured via Lyapunov's direct method. Furthermore, the presented approach employs nonlinear in parameter neural networks. Hence, the proposed scheme is applicable to systems with higher degrees of nonlinearity. Using a high-gain observer to reconstruct the states of the system, an output feedback controller is also presented. Finally, the simulation results performed on a Duffing-Holmes chaotic system, a generalized pendulum-type system, and a numerical system are presented to demonstrate the effectiveness of the suggested state and output feedback control schemes.