Conditional optimization of nonlinear adaptive control systems

The purpose of this paper is to study the positive almost periodic solutions to the nonlinear integral equation. Using Hilbert projective metric techniques and contraction mapping principle, we establish existence and uniqueness results for the integral equation. Some examples are given.

The objective of this study is to enhance the responsiveness and precision of control systems through the acceleration of evolutionary programming in the optimization of nonlinear fuzzy control systems. Nonlinear systems are ubiquitous in engineering practice, presenting significant challenges due to their complexity and uncertainty for traditional control methodologies. Fuzzy control, an intelligent control approach rooted in empirical rules, possesses the capability to navigate uncertain and nonlinear issues. However, conventional fuzzy controllers struggle to achieve optimal control performance when confronted with highly complex nonlinear systems. Consequently, this paper introduces the application of accelerated evolutionary programming (RGA) for the optimization of fuzzy controllers, aiming to augment their performance in nonlinear systems. By merging genetic algorithms with a fuzzy adaptive PID controller, the optimized fuzzy controller is better equipped to adapt to the dynamic changes of nonlinear systems, offering robust and efficient control strategies. The results of simulation experiments demonstrate a marked improvement in response time, stability, and error reduction with the fuzzy control system based on RGA optimization. This study offers novel insights and methodologies for the further optimization of control within nonlinear systems, while providing theoretical support for the practical applications of complex systems.

This paper establishes a comprehensive framework for fixed point theory in MR-metric spaces,a generalization of standard metric spaces that incorporates three-point relations. We present fourfundamental theorems:(1) A Banach contraction principle with optimal contraction constant k < 1/3R(2) A solvability theorem for Fredholm-type integral equations(3) A Krasnoselskii-type hybrid fixed point theorem(4) A Leray-Schauder alternative for generalized contractionsThe theoretical results are applied to:• Nonlinear integral equations in neutron transport theory• Optimization problems in neural networks• Boundary value problems for nonlinear ODEsKey innovations include the development of error estimates in the MR-metric framework and the derivation of precise existence conditions for operator equations. The work bridges theoretical mathematics with practical applications in physics and machine learning.

We develop new methods of robust stability analysis for equilibrium states and optimization of nonlinear feedback control systems. For a family of nonlinear systems with uncertain matrices of coefficients and measurable output feedback we formulate sufficient stability conditions for the zero state with a general quadratic Lyapunov function. We propose a solution for the general robust stabilization and estimation problem for a quadratic performance index for a family of nonlinear systems. We show an example of a stabilization system for a single-link robot manipulator.

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In this paper, the problem about optimal iterative learning control of general nonlinear discrete-time systems has been studied. Based on contraction mapping principle, if some mild assumptions are given, we can obtain some sufficient conditions for the existence of optimal iterative learning control of general nonlinear discrete-time systems. These conditions are generalizations of the existence conditions of optimal iterative learning control of linear discrete-time systems.

In this paper, we propose a numerical scheme to solve a kind of nonlinear Fredholm integral equations of the second kind in the complex plane. The periodic quasi-wavelets (PQWs) constructed on [0; 2π] are utilised as a basis of iteration method. Using the Banach fixed point theorem, we obtain some results concerning the error analysis. Illustrative examples are included to demonstrate the validity and applicability of the technique.

In this paper we study the existence and relaxation theory for distributed parameter systems driven by nonlinear elliptic differential equations. The existence theory is developed for systems with a priori feedback (closed loop systems), while the main results of the relaxation results are proved for open loop systems. We start with some existence theorems for nonlinear elliptic inclusions which are then used to establish the existence of admissible states for the optimal control problem. Then with the help of a convexity-type condition, we formulate and prove the main existence theorem for the problem. The proof employs the so-called reduction technique. Then we formulate three different versions of the relaxed problem, we show that they are equivalent and finally we show that they have the same value as the original problem and their set of states captures the asymptotic behavior of the sequences of original states.

In this paper, we are concerned with the controllability of damped second-order integrodifferential systems with impulses. Further the result is extended to study the controllability of nonlinear neutral systems with nonlocal conditions. The fixed point analysis approach is adopted in investigation. Sufficient conditions are formulated with a noncompact condition on the cosine family of operators. The results are obtained using the Banach fixed point theorem. An example is presented to illustrate the results.

Sufficient conditions for the controllability of nonlinear stochastic fractional boundary control systems are established. The equivalent integral equations are derived for both linear and nonlinear systems, and the control function is given in terms of the pseudoinverse operator. The Banach contraction mapping theorem is used to obtain the result. A controllability result for nonlinear stochastic fractional integrodifferential systems is also attained. Examples are included to illustrate the theory.

In this paper, we obtain an equivalent nonlinear integral equation to the stochastic neutral fractional system with bounded operator. Using the integral equation, the sufficient conditions for ensuring the complete controllability of the stochastic fractional neutral systems with Wiener and Lévy noise are obtained. Banach's fixed point theorem is used to obtain the results. Examples are provided to illustrate the theory.

The Numerical Solution of Integral Equations on the Half-Line

A novel learning-based model-free adaptive control (LMFAC) approach is presented in this article for a class of unknown nonaffine nonlinear discrete-time networked control systems (NCSs) subject to hybrid cyber attacks. The aperiodic denial-of-service (DoS) attacks and persistent deception attacks are assumed to arise in feedback channels, which could result in the absence or authenticity lackness of system signals sent to the controller. With the aid of dynamic linearizaton technology, the equivalent dynamic linearized data models of considered NCSs are first established only based on I/O information instead of the knowledge of mathematical models that are commonly used under the model-based control framework. Then, an LMFAC scheme is designed on the basis of occurred maximum DoS attacks interval to adaptively tune the attenuation coefficient of the input signal for improving system performance during the next DoS attacks interval. Finally, the boundedness of tracking error is rigorously proved through the contraction mapping principle and the effectiveness of the proposed pure data-driven LMFAC method is demonstrated via simulations.

A parameter dependent Riccati equation approach is taken to analyze the stability properties of an output feedback adaptive control law design. The adaptive controller is intended to augment a nominal, fixed gain, observer based output feedback control law. Although the formulation is in the setting of model following adaptive control, the realization of the adaptive controll er does not require implementing the reference model. In this regard, the cost of implementing the adaptive controller above that of a fixed gain control law is far less than that of other methods. The error signals are shown to be uniformly ultimately bounded and an expression for the ultimate bound is provided. The control design process and theoretical results are illustrated using a model for wing-rock dynamics. Research in adaptive output feedback control of uncertain nonlinear systems is motivated by the many emerging applications that employ novel actuation devices for active control of flexible structures and fluid flows. These applications include actuators such as piezo-electric films and s ynthetic jets, which are typically nonlinearly coupled to t he plant dynamics they are intended to control. Models for these applications vary from accurate low frequency models to models that crudely approximate the true dynamics even at low frequencies. Examples of applications include active damping of flexible structures, control of aeroservoelasti c aircraft, and active control of flows. Adaptive control can be used to satisfy performance requirements in the presence of large scale parameter uncertainty, and improved safety in the event of actuator failure.

This article investigates relative controllability of nonlinear switched fractional systems (SFSs). With the aid of Mittag‐Leffler functions and invariant subspace theory, two sufficient and necessary conditions for corresponding linear SFSs are first established. Then, piecewise continuous control functions and a novel nonlinear operator are constructed to overcome the difficulties arising from switching rules, nonlinearity, and fractional derivatives. Under different constraints on nonlinear functions, two controllability conditions depending on system parameters for nonlinear SFSs are proposed by applying Schauder's and Banach's fixed point theorems, respectively. The obtained criteria may well show the influence of coefficient matrices, fractional derivatives, and switching rules on relative controllability. In addition, our proposed method is also applicable for integer‐order switched systems. Finally, two simulated examples are worked out to verify the theoretical results.