Experimental Implementation of Neural Control Architectures for a Class of Nonlinear Dynamic Systems

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

Neural network (NN)-based controllers have emerged as a paradigm-shifting approach in modern control systems, demonstrating unparalleled capabilities in governing nonlinear dynamical systems with inherent uncertainties. This comprehensive review systematically investigates the theoretical foundations and practical implementations of NN controllers through the prism of Lyapunov stability theory, NN controller frameworks, and robustness analysis. The review establishes that recurrent neural architectures inherently address time-delayed state compensation and disturbance rejection, achieving superior trajectory tracking performance compared to classical control strategies. By integrating imitation learning with barrier certificate constraints, the proposed methodology ensures provable closed-loop stability while maintaining safety-critical operation bounds. Experimental evaluations using chaotic system benchmarks confirm the exceptional modeling capacity of NN controllers in capturing complex dynamical behaviors, complemented by formal verification advances through reachability analysis techniques. Practical demonstrations in aerial robotics and intelligent transportation systems highlight the efficacy of controllers in real-world scenarios involving environmental uncertainties and multi-agent interactions. The theoretical framework synergizes data-driven learning with nonlinear control principles, introducing hybrid automata formulations for transient response analysis and adjoint sensitivity methods for network optimization. These innovations position NN controllers as a transformative technology in control engineering, offering fundamental advances in stability-guaranteed learning and topology optimization. Future research directions will emphasize the integration of physics-informed neural operators for distributed control systems and event-triggered implementations for resource-constrained applications, paving the way for next-generation intelligent control architectures.

ABSTRACTBased on Radial Basis Function neural networks, a stable adaptive control scheme is proposed for a class of unknown nonlinear dynamic systems. It is shown that the scheme is stable and convergent in the sense that all the signal in the loop remain bounded, and in the ideal case, output tracking error will converge to zero and in the non-ideal case, the error will converge to a residue which is proportional to the modelling error bound. Simulation results are also provided to demonstrate performance of the scheme.

Motivated by the recent advance in adaptive output feedback control of affine nonlinear systems [8-10], an adaptive variable structure controller is proposed in this paper for solving the model reference adaptive control of nonlinear time-varying systems. Asymptotic output tracking performance can be achieved for relative degree one case. When the relative degree of the nonlinear system is greater than one, a systematic design procedure is given under a modified sector-type condition so that the closed-loop stability and the tracking performance are achieved similar to that in relative degree one case.

On a class of nonlinear stochastic dynamical systems: Analysis of the transient behaviour

Electrochemical sensors have been broadly applied in various areas for diagnostics and controls. However, many electrochemical sensors are often cross-sensitive to one or more interfering compounds, which can make it rather challenging in attaining accurate concentration of the target compound. The sensor cross-sensitivity can cause instability issues in feedback control systems and inaccurate diagnostics. In many cases, a state estimation problem with cross-sensitive output is equivalent to a state estimation problem with limited number of state candidates that can lead to the same output. In this study, an innovative estimation error-based observer is proposed for state estimation for a general class of 1st-order nonlinear dynamic systems with cross-sensitive output. By constructing observers for each potential candidate and analyzing the respective estimation errors, the true state (or mode) of the system can be determined based on the cross-sensitive output measurement. The proposed algorithm was applied to estimate the ammonia coverage ratio of a Diesel selective catalytic reduction system with ammonia cross-sensitive <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{NO}_{\mathrm{x}}$</tex> sensor output. Simulation results show that the true ammonia coverage ratio can be accurately estimated with this method at both low and high ammonia coverage ratios. This method can be applied to a broad class of nonlinear dynamic systems with cross-sensitive outputs for state estimation.

This paper presents a robust fault detection (FD) scheme for detecting and approximating state faults occurring in a class of nonlinear dynamical systems. In the presence of a failure, the values exported by the on-line approximator (OLA), are used as an estimate of the real nonlinear fault function. The general inspiration for constructing OLA model in FD is based on the radial basis function (RBF) neural network technology. Here we adopt a novel tunable activation function multi-layer forward neural network (TAF-MFNN) to construct the OLA due to its strong learning capability is proposed in this paper, and a systematic procedure for constructing nonlinear estimation algorithms is developed. Eventually, the simulation studies are used to illustrate the results.

A robust tracking control algorithm based mainly on the theory of variable structure systems and Lyapunov's direct method is developed in this paper, to treat the tracking control problem of a class of non-linear time-varying systems with uncertain dynamics. A nominal model is used instead of an exact one. together with a description of the bounds of plant uncertainty. The objective is to design a control law such that all the plants lying within a specified band of uncertainly will be driven to reach the goal. The modelling error, time-varying system dynamics, system uncertainties, and disturbances are all treated as general disturbances to the nominal system. This algorithm greatly eases the difficulties present in requiring a precise model of the physical system for the control purpose and for handling the non-linear time-varying system. The non-linear time-varying system is first linearized to a linear time-varying system (with time-varying coefficients completely defined) via the method of variable s...

While various industries heavily rely on electrochemical sensors for air and liquid quality monitoring and control, many electrochemical sensors are cross-sensitive to one or more interfering gases in addition to the target component, which may cause incorrect readings and lead to improper control measures. In this study, we proposed a direct algebraic approach-based state estimation and output decomposition algorithm which is suitable for state estimation for a class of nonlinear dynamic systems with output measurements that are highly cross-sensitive to multiple interfering gases. Using the cross-sensitive sensor measurement and its successive time derivatives, the proposed methodology can provide a closed-form solution for the actual system state estimation in a systematic way. The established state estimation algorithm was successfully validated in a numeric example. The proposed state estimation and output decomposition algorithm is applicable to a broad class of nonlinear dynamic systems which use sensors that are cross-sensitive to multiple interfering gases in order to improve the performance of the systems.

An experimentation environment for neural control of simulated systems

This paper discusses the developed Adaptive Neural Control architecture for on-line system identification and real-time adaptive control. After reviewing existing literature involving controls of structural vibration, we report new developments carried out under the adaptive neural control program for the USAF Phillips Laboratory. The new results include a neural control architecture suitable for MIMO systems subjected to tonal disturbances that is capable of optimizing vibration suppression in the presence of sensor or actuator failures. This architecture was demonstrated in a series of tests on the ASTREX facility.

In previous papers we have introduced a sufficient condition for uniform attractivity of the origin of a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform /spl delta/-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of u/spl delta/-PE which is conceptually equivalent to but technically different from its predecessors. We make connections between this property and similar properties previously used in the literature. We also show when this condition is necessary and sufficient for uniform (global) asymptotic stability for a large class of nonlinear time-varying systems.

In this paper, we are interested in adaptive neural PID control with a reference model for nonlinear systems. A recurrent neural network architecture is studied, and its parameters are computed to mimic a conventional PID controller. Two neural networks architectures, Feed Forward Neural Network (FFNN) and Recurrent Neural Network (RNN) are used for modeling nonlinear systems. To avoid the errors of the Jacobian system approximation, it is best to model the system with a neural network called an emulator. By adding an emulator in parallel with the dynamic system model, the emulator will be trained to learn the dynamics of the system.The back-propagation method is used as the basis for developing algorithms capable of modeling and controlling our nonlinear systems.

The authors investigate the incorporation of integral action for a neural net control system applicable to a class of nonlinear dynamical systems. The properties and performances of INC/NN (inverse nonlinear control/neural network) controllers are discussed and studied. Simulation results on applying the proposed INC/NN controller to a position control system with inherent nonlinearities are presented. The results have shown that the neural network control system can achieve load disturbance rejection with the incorporation of integral action. >

This paper presents an adaptive robust fuzzy control architecture for a class of nonlinear dynamic systems which are either ill-defined or rather complex. The control objective is to adaptively compensate for the unknown plant nonlinearity, which is represented as a fuzzy rule-base consisting of a collection of if-then rules. The algorithm embedded in the proposed architecture can automatically update fuzzy rules and, consequently, is guaranteed to be globally stable and to drive the tracking errors to a neighborhood of zero. Focused on realization, hardware limitations such as traditional long computation time and excessive memory-space usage are also relaxed by incorporating heuristic concepts, which reveals the flexible feature of this architecture. Simulations are run for the control of a simplified circuit system, and results show that the proposed control architecture is featured in fast convergence.