Unknown System Parameters Research Articles

Adaptive synchronization and anti-synchronization of Julia sets generated by the competitive model

In this paper, we study the fractal behaviour of a competitive model that describes the interaction of plankton allelopathy. This paper aims to establish synchronization and anti-synchronization of Julia sets of two competitive systems with some different parameters by using an adaptive control strategy. Firstly, a discrete version of the competitive model is obtained, and then the Julia set of the discrete version is generated by using the escape-time algorithm. Adaptive controllers and parameter update laws for unknown parameters are designed to achieve synchronization and anti-synchronization of Julia sets. Furthermore, we can determine unknown parameters of the competitive system by using this adaptive control technique. Here, the adaptive synchronization and anti-synchronization of Julia sets are accomplished by its trajectories synchronization and anti-synchronization due to the close relation of trajectories of the system with the Julia set of the system. Numerical simulations are carried out to validate several key theoretical results as well as the efficacy and accuracy of the applied methodologies. Moreover, with the help of this analysis, we can study other models of a similar type.

Concurrent learning for adaptive pontryagin's maximum principle of nonlinear systems with inequality constraints

AbstractIn this article, a finite‐horizon adaptive Pontryagin's maximum principle is presented for nonlinear systems with state inequality constraints. Concurrent learning (CL) technique is adopted to identify the unknown parameters of the dynamic systems. Based on the identification model, a novel adaptive iterative algorithm under the Pontryagin's framework is introduced to learn the finite‐horizon optimal control solution. Convergence analysis of the algorithm is provided by showing that the cost function sequence is monotonically decreasing. Furthermore, we extend the adaptive iterative algorithm to time‐varying nonlinear systems. The new algorithm overcomes the technical obstacles of the existing adaptive/approximate dynamic programming (ADP) approaches to deal with the time‐varying characteristic of Hamilton–Jacobi–Bellman (HJB) partial differential equation (PDE), especially when state constraints exist. Simulation examples are carried out to validate the effectiveness of the theoretical results.

Data-driven discrete fractional chaotic systems, new numerical schemes and deep learning.

Parameter estimation is important in data-driven fractional chaotic systems. Less work has been reported due to challenges in discretization of fractional calculus operators. In this paper, several numerical schemes are newly derived for delay fractional difference equations of Caputo and Riemann-Liouville types. Then, loss functions are constructed and unknown parameters of the discrete fractional chaotic system are estimated by a neural network method. Parameter estimation results demonstrate high accuracy compared with real values. Robust analysis is provided under different noise levels. It can be concluded that this paper provides an efficient deep learning method based on fractional discrete-time systems.

Φ-DVAE: Physics-informed dynamical variational autoencoders for unstructured data assimilation

Incorporating unstructured data into physical models is a challenging problem that is emerging in data assimilation. Traditional approaches focus on well-defined observation operators whose functional forms are typically assumed to be known. This prevents these methods from achieving a consistent model-data synthesis in configurations where the mapping from data-space to model-space is unknown. To address these shortcomings, in this paper we develop a physics-informed dynamical variational autoencoder (Φ-DVAE) to embed diverse data streams into time-evolving physical systems described by differential equations. Our approach combines a standard, possibly nonlinear, filter for the latent state-space model and a VAE, to assimilate the unstructured data into the latent dynamical system. Unstructured data, in our example systems, comes in the form of video data and velocity field measurements, however the methodology is suitably generic to allow for arbitrary unknown observation operators. A variational Bayesian framework is used for the joint estimation of the encoding, latent states, and unknown system parameters. To demonstrate the method, we provide case studies with the Lorenz-63 ordinary differential equation, and the advection and Korteweg-de Vries partial differential equations. Our results, with synthetic data, show that Φ-DVAE provides a data efficient dynamics encoding methodology which is competitive with standard approaches. Unknown parameters are recovered with uncertainty quantification, and unseen data are accurately predicted.

Robust adaptive control of delayed systems with multiple uncertainties and polynomial nonlinearities

This work discusses the issue of robust adaptive control for delayed systems with multiple uncertain factors. The system uncertainties cover uncertain dynamics, unknown system parameters, and external disturbances. Besides, the growing conditions have both low-order and high-order polynomial nonlinearities, which bring in numerous challenges for control design. The suitable transformations are first introduced to obtain a new system with a dynamic gain. Then, the control design of an auxiliary system is considered. By introducing the Lyapunov–Krasovskii (L–K) functional method, and providing an important result for an auxiliary system, the adaptive homogeneous control strategy is proposed to achieve global asymptotic stability (GAS) of the entire system. Besides, by considering the external disturbances, the method is also extended to design robust adaptive tracking controller. Numerical and practical examples are provided to verify the theory.

Adaptive PI Control Based Stability Margin Configuration of Aircraft Control Systems with Unknown System Parameters and Time Delay

Adaptive PI Control Based Stability Margin Configuration of Aircraft Control Systems with Unknown System Parameters and Time Delay

Model-Free Optimal Vibration Control of a Nonlinear System Based on Deep Reinforcement Learning

Optimal control of nonlinear vibration requires precise knowledge of the system and the solution to Hamilton–Jacobi–Bellman (HJB) equation. However, in practical engineering applications, acquiring precise system parameters poses challenges, and the analytical solutions for the HJB equation are difficult to obtain. In this paper, two reinforcement learning algorithms, Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and Soft Actor-Critic (SAC) algorithm, are employed to train neural network-based optimal controllers for the van der Pol vibration system in the presence of unknown system parameters. To validate their performance, the controllers undergo testing in a series of experiments, including assessments of free vibration, frequency sweep excitation, and Gaussian noise excitation. The results indicate that both the TD3-trained and SAC-trained neural network-based controller are capable of proficiently suppress the vibration of the van der Pol oscillator. Additionally, these two model-free controllers can approximate the optimal control law which solved based on the dynamic model of the nonlinear system.

Neural network-based robust adaptive super-twisting sliding mode fault-tolerant control for a class of tilt tri-rotor UAVs with unmodeled dynamics

Abstract Aiming at alleviating the adverse influence of coupling unmodeled dynamics, actuator faults and external disturbances in the attitude tracking control system of tilt tri-rotor unmanned aerial vehicle (UAVs), a neural network (NN)-based robust adaptive super-twisting sliding mode fault-tolerant control scheme is designed in this paper. Firstly, in order to suppress the unmodeled dynamics coupled with the system states, a dynamic auxiliary signal, exponentially input-to-state practically stability and some special mathematical tools are used. Secondly, benefiting from adaptive control and super-twisting sliding mode control (STSMC), the influence of the unexpected chattering phenomenon of sliding mode control (SMC) and the unknown system parameters can be handled well. Moreover, NNs are employed to estimate and compensate some unknown nonlinear terms decomposed from the system model. Based on a decomposed quadratic Lyapunov function, both the bounded convergence of all signals of the closed-loop system and the stability of the system are proved. Numerical simulations are conducted to demonstrate the effectiveness of the proposed control method for the tilt tri-rotor UAVs.

Event‐triggered adaptive estimated inverse neural network control of uncertain nonlinear systems with unknown hysteresis effects

AbstractThis article investigates an event‐triggered adaptive estimated inverse control scheme for uncertain nonlinear systems with hysteresis effects, parametric uncertainties, and unknown disturbances. An online estimated inverse hysteresis compensation mechanism is developed, in which an adaptive technique is designed to obtain the value of unknown hysteresis parameters. Compared with common approaches, its biggest advantage lies in the fact that it eliminates the need for experimental determination of hysteresis parameters, thereby reducing time‐consuming offline identification work and enhance the compatibility of the proposed method. Additionally, an adaptive radial basis functions neural network is applied to approximate the unknown disturbances, and its weight coefficients, along with unknown system parameters, are estimated by means of the adaptive method. Furthermore, the introduction of relative threshold event‐triggered control significantly reduces communication costs resulting from the hysteresis compensation. Through Lyapunov analysis, the proposed controller guarantees all signals are bounded and the errors are convergent. Numerical simulation results demonstrate the superiority of the developed controller.

Fixed-Time Adaptive Parameter Estimation for Hammerstein Systems Subject to Dead-Zone

The Hammerstein model has proven its ability for modeling many industrial servo systems, but the corresponding parameter estimation remains as a challenging problem, especially for the purpose of achieving fast convergence. This paper presents a fixed-time (FxT) adaptive parameter estimation scheme for Hammerstein systems with an asymmetric dead-zone to ensure the convergence of estimated parameters in fixed-time. A continuous piecewise linear (CPL) function is adopted to model the nonlinear dead-zone dynamics to remedy the use of intermediate variable. To avoid using the system state information, a K-filter is used to construct a relationship between the unknown system parameters and the input/output signals. Then a new adaptive law based on the parameter error and the FxT scheme is developed to online estimate the lumped unknown parameters and ensure the fixed-time convergence, where an online updated auxiliary variable of regressor is suggested to eliminate the impact of the regressor on the convergence performance. Both numerical simulations and experimental results are given to demonstrate the effectiveness of proposed methods.

Entirely Coupled Recurrent Neural Network-Based Backstepping Control for Global Stability of Power System Networks

In an interconnected power system network, global performance is affected by various unknown power system parameters subjected to system uncertainties. These unknown parameters in the control expression deteriorate the performance of the power system network. Therefore, these terms associated with the control expression must be estimated precisely. This paper proposes an adaptive backstepping scheme using an entirely coupled recurrent neural network (ECRNN) to estimate these control terms. Three continuous differentiable functions are used to design control input, virtual signals, and adaptive control laws to achieve global performance. The objective of ECRNN is to reduce the control complexity by estimating the associated nonlinear term in the control expression. It will facilitate the complex formulation of the controller and improve system performance. The robust functional estimation ability of ECRNN will make the system immune to uncertainties that may appear due to external disturbances. In ECRNN, feedback loops are added to each neuron layer to achieve additional estimation accuracy. The proposed adaptive law enhances the online weight update speed and accuracy. Verification of the proposed scheme is carried out in MATLAB/Simulink. It is also verified in the real-time digital simulator (RTDS) platform using the IEEE standard New England 39-bus, 10-machine power system model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the existing limitations in the global performance of a multimachine power system network due to uncertainty in the system parameters. Uncertainties in the power system network primarily appeared due to penetration of renewable power sources, load uncertainty, or occurrence of an uncertain fault in the network. As power system networks are complex nonlinear interconnected systems, these perturbations in the generator states may cause economic losses, load demand uncertainty, or electric scarcity. Thus, a control scheme is required to address the global performance of such networks. This article proposes uniform ultimate bounded stability of synchronous generators in a multimachine power system network with a robust ECRNN-based backstepping control design. The other available technique has not adequately addressed the global performance under uncertainties. The efficacy of the proposed scheme is verified in a real-time environment via a real-time digital simulator which may be a feasible solution for designing excitation control for the synchronous machine in an extensive industrial network.

Adaptive predictor-based control for a helicopter system with input delays: Design and experiments

In this paper, we consider a 2-degrees-of-freedom (DOF) helicopter system subject to long input delays and uncertain system parameters. To address the challenges including unknown system parameters and input delays in control design, we develop an adaptive predictor-feedback control law to achieve trajectory tracking. Stability of the closed-loop system is further established, where the tracking errors are shown to converge towards zero. Through simulation and experiments on the helicopter system, we illustrate that tracking of a desired trajectory is achieved with the proposed control scheme.

Adaptive Output Feedback Control for Uncertain Nonlinear Systems with Unknown Modeling Errors

AbstractIt is well known that unknown modeling errors cannot be avoided in practice. Such unmeasured uncertainties are usually denoted as unknown nonlinear functions that exist in every channel of the system equation. This paper aims to develop an output feedback adaptive control scheme by constructing state estimation filters to address such unknown modeling errors. In the controller design, these uncertainties caused by modeling errors will be accumulated to the last step for compensation. Unknown parameters existing in the upper bound functions of unknown nonlinear functions and system parameters are estimated synchronously based on tuning function approaches. It is shown that the designed output feedback controller can ensure the stability and tracking performance of the closed‐loop system, and the transient performance in terms of a truncated norm is also established.

An event‐triggered subspace predictive control method for partially unknown linear parameter‐varying systems

AbstractThis article develops a novel event‐triggered subspace predictive control (ET‐SPC) method for discrete‐time linear parameter‐varying (LPV) systems with partially unknown system parameters. An event‐triggered law is developed to alleviate the heavy load of data transmission and computation in the conventional subspace predictive control methods for the LPV systems. The design of the event‐triggered law relies on the input‐to‐state stability (ISS) theory and applies the robust stability condition based on linear matrix inequalities (LMIs), which guarantees the stability of the proposed method. Consequently, the input component can be directly transmitted to the system without receding horizon optimization when the event‐triggered law evaluates that the system satisfies the stability condition. The simulation results illustrate its satisfactory performance, which indicates its potential application involving a considerable amount of data transmission and computation such as the network control systems (NCSs).

Distributionally robust system identification for continuous fermentation nonlinear switched system under moment uncertainty of experimental data

In this paper, we consider a nonlinear switched dynamical system (NSDS) with unknown system parameters in the context of uncertain experimental data. This system is employed to model the continuous fermentation for the production of 1,3-propanediol through glycerol bioconversion. The uncertain experimental data points are regarded as stochastic variables and only their first-order moment information of the probability distributions is available. The target of this paper is to optimize these system parameters under the environment of uncertain experimental data. Taking these factors into account, we propose a distributionally robust system identification (DRSI) problem (i.e., a bi-level system identification problem) governed by the NSDS. The objective functional comprises two level objectives: (i) the inner-level objective aims to maximize the expectation of the relative error between the solution of the NSDS and the uncertain experimental data with respect to their probability distributions at approximately stable time; and (ii) the outer-level objective is to minimize the expectation with respect to these system parameters. The DRSI problem is equivalently transformed into a single-level system identification (SLSI) problem with non-smooth term through the application of the duality theory in the probability space. A smoothing technique is employed to approximate the non-smooth term in the SLSI problem. Subsequently, an error analysis of the employed smoothing technique is derived. The gradients of the objective functional in the SLSI with respect to these system parameters are obtained. An optimization algorithm is designed to solve the SLSI problem. Finally, the paper concludes with simulation results.

Finite-Time Tracking Control of a Flexible Link Manipulator Based on an Extended State Observer

In this paper, the finite-time trajectory tracking control problem of a flexible link manipulator (FLM) system with unknown parameters is investigated in joint space. An adaptive nonsingular terminal sliding mode (ANTSM) controller based on an extended state observer (ESO) is proposed to ensure that the tracking error converges to a small neighborhood of zero. Firstly, an adaptive ESO is introduced, which is used to estimate unknown system parameters, including the unknown rigid-flexible coupling coefficient and the unknown control gain. Then, an ESO based on the parameters estimated above is proposed to estimate the unmodeled dynamics and external disturbances of the system in real-time. Finally, an ANTSM controller based on ESO is studied to achieve finite-time trajectory tracking control and vibration suppression without any prior knowledge of system uncertainties and external disturbances. The finite-time convergence ability of the closed-loop system is proved by Lyapunov theory. Experimental results on the Quanser Flexible Link System verify the effectiveness of the proposed controller.

Distributed Adaptive Fault-Tolerant Formation-Containment Control With Prescribed Performance for Heterogeneous Multiagent Systems.

This article proposes a distributed adaptive fault-tolerant formation-containment control with prescribed performance for heterogeneous multiagent systems (MASs) consisting of multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) in the presence of actuator faults. First, utilizing the neighborhood formation error information, the distributed fault-tolerant formation control strategy is developed for the trajectory dynamics of each UAV to achieve the formation tracking, that is, all UAVs track the virtual leader and perform the prespecified formation configuration. Then, the adaptive fault-tolerant containment algorithm, independent of the positions of the leaders, is proposed to guarantee the UGVs converge to the convex hull formed by the leader UAVs. The adaptive estimation scheme is constructed to compensate for the unknown system parameters and actuator loss-of-effectiveness and bias faults. The formation-containment tracking performance is analyzed based on Lyapunov theory with the synchronization errors satisfying the prescribed performance. A simulation example based on UAVs-UGVs systems is adopted to verify the effectiveness of the proposed control strategy.

Chaotic signal denoising based on energy selection TQWT and adaptive SVD.

Aiming at the problem of denoising chaotic signals with low signal-to-noise ratio and unknown dynamic system parameters, a new chaotic signal denoising algorithm is proposed, which combines adjustable Q-factor wavelet transform (TQWT) and adaptive singular value decomposition (ASVD). This method uses TQWT to decompose the noisy chaotic signal. According to the maximum wavelet entropy theory and energy threshold rule, the subband of TQWT is accurately divided into signal subband and noise subband. For noise subbands, adaptive SVD is used to denoise them, to achieve preliminary denoising. In ASVD, the standard deviation of the singular value subset is used to determine the effective reconstruction order to improve the noise suppression effect. To further remove noise in the signal subband, TQWT reconstruction is performed on the preliminarily denoised signal, and ASVD is used to denoise the reconstructed signal again to obtain the chaotic signal after secondary denoising. Chua's simulated signal and four kinds of underwater radiated noise measured by TQWT-ASVD were denoised, and compared with the SVD denoising method, TQWT denoising method, complete ensemble empirical mode decomposition with adaptive noise and threshold denoising method (CEEMDAN-WT) and modified ensemble empirical mode decomposition combined with least squares denoising method (MEEMD-LMS), The experimental results show that the TQWT-ASVD method can reduce the noise of chaotic signals more effectively. Compared with SVD, TQWT, CEEMDAN-WT, MEEMD-LMS, and Chua's signal denoising method, the signal-to-noise ratio (SNR) of this method increased by 23.22%, 26.46%, 18.79%, 16.11% the root mean square error (RMSE) decreased by 32.53%,39.48%, 30.96%, 27.94%, and the row entropy (PE) decreased by 40.44%, 41.96%, 22.78%, 20.59%; After reducing the radiation noise of cargo ships, the PE value of this method is reduced by 13.91%, 10.18%, 10.88%, 8.68% respectively, and the FE value is reduced by 33.66%, 31.42%, 26.98%, 21.32% respectively.

Event-triggered adaptive prescribed performance control of flexible-joint manipulators with output constraint

PurposeThis paper aims to design an event-triggered adaptive prescribed performance controller for flexible manipulators, with the primary objectives of achieving output performance constraints and addressing communication resource limitations.Design/methodology/approachThe authors propose a novel prescribed performance barrier Lyapunov function (PP-BLF) that considers both output and tracking performance constraints. The PP-BLF ensures that the system's output, transient behavior and steady-state performance, adhere to prescribed constraints. The boundary of the PP-BLF is established by an exponential function that decays over time. Notably, the PP-BLF can be applied seamlessly in unconstrained cases without necessitating controller redesign. Moreover, the controller design incorporates an event-triggered mechanism, effectively reducing the frequency of controller updates and optimizing the utilization of communication resources. Additionally, the authors employ adaptive techniques to estimate the system's unknown parameters and approximate unknown nonlinear functions using radial basis function neural networks (RBFNN). To address the challenge of “complexity explosion”, dynamic surface technology is employed.FindingsNumerical simulations are conducted under five different cases to verify the effectiveness of the proposed controller. The results demonstrate that the controller successfully constrains the output tracking error within the prescribed performance boundary. Moreover, compared with the traditional time-triggered mechanism, the event-triggered mechanism significantly reduces the controller's update frequency, resolving the problem of limited communication resources.Originality/valueThe paper reduces the update frequency of control signals and improves resource utilization through an event-triggered mechanism in the form of relative thresholds. The authors recognize that the event-triggered mechanism may impact the output performance of the system. To address this challenge, the authors propose a prescribed performance Barrier Lyapunov Function (PP-BLF). The PP-BLF is designed to effectively constrain the output performance of the system, ensuring satisfactory control even when the control signal updates are reduced.

Estimation of Multiple Unknown Parameters Using Adaptive Observers for Lipschitz Nonlinear Systems

This work presents the design of an adaptive observer for a class of Lipschitz nonlinear systems, where the observer is able to estimate more than one unknown parameter. Thanks to this, it is possible to estimate the system states, which facilitates the monitoring of nonlinear Lipschitz systems. The proposed observer is tested for monitoring a semiactive suspension, in order to know the stiffness parameters of the tire and chassis, allowing the detection of possible anomalies in the system. To ensure observer stability, the gains are calculated by LMI obtained by Lyapunov analysis. The proposed observer is evaluated by estimating the unknown states and parameters of a mechanical system allowing monitoring of its performances.