Unknown System Parameters Research Articles

Event-triggered synchronisation of unknown heterogeneous coupled harmonic oscillators

This note concentrates on event-triggered synchronisation problem of unknown heterogeneous coupled harmonic oscillators (CHOs). We develop an event-triggered synchronisation algorithm that does not rely on any continuous information transmission among oscillators and global topology information. For this end, we first design an observer to estimate unknown system parameter for each oscillator. Second, each oscillator uses information received from its neighbours to estimate the frequency of leader oscillator and its neighbours' states. Based on estimated frequencies and states, we design an adaptive synchronisation algorithm for CHOs to solve synchronisation problem. We prove that CHOs, under proposed synchronisation algorithm, reach state synchronisation, and there is no Zeno behaviour. In the end, a simulation is presented to check proposed synchronisation algorithm.

Discrete adaptive sliding mode control for uncertain fractional-order Hammerstein system

This study explores controlling discrete fractional-order Hammerstein systems through two different approaches. The first method involves a detailed exploration of discrete sliding mode control (SMC), while the second method employs adaptive sliding mode techniques to address challenges posed by unknown time-varying system parameters. The aim is to enhance control strategies for these systems by ensuring stability and robustness amid evolving parameters. Stability analysis using Lyapunov Theory is carried out to establish the stability of the proposed control schemes. Comprehensive reachability analysis is then performed to show that the system reaches a quasi-sliding mode in finite time. The effectiveness of the proposed methods is thoroughly evaluated using simulation cases, covering three distinct scenarios. Finally, a discussion section analyzes the simulation outcomes and assesses the efficiency methodologies in handling complex system dynamics. Through comparative analysis and discussion, this study contributes to advancing control strategies tailored for systems characterized by fractional-order dynamics and varying parameters.

Data-driven fault diagnosis for aero-engine gas path systems with unknown system parameters

This paper is concerned with the fault diagnosis problem for aero-engine gas path systems. Due to the complexity of the aero-engine structure, it is hard to establish an accurate model with known system parameters to describe its physical characterisations. To tackle this problem, two neural networks are introduced to learn the input–output relationship for both fault-free and faulty cases. Specifically, the first neural network is mainly constructed to generate residual signals for fault detection, and the second one is designed by extracting features of different fault types such that the fault isolation problem is solved based on the extracted data. Meanwhile, considering the weak fault features, a fuzzy logic system incorporating expert knowledge is embedded to enhance the isolation accuracy. Moreover, a data-driven fault estimator is designed by using Markov parameters identification and optimisation method, and it is shown that the estimation performance is improved compared with the existing results.

Identification of Physical Dynamical Processes via Linear Structure Models (Part 1)

The article discusses methods for identifying parameters of partial differential equations. Identification problems are often called poorly conditioned. However, the reason is the ambiguity of the solution, even at the point of minimality of the criterion. In particular, the article discusses: (1) An analysis of singular values for identify the unambiguous solution. The basis of these methods is a singular value decomposition of the matrix of experimental data, what makes it possible to abandon the inversion of matrices and, as a consequence, translate the problem of ill-conditioned problems into the problem of ambiguity of the solution. (2) The issues of anomalous measurements and combination of various experiments. (3) A universal optimization method for identifying parameters by their complete simple enumeration. The method is based on fast calculation of points on a multidimensional sphere. (4) The issues of identifiability of linear structure models and construction of experiments guaranteeing identification. (5) A method for identifying parameters via projecting linear structure model elements onto the plane of guarantors. (6) An approach to constructing histograms of unknown parameters of dynamic systems before calculating them using any algorithm. The approach is based on linear structure models with parameters on a sphere and a rather unexpected application of singular value decomposition. (7) The methods are accompanied by examples of heat equations. The Appendix containsalgorithmsintheMATLABlanguageforallexamples. (8)The presented optimization, projection and statistical methods based on the concept of linear structure models allow solving the same identification problem in fundamentally different ways, which significantly increases the reliability of the results obtained.

Time-Delay-Based Sliding Mode Tracking Control for Cooperative Dual Marine Lifting System Subject to Sea Wave Disturbances

Dual marine lifting systems are complicated, fully actuated mechatronics systems with multi-input and multi-output capabilities. The anti-swing cooperative lifting control of dual marine lifting systems with dual ships’ sway, heave, and roll motions is still open. The uncertainty regarding system parameters makes the task of achieving stable performance more challenging. To adjust both the attitude and position of large distributed-mass payloads to their target positions, this paper presents a time-delay-based sliding mode-tracking controller for cooperative dual marine lifting systems impacted by sea wave disturbances. Firstly, a dynamic model of a dual marine lifting system is established by using Lagrange’s method. Then, a kinematic coupling-based cooperative trajectory planning strategy is proposed by analyzing the coupling relationship between the dual marine lifting system and dual ship motion. After that, an improved sliding mode tracking controller is proposed by using time-delay estimation technology, which estimates unknown system parameters online. The finite-time convergence of full-state variables is rigorously proven. Finally, the simulation results verify the designed controller in terms of anti-swing control performance. The hardware experiments revealed that the proposed controller significantly reduces the actuator positioning errors by 83.33% compared with existing control methods.

Adaptive robust control of tank gun pitching stabilization system considering uncertainty

Abstract Aiming at the complex nonlinearity, uncertainty and coupling of the tank gun pitching stabilization system, an adaptive robust control strategy for the tank gun pitching stabilization system is proposed by combining adaptive control and deterministic robust control. Considering that the tank gun pitching stabilization system is a kind of uncertainty as well as nonlinear coupled dynamics system, a mechanical dynamics model and an electrical control model under the high mobility environment are established. Based on the backstepping concept fusion adaptive robust idea, the parameter adaptive law is constructed to eliminate the effect of unknown system parameter, and the adaptive robust function is designed to inhibit the interference for unmodeled disturbance of the system control precision. The designed controller synthesizes the advantages of adaptive control methods as well as robust control methods to improve the practical value in engineering. Based on Lyapunov theory, the analysis indicates that the tank gun pitching stabilization system can be controlled asymptotically only by unknown parameter effects, and the ideal stabilization accuracy of the system can be ensured when both parameter uncertainty and uncertain nonlinearity exist in the system. A large number of comparative co-simulations based on Recurdyn-Simulink demonstrate the superiority of the presented technique in this study.

Anti-Sway Adaptive Fast Terminal Sliding Mode Control Based on the Finite-Time State Observer for the Overhead Crane System

This work proposes an adaptive rapid terminal SMC (sliding mode control) approach based on the FFTSO (fast finite-time state observer) for overhead crane trajectory tracking and anti-swing control in the presence of external disturbances and parameter uncertainty. First, the system state observation under the constraint of unknown system parameters is accomplished by designing the FFTSO based on finite-time theory. Next, a parameter-adaptive fast terminal SMC is created for an overhead crane based on the model transformation. This technique can still monitor the intended trajectory and reduce payload swing even in cases when the payload mass and wire rope length are uncertain. Next, the Lyapunov theorem is used to demonstrate the stability of the overhead crane system’s positioning and anti-swing angle control mechanism. Lastly, the platform experiments confirm that the suggested closed-loop system control technique is successful.

Reaction Transport Analysis and Parameter Identification for Designing Lithium–Sulfur Battery Electrodes

Electrical energy storage systems for renewable energy sources and the popularization of next-generation vehicles with low CO2 emissions and high energy efficiencies are required to realize a sustainable society. However, current cathode materials such as lithium–containing oxides used in lithium-ion batteries (LiBs) have limited storage capacities, and their energy density peaks at approximately 150–250 Wh/kg. To improve this, lithium–sulfur batteries (LiSBs) with high theoretical energy densities are currently being developed and expected to be deployed as the next-generation battery technology. In LiSBs, the complex dissolution and precipitation reactions of sulfur are the driving forces. However, the complex operating mechanisms of LiSBs are yet to be investigated. Ren et al. (1) modeled the precipitation mechanism of lithium sulfide by focusing on the characteristics of a two-step discharge reaction to clarify the relationship between the complex reaction mechanism and the battery characteristics of LiSBs. In addition to considering multistep polysulfide dissolution and reduction, they describe the rate-dependent Li2S precipitation phenomenon using electro-crystallization kinetics based on nucleation and growth theory. Thus far, research has been actively conducted on clarifying the complicated reaction mechanisms of LiSBs. These studies only simplify the reaction mechanisms and calculations using estimates of many dynamic parameters of intermediate products that are otherwise difficult to measure. However, if such a numerical analysis is applied to a new electrode system, it can lead to incorrect conclusions regarding the reaction mechanisms. In our previous study, we established a technique to identify parameters that are difficult to measure after cell assembly by fitting the measured and calculated values of the fully discharged characteristics of LiBs using a complex nonlinear optimization method (2). For LiSBs, combining actual measurements and calculations is useful to estimate the unknown parameters of a new electrode system. In LiSBs, the volume change of sulfur during charging and discharging is problematic. During discharge, the volume expands by approximately 1.8 times when sulfur combines with lithium and changes to lithium sulfide (3). Although the microstructure of the electrode is expected to be destroyed by volume expansion, which affects the battery performance, only a few studies have verified the volume change by numerical analysis with complicated mechanisms. In contrast, in our study, reaction transport analysis models that consider volume changes were established for LiBs (4). Therefore, we aimed to construct a lithium–sulfur battery design support system that combines a numerical analysis method for lithium–sulfur batteries considering volume changes with an optimization method.In this study, we examined the effect of sulfur-filled microporous activated carbon. Recently, it was reported that this microporous carbon with sulfur can be repeatedly cycled as a sulfur cathode exhibiting a high coulombic efficiency of almost 100% (5). Firstly, by using numerical simulation and optimization method, we evaluated mass transport and reaction properties with various parameters of pore structure. Next, we simulated the discharge performance with or without this activated pore. From this data, it was found that pore size strongly affects effective surface area and Li+ conduction and diffusion performance. As described above, it was suggested that an optimum pore structure exists from the viewpoint of the balance of reaction and mass transport, and the effect of different structures on transport properties was qualitatively evaluated. In the future, it is necessary to confirm the validity of the optimal structure through experiments and to quantitatively evaluate the effect of different CB.AcknowledgmentThis study was supported by JST GteX, Development of lithium-sulfur batteries with low environmental impact and high performance, Grant JPMJGX23S0, Japan.(1) M. Hagen et al., Adv. Energy Mater., 5(16), 1401986 (2015).(2) G. Inoue et al., J. Chem. Eng. JAPAN, 54(5), 207–212 (2021).(3) M. M. Islam et al., Phys. Chem. Chem. Phys., 17(5), 3383–3393 (2015).(4) G. Inoue et al., ECS Trans., 80(10), 275-282, (2017).(5) T. Tonoya et al., Electrochemistry Communications, 140, 107333 (2022).

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.