Feedback Control Research Articles

Analytical Solutions for a Nonlinear Quadratic Delayed Functional Integral Inclusion With Feedback Control on the Real Half-Line

Let E be a reflexive Banach space. In this research, we are interested in the solvability of the nonlinear quadratic delayed functional integral inclusion (NQDFII) with a feedback control condition on the real half-axis. Our examination is found within the space BC(R+, E) of bounded continuous functions on the real half-axis R+ and takes values in a reflexive Banach space E beneath the assumption that the set-valued function G satisfy Lipschitz condition in E. The base we depend on in this study is the procedure related to a measure of noncompactness in the space BC(R+, E) by a given norm of continuity and applying Darbo’s fixed point theorem. Moreover, the asymptotic stability of the solution and the asymptotic dependency of the solution on the set of selections SG will be examined. Also, we give an example to illustrate the adequacy and esteem of our comes about.

Stability analysis and stabilization of discrete-time switched nonlinear systems with mode-dependent average dwell time under nested actuator saturation

In this paper, the stability analysis and stabilization of a class of mode-dependent mean residence time-based discrete-time switching nonlinear systems are addressed. More specifically, under the mode-dependent average dwell time (MDADT) switching mode, combined with the practical problem, the nonlinear factor of nested actuator saturation (NAS) is introduced. Firstly, in order to ensure the system stability, based on the parameter-dependent discontinuous switching Lyapunov function and several basic lemmas, a state feedback controller is designed that makes the closed-loop system (CLS) achieve local exponential stability (LES) by solving the optimal problem in terms of linear matrix inequalities (LMIs). Secondly, the system considers the maximum attraction domain that can be achieved by the NAS system under the conditions. The simulation results show the effectiveness of the proposed design method. At the same time, the efficiency of the proposed method is verified via a water tank example.

Consensus Control of Leader–Follower Multi-Agent Systems with Unknown Parameters and Its Circuit Implementation

With the development and progress of Internet and data technology, the consensus control of multi-agent systems has been an important topic in nonlinear science. How to effectively achieve the consensus of leader–follower multi-agent systems at a low cost is a difficult problem. This paper analyzes the consensus control of complex financial systems. Firstly, the dynamic characteristics of the financial system are analyzed by the equilibrium points, bifurcation diagrams, and Lyapunov exponent spectra. The behavior of the financial system is discussed by different parameter values. Secondly, according to the Lyapunov stability theorem, the consensus of master–slave systems is proposed by linear feedback control, wherein the controllers are simple and low cost. And an adaptive control method for the consensus of master–slave systems is investigated based on financial systems with unknown parameters. In theory, the consensus of the leader–follower multi-agent systems is proved by the parameter identification laws and linear feedback control method. Finally, the effectiveness and reliability of the consensus of leader–follower multi-agent systems are verified through the experimental simulation results and circuit implementation.

A Multilinear HJB-POD Method for the Optimal Control of PDEs on a Tree Structure

Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is via the Dynamic Programming principle. Nevertheless, despite many theoretical results, this method has been applied only to very special cases since it suffers from the curse of dimensionality. Our goal is to mitigate this crucial obstruction developing a version of dynamic programming algorithms based on a tree structure and exploiting the compact representation of the dynamical systems based on tensors notations via a model reduction approach. Here, we want to show how this algorithm can be constructed for general nonlinear control problems and to illustrate its performances on a number of challenging numerical tests introducing novel pruning strategies that improve the efficacy of the method. Our numerical results indicate a large decrease in memory requirements, as well as computational time, for the proposed problems. Moreover, we prove the convergence of the algorithm and give some hints on its implementation.

Self-Adaptive Intelligent Metasurface Cloak System with Integrated Sensing Units.

Metasurfaces, which are ultrathin planar metamaterials arranged in certain global sequences, interact uniquely with the surrounding light field and exhibit unusual effects of light modulation. Many interesting applications have been discovered based on metasurfaces, particularly in invisibility cloaks. However, most invisibility cloaks are limited to working in specific directions. Achieving effectiveness in multiple directions requires the metasurface to be designed with both perception and modulation capabilities. Current multi-directional metasurface cloak systems are implemented with discrete components rather than an integrated sensing component. Here, we propose an intelligent metasurface cloak system that integrates sensing units, resulting in the cloaking effect with the help of a real-time direction sensor and an adaptive feedback control system. A reconfigurable reflective meta-atom based on phase modulation is presented. Sensing units replace parts of the meta-atoms in the designed tunable metasurface, integrating with an FPGA responsible for measuring the direction and frequency of the incident wave, constituting a closed-loop system together with the feedback parts. Experimental results demonstrate that the metasurface cloak system can recognize the different directions of the incoming wave, and can adaptively manipulate the reflected phase of EM waves to conceal objects without any human participation.

Sliding mode control to stabilization of coupled time fractional parabolic PDEs subject to disturbances

AbstractIn this article, the stabilization of coupled time fractional parabolic partial differential equations subject to external disturbances is investigated. By using sliding mode control method and backstepping approach, a boundary state feedback controller is designed to reject the matched disturbance and achieve the Mittag‐Leffler input‐to‐state stability of closed‐loop system. The existence of the generalized solution to the closed‐loop system is proven by Galerkin approximation scheme. Simulations are presented to illustrate the validity of our theoretical results.

Quantum Fluctuation Theorem for Arbitrary Measurement and Feedback Schemes.

Fluctuation theorems and the second law of thermodynamics are powerful relations constraining the behavior of out-of-equilibrium systems. While there exist generalizations of these relations to feedback controlled quantum systems, their applicability is limited, in particular when considering strong and continuous measurements. In this Letter, we overcome this shortcoming by deriving a novel fluctuation theorem, and the associated second law of information thermodynamics, which remain applicable in arbitrary feedback control scenarios. In our second law, the entropy production is bounded by the coarse-grained entropy production that is inferrable from the measurement outcomes, an experimentally accessible quantity that does not diverge even under strong continuous measurements. We illustrate our results by a qubit undergoing discrete and continuous measurement, where our approach provides a useful bound on the entropy production for all measurement strengths.

Heterogeneously Networked Evolutionary Games With Intergroup Conflicts.

Network games primarily explore the intricacies of individual interactions and adaptive strategies within a network. Building upon this framework, the present study delves into the modeling, analysis, and control of heterogeneously networked evolutionary games with intergroup conflict (HNEG-IC), where attacking players possess area-monitoring capabilities with limited attacking power. To begin with, a mathematical model is introduced to capture intragroup strategy dynamics and intergroup conflicts of HNEGs-IC via the algebraic state space representation (ASSR). A necessary and sufficient condition for achieving global cooperation of HNEGs-IC is established. Then, a criterion for verifying the κ -cooperation below a certain mortality is presented. Considering the HNEGs-IC with strategy feedback control, it is proven that the feedback control, subject to global cooperation, is robust to conflicts when the intersection of the strategy threshold set and the reachable set of the preset initial strategy profiles is empty. Finally, for verification and demonstration, the obtained results are applied to a simplified virtual game model of the NATO and the Warsaw Pact.

Deep learning-based rapid prediction of temperature field and intelligent control of molten pool during directed energy deposition process

In this work, deep learning-based approaches are proposed to provide promising solutions to address the challenges in realizing intelligent manufacturing and digital twins for directed energy deposition (DED) process. Firstly, a rapid and accurate prediction of part temperature is realized by innovatively combining graph neural networks (GNNs) and recurrent neural networks (RNNs). Twenty parts with different structures are selected for demonstration. GPU parallel computing technique is adopted to accelerate the thermal finite element analysis, which is used to quickly construct the simulated graph dataset with sufficient samples. By embedding the memory optimization method into the GNN block, deeper GNNs with more trainable parameters are successfully trained with a 79.4% lower GPU memory footprint, which solves the difficulty of deeper GNNs are hard to train on large graph datasets, and the accuracy of temperature prediction on unseen DED parts is significantly improved. Secondly, for intelligent molten pool regulation, a semi-analytic temperature solution method is used to create an efficient DED environment in reinforcement learning (RL) workflows. The intelligent control of molten pool depth under complex deposition strategy is realized based on the environmental state represented by molten pool images. A tailored convolutional neural networks (CNNs) model is employed as the agent to output varying laser power and continuously interact with the dynamic environment. Compared with the traditional artificial neural network agent, the total reward scored by the CNN agent is improved by 9.7% in the zigzag deposition process, mitigating the fluctuations in the controlled molten pool depths. Moreover, CNNs are more compatible with in-situ thermal images. This work can provide theoretical and technical support for realizing real-time and even ahead-of-time temperature prediction and the corresponding feedback control during DED process.

Phase-space density control based on configuration invariant of spacecraft swarm

This paper investigates a phase-space density control based on configuration invariant for large-scale spacecraft swarms. By introducing Jordan-reduced dynamics and the configuration invariant to characterize relative orbits, the macroscopic swarm dynamics is presented with respect to the temporal evolution of phase space density. The density migration of the spacecraft swarm in phase space is modeled as a specific convection–diffusion process, where the diffusion term promotes swarm spreading and the convection term guides the swarm towards a designated region for uniform distribution. Through local density estimation and defining the convection and diffusion terms, the feedback control’s specific form is proposed and its exponential stability is proved. Particularly, the formulation of the convection term outside the target region and the combined kernel function for local density estimation help in avoiding sporadic isolated spacecraft. Numerical results of spacecraft swarm deployment validate the effectiveness and superiority of phase-space density control.

Steam Pressure Control of Marine Boiler Based on AFSA-PSO-LSSVM

Abstract To solve the problem that the main steam pressure fluctuates greatly when the load of the combustion control system of the marine main boiler changes suddenly, present a combined inverse control system of Support vector machine and PID to control the steam pressure intelligently. The inverse model of the nonlinear system identified by LSSVM is used as the feedforward controller and the PID controller is used as the feedback controller. The hybrid intelligent algorithm of artificial fish swarm Algorithm and particle swarm optimization is used to optimize the parameters of the control system. The AFSA algorithm is used to search the initial values of the parameters and the PSO algorithm is locally updated. Finally, the mechanism of the steam pressure control system of the marine boiler is modeled and simulated, and the algorithm models of AFSA-PSO-LSSVM-PID, AFSA-LSSVM-PID, PSO-LSSVM-PID and LSSVM-PID are established. The experimental results show that the AFSA-PSO-LSSVM-PID model has a good dynamic, stability, anti-interference ability and robustness.

Real-time hybrid testing using iterative control for periodic oscillations

Real-time hybrid testing is a method in which a substructure of the system is realized experimentally and the rest numerically. The two parts interact in real time to emulate the dynamics of the full system. Such experiments, however, are often difficult to realize as the actuators and sensors, needed to ensure compatibility and force–equilibrium conditions at the interface, can seriously affect the predicted dynamics of the system and result in stability and fidelity issues. The traditional approach of using feedback control to overcome the additional unwanted dynamics is challenging due to the presence of an outer feedback loop, passing interface displacements or forces to the numerical substructure. We, therefore, advocate for an alternative approach, removing the problematic interface dynamics with an iterative scheme to minimize interface errors, thus, capturing the response of the true assembly. The technique is examined by hybrid testing of a bench-top four-storey building with different interface configurations, where using conventional hybrid measurement techniques is very challenging. A case where the physical part exhibits nonlinear restoring force characteristics is also considered. These tests show that the iterative approach is capable of handling even scenarios which are theoretically infeasible with feedback control.

Minimizing phase delay of feedback control signals for electromagnetic vibrators to reduce measurement uncertainty in ultra-low frequency vibration calibration

Suppressing the distortion of ultra-low frequency (ULF) vibration waveforms produced by an electromagnetic vibrator (EMV) presents significant challenges, leading to considerable measurement uncertainty during vibration calibration. A phase delay minimization method for feedback control signals is proposed to reduce the harmonic distortion of ULF vibration waveforms. The method quantitatively describes the influence law of the active viscoelastic approach on system frequency response characteristics. By selecting appropriate active stiffness and damping coefficients, the method minimizes the phase delay of the feedback control signal, thereby enhancing the disturbance suppression capability of the displacement and velocity composite negative feedback control. Experimental results indicate that harmonic distortion of the vibration waveform is reduced to less than 1.70 % within the ULF frequency range of 0.001 Hz ≤ f ≤ 1 Hz. Furthermore, the amplitude sensitivity calibration uncertainty, which arises from vibration waveform distortion, has been reduced to 0.038 % (k = 1.8), thereby improving the accuracy of vibration calibration.

Does pre-speech auditory modulation reflect processes related to feedback monitoring or speech movement planning?

Previous studies have revealed that auditory processing is modulated during the planning phase immediately prior to speech onset. To date, the functional relevance of this pre-speech auditory modulation (PSAM) remains unknown. Here, we investigated whether PSAM reflects neuronal processes that are associated with preparing auditory cortex for optimized feedback monitoring as reflected in online speech corrections. Combining electroencephalographic PSAM data from a previous data set with new acoustic measures of the same participants’ speech, we asked whether individual speakers’ extent of PSAM is correlated with the implementation of within-vowel articulatory adjustments during /b/-vowel-/d/ word productions. Online articulatory adjustments were quantified as the extent of change in inter-trial formant variability from vowel onset to vowel midpoint (a phenomenon known as centering). This approach allowed us to also consider inter-trial variability in formant production, and its possible relation to PSAM, at vowel onset and midpoint separately. Results showed that inter-trial formant variability was significantly smaller at vowel midpoint than at vowel onset. PSAM was not significantly correlated with this amount of change in variability as an index of within-vowel adjustments. Surprisingly, PSAM was negatively correlated with inter-trial formant variability not only in the middle but also at the very onset of the vowels. Thus, speakers with more PSAM produced formants that were already less variable at vowel onset. Findings suggest that PSAM may reflect processes that influence speech acoustics as early as vowel onset and, thus, that are directly involved in motor command preparation (feedforward control) rather than output monitoring (feedback control).

Developing and testing personalised nutrition feedback for more sustainable healthy diets: the MyPlanetDiet randomised controlled trial protocol.

Agriculture and food production contribute to climate change. There is mounting pressure to transition to diets with less environmental impact while maintaining nutritional adequacy. MyPlanetDiet aimed to reduce diet-related greenhouse gas emissions (GHGE) in a safe, nutritionally adequate, and acceptable manner. This paper describes the trial protocol, development, and testing of personalised nutrition feedback in the MyPlanetDiet randomised controlled trial (RCT). MyPlanetDiet was a 12-week RCT that provided standardised personalised nutrition feedback to participants based on new sustainable healthy eating guidelines (intervention) or existing healthy eating guidelines (control) using decision trees and corresponding feedback messages. To test the personalised nutrition feedback, we modelled a sample of 20 of the MyPlanetDiet participants baseline diets. Diets were modelled to adhere to control and intervention decision trees and feedback messages. Modelled nutrient intakes and environmental metrics were compared using repeated measure one-way analysis of covariance. Intervention diets had significantly lower (p < 0.001) diet-related GHGE per 2500 kilocalories (kcal) (4.7kg CO2-eq) relative to control (6.6kg CO2-eq) and baseline (7.1kg CO2-eq). Modelled control and intervention diets had higher mean daily intakes of macronutrients (carbohydrates, fibre, and protein) and micronutrients (calcium, iron, zinc, and iodine). Modelled control and intervention diets had lower percent energy from fat and saturated fat relative to baseline. Adherence to the MyPlanetDiet personalised nutrition feedback would be expected to lead to better nutrient intakes and reduced diet-related GHGE. The MyPlanetDiet RCT will test the effectiveness and safety of personalised feedback for a more sustainable diet. Clinical trials registration number: NCT05253547, 23 February 2022.

A continuum of balance performance between children with developmental coordination disorder, spastic cerebral palsy, and typical development.

Balance deficits are one of the most common impairments in developmental coordination disorder (DCD) and cerebral palsy (CP), with shared characteristics between both groups. However, balance deficits in DCD are very heterogeneous, but unlike in CP, they are poorly understood. To unravel the heterogeneity of balance performance in children with DCD by comparing them with CP and typical development (TD). Cross-sectional case-control study. Different outpatient settings and the community. Children aged 5-10.9 years with TD (N.=64, boys: 34, mean [SD] age: 8.1 [1.6]), DCD (N.=39, boys: 32, mean [SD] age: 8.1 [1.5], formal diagnosis [N.=27]), and CP (N.=24, boys: 14, mean [SD] age: 7.5 [1.4], GMFCS level I [N.=14]/II [N.=10], unilateral [N.=13]/bilateral [N.=11]). We evaluated balance performance with the extended version of the Kids-Balance Evaluation Systems Test (Kids-BESTest). Between-group differences in domain and total scores (%) were assessed via ANCOVA (covariate: age), with Tukey post-hoc analyses (P≤0.01). Children with DCD and CP performed poorer than TD children on total and domain scores with large effects (domains: η2=0.25-0.66 [P<0.001], total: η2=0.71 [P<0.001]). Still, post hoc comparisons revealed that DCD children scored significantly better than CP on the total score and four domains (P≤0.009), while performing similarly on tasks related to stability limits (P=0.999) and gait stability (P=0.012). There is a continuum of balance performance between children with TD, DCD and CP, but with great inter- and intra-individual heterogeneity in DCD and CP. DCD and CP children have difficulties with tasks requiring anticipatory postural adjustments, fast reactive responses, and with tasks that require complex sensory integration, suggesting an internal modeling deficit in both groups. This implies that these children must rely on slow conscious feedback-based control rather than fast feedforward control and fast automatic feedback. The performance of both DCD and CP children on their stability limits/verticality is similarly poor which further emphasizes a potential deficit in their sensory input and/or integration. Future research must focus on unraveling the control mechanisms, to further understand the heterogeneity of these balance deficits. The heterogeneous balance performances in both children with DCD and CP underscore the importance of comprehensively evaluating balance deficits in both groups. This comprehensive assessment contributes to a better understanding of individual balance deficits, thereby facilitating more tailored treatment programs.

Iterative control decoupling tuning for precision MIMO motion systems: A matrix update method

Control decoupling is the basic control step for precision MIMO (Multi-Input-Multi-Output) motion systems. After decoupling, the MIMO logical controlled plant can be diagonal dominant so that the control design for each DOF (Degree of Freedom) can be separately treated. However, due to the manufacturing tolerances and the assembling errors, the actual CoG (Center of Gravity) and actuator positions are inconsistent with the designed values. The nominal static control decoupling matrix is inaccurate, which significantly deteriorates the decoupling performance. To address the problem, this paper develops a matrix update based iterative control decoupling tuning method. Tuning with feedback control signals to achieve accurate tuning is its first distinct feature. By employing rigid-body model information to construct more accurate basis functions, fast tuning can also be achieved, especially for relatively low control bandwidth occasions. Differing from the feedforward compensation based iterative control decoupling tuning method, the matrix update method improves the dynamics of the logical controlled plant, does not increase the control complexity and is more robust to the inaccuracy of the model information. Experimental results on the short-stroke module of a precision motion stage which is the key subsystem of the lithographic projection lens testing system present significant control decoupling performance improvement (for example the peak value of the Rx-DOF servo error caused by the Z-DOF movement is reduced from 1.29 ×10−5 m to 3.19 ×10−6 m) after just two trials.

Two-stage dynamic real-time optimization framework using parameter-dependent differential dynamic programming

The purpose of chemical process control includes proactive adjustment of the operation to make the most profit out of it. Within this context, real-time optimization (RTO) is proposed and extended to dynamic RTO (DRTO) in the hierarchical control structure, usually having model predictive control (MPC) below. However, online tractability confined the model complexity of RTO and MPC, which results in model inconsistency and, even, incompatible solutions. Here we use parameter-dependent differential dynamic programming (PDDP) to incorporate the closed-loop behavior of the controller in an RTO layer to reduce problem complexity and online computation time. The adaptive control performance of PDDP and the efficacy of closed-loop DRTO formulation with PDDP is demonstrated with the reaction-storage-separation network system control. Consequently, PDDP provides a useful parameterization method to express closed-loop system dynamics, which enables fast feedback control and integrated plant optimization.

Estimations of global Mittag–Leffler bounds and synchronization for fractional-order permanent magnet synchronous motor systems

This article investigates the global Mittag-Leffler bounds (GM-LBs) and synchronization of fractional-order permanent magnet synchronous motors (FOPMSMs). To begin with, by using some appropriate generalized Lyapunov functions, the extremum principle of function and fractional differential inequalities, a few new bounds for the three-dimensional cylindrical and ellipsoidal domains and a rotatory parabolic body of FOPMSMs are estimated by utilizing the parameters in the systems, which improves the earlier studies and may conclude some new estimates. Moreover, linear feedback control strategies owning one or two inputs and fractional adaptive control owning both single input and single state are accepted to come true the global Mittag-Leffler synchronization (GM-LS) and global asymptotic synchronization (GAS) of two FOPMSMs. Some new criteria for the synchronization are acquired by utilizing some inequality approaches. Finally, the feasibility of the proposed control schemes is verified by numerical simulations.

Non-fragile event-triggered control for switched positive linear systems using state-dependent switching method

This article is concerned with the issues of stability and L1-gain characteristic for switched positive linear systems utilizing bumpless transfer (BT) technique and event-triggered (ET) strategy. Under the state-driven switching policy, a regulatory approach that couples BT and ET is introduced to attenuate the hybrid bumps stemming from switching and triggering moments. Compared with traditional state-driven switching, the proposed hysteresis switching can delay the occurrence of switching. Based on multiple copositive Lyapunov functions, a state feedback controller with an ET mechanism is constructed for positive systems, which reduces the update frequency of the actuator, and this control strategy is extended to the case of actuator faults. It is confirmed that the proposed control scheme can assure the positivity, stability, and L1-gain performance of the system. Additionally, the Zeno phenomenon is addressed via establishing a positive lower bound for the ET interval. Ultimately, simulation examples containing a turbofan engine model are provided to demonstrate the effectiveness of the proposed approach.