Complex Nonlinear Dynamics Research Articles

Spatiotemporal dissipative soliton resonances in multimode fiber lasers

Spatiotemporal mode-locking in multimode fiber lasers is intriguing for the complex nonlinear dynamics and the increase of theoretical energy limit. In this paper, we enrich spatiotemporal mode-locking with dissipative soliton resonances, a kind of solitons which is characterized by large pulse energy in single mode fiber lasers, and demonstrate their emergence in multimode fiber lasers by employing the reverse saturable absorption effect from real saturable absorbers. The spatiotemporal dissipative soliton resonances are expected to raise the energy limit further by the locking of dissipative soliton resonances in different transverse modes, whose energy is about twice the maximum single-mode energy in our results. Moreover, properties of spatiotemporal dissipative soliton resonances are investigated by tailoring parameters of the multimode fiber laser, where evolution and transformation of the proposed pulses including shaping and broadening are disclosed. The spatiotemporal dissipative soliton resonances in multimode fiber lasers may open up new avenue for high-power and spatiotemporally engineered coherent light fields in laser dynamics and nonlinear optics.

Transient dynamics of dissipative solitons formation in a net-normal dispersion mode-locked fiber laser based on nonlinear polarization evolution.

In mode-locked fiber lasers, the formation of ultrashort pulses from noisy or unstable states is a crucial area of research. Investigating these complex nonlinear dynamics can lead to valuable insights and new practical engineering techniques, particularly for the design and optimization of optical systems. Time-stretch dispersive Fourier transform, utilized in our study to investigate dissipative solitons formation in a net-normal dispersion nonlinear polarization evolution mode-locked fiber laser, provides a window into the intricate dynamics of such systems. In our experiments, the identification of five distinct transient stages in the formation process sheds light on the underlying mechanisms of dissipative soliton (DS) formation. The five distinct transient stages involved in the formation process include relaxation oscillation, modulation instability, spectral broadening, soliton explosions (SEs), and stable mode-locking. Notably, we also observed the generation of dissipative rogue waves during the SE stage. Our findings shed light on the intricate dynamics of DS formation and offer valuable insights for the design and optimization of mode-locked fiber lasers.

Distributions of nonlinear dynamics, stress and fatigue damage along a steel catenary riser in current affected by top-end surge

A numerical model for computing the complex nonlinear dynamics and fatigue damage of steel catenary riser (SCR) system is proposed in this paper. The structural model of SCR is described by the absolute nodal coordinate formulation (ANCF), which is further coupled with Morrison equation to incorporate the hydrodynamic loads. The hysteretic riser-soil interaction model and Coulomb friction ‘bilinear’ model are applied to simulate the seabed reactions. After validation, the distributions of nonlinear motions along the SCR, the response characteristics of touchdown point (TDP) and the corresponding stress and fatigue are fully discussed. It is found that the motion trajectory in x-z plane presents various regimes along the SCR, relating to the phase difference between x- and z-motions induced by the variations of primary and harmonic frequencies. The secondary uplift of z-motion, accompanying by the sharp decline of vertical seabed force, is captured for TDP. The values of secondary uplift and seabed force decline increase or decrease with growing surge amplitude or period in step style. Both the amplitude and period of top-end surge affect the features of axial tension, bending moment, stress and fatigue damage, where the former plays a more significant role in the concerned parameter range.

Dynamical analysis of a class of SEIR models through delayed strategies

In recent decades, the mathematical modeling of infectious diseases, real-world problems, non-linear dynamical complex systems, etc., has increased significantly. According to World Health Organization, tobacco use is the cause of about 22% of cancer deaths. Another 10% are due to obesity, poor diet, lack of physical activity, and excessive drinking of alcohol. Approximately 5%–10% of cancers are due to inherited genetic defects. The objective is to investigate the impact of time delays in implementing control measures on the epidemic dynamics. The classification of cell population has four compartments: susceptible cells (x), cancer-infected cells (y), virus-free cells (v), and immune cells (z). Our focus is to find the equilibria of the problem and their stability. The stability of the solutions is of two types: locally asymptotic and globally asymptotic. The Routh–Hurwitz criterion, Volterra-type Lyapunov function, and LaSalle’s invariance principle are used to verify the stability of solutions. The graphical behavior depicts the stable solutions to a real-world problem and supports the stability analysis of the problem. The findings contribute to the understanding of epidemic dynamics and provide valuable information for designing and implementing effective intervention strategies in public health systems.

Chaotic attractors of discrete dynamical systems used in the core of evolutionary algorithms: state of art and perspectives

This paper delves into the intersection between discrete dynamical systems and bio-inspired metaheuristic algorithms. Chaos, an inherent phenomenon manifested by both continuous and discrete dynamic nonlinear systems has become an essential component of engineering design. This study examines the relationship between chaos and bio-inspired metaheuristic algorithms from two distinct angles: the presence of chaos within the realm of algorithms, and the application of bio-inspired algorithms for the identification, control, or synthesis of complex systems. Furthermore, this paper offers an in-depth exploration of the interplay between metaheuristics and complex nonlinear dynamics, including potential avenues for future research. The presented simulation studies, along with the design of objective functions for optimization and the implementation of metaheuristics, serve as a valuable foundation for subsequent experiments involving discrete nonlinear systems and complex systems with time delays. Such systems may benefit from multiparametric or multicriteria optimization approaches, paving the way for novel advancements in the field.

Bidirectional recurrent learning of inverse dynamic models for robots with elastic joints: a real-time real-world implementation.

Collaborative robots, or cobots, are designed to work alongside humans and to alleviate their physical burdens, such as lifting heavy objects or performing tedious tasks. Ensuring the safety of human-robot interaction (HRI) is paramount for effective collaboration. To achieve this, it is essential to have a reliable dynamic model of the cobot that enables the implementation of torque control strategies. These strategies aim to achieve accurate motion while minimizing the amount of torque exerted by the robot. However, modeling the complex non-linear dynamics of cobots with elastic actuators poses a challenge for traditional analytical modeling techniques. Instead, cobot dynamic modeling needs to be learned through data-driven approaches, rather than analytical equation-driven modeling. In this study, we propose and evaluate three machine learning (ML) approaches based on bidirectional recurrent neural networks (BRNNs) for learning the inverse dynamic model of a cobot equipped with elastic actuators. We also provide our ML approaches with a representative training dataset of the cobot's joint positions, velocities, and corresponding torque values. The first ML approach uses a non-parametric configuration, while the other two implement semi-parametric configurations. All three ML approaches outperform the rigid-bodied dynamic model provided by the cobot's manufacturer in terms of torque precision while maintaining their generalization capabilities and real-time operation due to the optimized sample dataset size and network dimensions. Despite the similarity in torque estimation of these three configurations, the non-parametric configuration was specifically designed for worst-case scenarios where the robot dynamics are completely unknown. Finally, we validate the applicability of our ML approaches by integrating the worst-case non-parametric configuration as a controller within a feedforward loop. We verify the accuracy of the learned inverse dynamic model by comparing it to the actual cobot performance. Our non-parametric architecture outperforms the robot's default factory position controller in terms of accuracy.

A comparison between Sobol’s indices and Shapley’s effect for global sensitivity analysis of systems with independent input variables

The model-based system engineering approach consists of assembling subsystems together to model a complete system. In this context, some functional blocks can have a considerable influence on the overall behaviour of the system. A preliminary identification of the influence of the subsystems on the output responses can help reducing the complexity of the overall system, with a negligible impact on the overall accuracy. Therefore, pertinent indicators must be introduced to achieve this goal. To this purpose, in this work, some well-established methods and algorithms for global sensitivity analysis (GSA) of linear and non-linear systems with independent input variables, i.e., approaches based on Sobol’s indices (different algorithms are considered), and Shapley’s effect, are compared on both benchmark functions and real-world engineering problems. Specifically, in this paper, real-world engineering problems dealing with linear and non-linear systems are modelled through commercial finite element software and/or dedicated programming languages for solving complex non-linear dynamics models, like Modelica. Regarding Modelica models, an efficient strategy based on functional mock-up units is presented to speed up the simulation of highly non-linear dynamic systems. All numerical models are interfaced with the algorithms used for GSA through ad-hoc routines coded in Python environment. For each problem, a systematic comparison between the results provided by the different algorithms making use of Sobol’s indices and Shapley’s indices is performed, in terms of reliability, accuracy and computational costs.

Predicting chaotic dynamics from incomplete input via reservoir computing with (D+1)-dimension input and output.

Predicting future evolution based on incomplete information of the past is still a challenge even though data-driven machine learning approaches have been successfully applied to forecast complex nonlinear dynamics. The widely adopted reservoir computing (RC) can hardly deal with this since it usually requires complete observations of the past. In this paper, a scheme of RC with (D+1)-dimension input and output (I/O) vectors is proposed to solve this problem, i.e., the incomplete input time series or dynamical trajectories of a system, in which certain portion of states are randomly removed. In this scheme, the I/O vectors coupled to the reservoir are changed to (D+1)-dimension, where the first D dimensions store the state vector as in the conventional RC, and the additional dimension is the corresponding time interval. We have successfully applied this approach to predict the future evolution of the logistic map and Lorenz, Rössler, and Kuramoto-Sivashinsky systems, where the inputs are the dynamical trajectories with missing data. The dropoff rate dependence of the valid prediction time (VPT) is analyzed. The results show that it can make forecasting with much longer VPT when the dropoff rate θ is lower. The reason for the failure at high θ is analyzed. The predictability of our RC is determined by the complexity of the dynamical systems involved. The more complex they are, the more difficult they are to predict. Perfect reconstructions of chaotic attractors are observed. This scheme is a pretty good generalization to RC and can treat input time series with regular and irregular time intervals. It is easy to use since it does not change the basic architecture of conventional RC. Furthermore, it can make multistep-ahead prediction just by changing the time interval in the output vector into a desired value, which is superior to conventional RC that can only do one-step-ahead forecasting based on complete regular input data.

A data-driven optimization framework for industrial demand-side flexibility

Securing profits while offering industrial demand-side flexibility in both energy and reserve markets is critical to ensure the profitability of energy-intensive industrial plants to make available their flexible assets in the electricity markets and hence accelerating the energy transition. Proposing efficient bidding strategies for simultaneous participation in the energy and reserve market is challenging since it requires the integration of different market mechanisms in a single optimization problem (combining energy and reserve markets), as well as an accurate mathematical model of industrial processes from which to obtain energy flexibility. Often, such mathematical models are either not available or are described through complex simulators, making the design of a computationally efficient bidding strategy a complicated task.This paper introduces a novel framework to support energy-intensive industrial plants to offer energy flexibility in the joint energy and reserve market. We use a neural network to model the complex nonlinear dynamics of the industrial flexible process. Then, to reduce the complexity of the resulting optimization process we convert the neural network into linear constraints, formulating the problem of bidding energy flexibility into the electricity market as a mixed-integer linear program. The uncertainties of the process variables are considered using a scenario-based approach.A realistic simulation considering the case of an evaporative cooling tower used in the chemical industry, participating in the Belgian electricity market is carried out to demonstrate the applicability of the proposed scheme.

Predicting behavior of photonic crystal fiber lasers using artificial neural networks

Simulating pulse propagation within fiber lasers is a difficult and computationally demanding task, which limits the ability to accurately capture their complex nonlinear dynamics. This paper leverages artificial intelligence (AI) and artificial neural networks (ANN) to predict the output pulse shape parameters for a ring cavity fiber laser, thus avoiding the need for traditional complex numerical calculations and reducing the overall computational cost. This study focuses on a dissipative soliton resonance (DSR) ring cavity fiber laser, incorporating a photonic crystal fiber (PCF) and mode locked by a real saturable absorber. The integration of the PCF into the laser cavity design enhances the control of both dispersion and nonlinearity, allowing for a greater range of output pulse shapes and parameters. The proposed approach demonstrates the effectiveness of artificial neural networks in predicting pulse parameters, and could pave the way for more efficient design and optimization of fiber lasers. The results of the study show that the ANN model can accurately predict the output pulse shape parameters for the DSR ring cavity fiber laser, and thus offers a promising tool for future research in the field.

Exploring Climate-Driven agricultural water shortages in a Snow-Fed basin using a water allocation model and Machine learning

Water allocation models (WAM) can capture complex feedbacks between water infrastructure, water supply, water demand, and water rights structure. They are an important tool for water managers to reduce conflict and aid in future water resource planning. Future streamflow reductions and shifts in timing are anticipated in snow-dominated watersheds of the western United States due to projected reductions in snow water storage. These basins tend to be water-limited and rely on groundwater to support agricultural demand. Water managers in the snow-fed, agricultural Walker River Basin (WRB) in California and Nevada use a dynamically coupled WAM and physically based groundwater flow model as a decision support tool. Large computation time is required to simulate groundwater dynamics, limiting the number of model scenarios that can feasibly be run to test alternative management scenarios under climate change. Machine learning (ML) techniques have been used to capture complex nonlinear hydrologic dynamics in other contexts, but to our knowledge there have not been efforts to use ML to increase computational efficiency in modeling groundwater responses to agricultural water use. We use extreme gradient boosting to replace the groundwater sub-model for the WRB decision support tool, resulting in accurate estimates of reservoir storage (monthly error almost always < 5% of reservoir capacity), streamflow (total outflow errors from −3% to 20% depending on scenario) and agricultural water shortages (-12% to 18% error in total shortage depending on scenario). For comparison, we found that omitting groundwater modeling from the WAM results in a larger overprediction of outflows (2 to 58%) and underprediction in agricultural water shortages (0 to 41%) across a range of scenarios. We use this validated ML method to explore the sensitivity of agricultural water availability to a range of streamflow volumes and streamflow timings. Results indicate that agricultural water shortages are more sensitive to annual streamflow volume in comparison to shifts in streamflow timing. Our model shows that reservoirs can buffer the impact of altered flow timing on agricultural production, except under extreme conditions in which all precipitation falls as rain (no snow storage) and streamflow peaks in the winter. Future work will explore these thresholds in more detail. While the results here are site-specific, the methodology for coupling a WAM with a ML representation of surface–groundwater interactions can be applied to a wide variety of water resource modeling applications. These results also provide a stark example of the importance of snowpack storage and groundwater management to western US water infrastructure.

Experimental Demonstration of In-Memory Computing in a Ferrofluid System.

Magnetic fluids are excellent candidates for several important research fields including energy harvesting, biomedical applications, soft robotics, and exploration. However, notwithstanding relevant advancements such as shape reconfigurability, that have been demonstrated, there is no evidence for their computing capability, including the emulation of synaptic functions, which requires complex non-linear dynamics. Here, it is experimentally demonstrated that a Fe3 O4 water-based ferrofluid (FF) can perform electrical analogue computing and be programmed using quasi direct current (DC) signals and read at radio frequency (RF) mode. Features have been observed in all respects attributable to a memristive behavior, featuring both short and long-term information storage capacity and plasticity. The colloid is capable of classifying digits of a 8×8 pixel dataset using a custom in-memory signal processing scheme, and through physical reservoir computing by training a readout layer. These findings demonstrate the feasibility of in-memory computing using an amorphous FF system in a liquid aggregation state. This work poses the basis for the exploitation of a FF colloid as both an in-memory computing device and as a full-electric liquid computer thanks to its fluidity and the reported complex dynamics, via probing read-out and programmingports.

Dynamic mode decomposition type algorithms for modeling and predicting queue lengths at signalized intersections with short lookback

This article explores a novel data-driven approach based on recent developments in Koopman operator theory and dynamic mode decomposition (DMD) for modeling signalized intersections. On signalized intersections, vehicular flow and queue formation have complex nonlinear dynamics, making system identification, modeling, and controller design challenging. We employ a DMD-type approach to transform the original nonlinear dynamics into locally linear infinite-dimensional dynamics. The data-driven approach relies entirely on spatio-temporal snapshots of the traffic data. We investigate several key aspects of the approach and provide insights into the usage of DMD-type algorithms for application in adaptive signalized intersections. To validate the obtained linearized dynamics, we perform prediction of the queue lengths at the intersection and compare the results with the benchmark methods such as ARIMA and long short term memory (LSTM). The case study involves intersection pressure and queue lengths at two Orlando area signalized intersections during the morning and evening peaks. It is observed that DMD-type algorithms are able to capture complex dynamics with a linear approximation to a reasonable extent. The merits include faster computation times and significantly less requirement for a “lookback” (training) window.

Detecting memory content in firing rate signals using a machine learning approach: A fractal analysis

While top-down modulation can be observed by increases in neuronal firing in some brain areas, modulation in other areas demonstrates complex nonlinear dynamics. When these signal modifications cannot be identified by classical methods, fractal analysis can be used to better describe the resulting changes. It was previously shown that the Higuchi dimension could detect such modification. However, these changes likely extend to multiple fractal dimensions. In this paper, machine learning algorithms were employed to extract the fractal features of neuronal firing and detect the occurrence of top-down modulation. We assessed the performance of classifiers trained on different fractal features as well as the Fourier transform and wavelet transform-based features obtained from the firing rate signals during a spatial memory task to measure the ability of individual neurons in the middle temporal cortex to hold memory information. By comparing the results of the different classifiers, Higuchi fractal dimension was confirmed as the strongest indicator of working memory content in cortical firing patterns compared to other fractal features. We demonstrated the utility of this approach and observed that the middle temporal cortex likely encodes spatial working memory based on linear and nonlinear temporal features rather than simply increasing the average firing rate.

Neuroadaptive Optimal Fixed-Time Synchronization and its Circuit Realization for Unidirectionally Coupled FO Self-Sustained Electromechanical Seismograph Systems.

This article investigates the neuroadaptive optimal fixed-time synchronization and its circuit realization along with dynamical analysis for unidirectionally coupled fractional-order (FO) self-sustained electromechanical seismograph systems under subharmonic and superharmonic oscillations. The synchronization model of the coupled FO seismograph system is established based on drive and response seismic detectors. The dynamical analysis reveals this coupled system generating transient chaos and homoclinic/heteroclinic oscillations. The test results of the constructed equivalent analog circuit further testify its complex nonlinear dynamics. Then, a neuroadaptive optimal fixed-time synchronization controller integrated with the FO hyperbolic tangent tracking differentiator (HTTD), interval type-2 fuzzy neural network (IT2FNN) with transformation, and prescribed performance function (PPF) together with the constraint condition is developed in the backstepping recursive design. Furthermore, it is proved that all signals of this closed-loop system are bounded, and the tracking errors fall into a trap of the prescribed constraint along with the minimized cost function. Extensive studies confirm the effectiveness of the proposed scheme.

Simulation Approach for Torque Ripple Minimization of BLDC Motor

This project presents the design and implementation of neural network controller for reducing torque ripples in permanent magnet brushless DC (PMBLDCM) motor drive with trapezoidal back-emf. The performances of the proposed neural network controller are compared with the corresponding fuzzy PI controller and conventional PI controller. Simulation results are used to show the abilities and shortcomings of the proposed speed regulation scheme for brushless dc motor which is considered as a highly nonlinear dynamic complex system. Matlab/Simulink software was used to simulate the proposed model. Buck-boost converter connected in between the input DC source and three phase bridge inverter, used for minimizing the commutation torque ripples in Permanent Magnet Brushless DC Motor is presented in this paper. Torque during the commutation period depends on phase current which is not undergoing commutation, so by controlling it, torque ripple can be minimized. Moreover, a greater DC link voltage is needed during the commutation time period in comparison to the normal conduction period. The Buck-boost converter operates in boost mode in commutation period for stepping up the DC voltage to the inverter. A simple mode switching circuit is employed to amend the output modes of the Buck-boost converter in normal and commutation time intervals. Simulation studies of this topology are carried out in MATLAB/Simulink environment. Index Terms – Permanent Magnet Brushless DC Motor (PMBLDCM), Buck-boost Converter, Commutation Time period,PI Controller.

A data-driven statistical-stochastic surrogate modeling strategy for complex nonlinear non-stationary dynamics

We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the purely statistical modeling approach that is practically limited to the homogeneous statistical regime for high-dimensional state variables. The new closure system allows one to overcome several practical issues that emerge in the non-homogeneous statistical regimes. First, the proposed ensemble modeling that couples the mean statistics and stochastic fluctuations naturally produces positive-definite covariance matrix estimation, which is a challenging issue that hampers the purely statistical modeling approaches. Second, the proposed closure model, which embeds a non-Markovian neural-network model for the unresolved fluxes such that the variance of the dynamics is consistent, overcomes the inherent instability of the stochastic fluctuation dynamics. Effectively, the proposed framework extends the classical stochastic parametric modeling paradigm for the unresolved dynamics to a semi-parametric parameterization with a residual Long-Short-Term-Memory neural network architecture. Third, based on empirical information metric, we provide an efficient and effective training procedure by fitting a loss function that measures the differences between response statistics. Supporting numerical examples are provided with the Lorenz-96 model, a system of ODEs that admits the characteristic of chaotic dynamics with both homogeneous and inhomogeneous statistical regimes. In the latter case, we will see the effectiveness of the statistical prediction even though the resolved Fourier modes corresponding to the leading mean energy and variance spectra do not coincide.

Altered brain entropy and functional connectivity patterns in generalized anxiety disorder patients

BackgroundGeneralized anxiety disorder (GAD) is a highly prevalent disease characterized by chronic, pervasive, and intrusive worry. Previous resting-state functional MRI (fMRI) studies on GAD have mainly focused on conventional static linear features. Entropy analysis of resting-state functional magnetic resonance imaging (rs-fMRI) has recently been adopted to characterize brain temporal dynamics in some neuropsychological or psychiatric diseases. However, the nonlinear dynamic complexity of brain signals has been rarely explored in GAD. MethodsWe measured the approximate entropy (ApEn) and sample entropy (SampEn) of the resting-state fMRI data from 38 GAD patients and 37 matched healthy controls (HCs). The brain regions with significantly different ApEn and SampEn values between the two groups were extracted. Using these brain regions as seed points, we also investigated whether there are differences in whole brain resting-state function connectivity (RSFC) pattern between GADs and HCs. Correlation analysis was subsequently conducted to investigate the association between brain entropy, RSFC and the severity of anxiety symptoms. A linear support vector machine (SVM) was used to assess the discriminative power of BEN and RSFC features among GAD patients and HCs. ResultsCompared to the HCs, patients with GAD showed increased levels of ApEn in the right angular cortex (AG) and increased levels of SampEn in the right middle occipital gyrus (MOG) as well as the right inferior occipital gyrus (IOG). Contrarily, compared to the HCs, patients with GAD showed decreased RSFC between the right AG and the right inferior parietal gyrus (IPG). The SVM-based classification model achieved 85.33 % accuracy (sensitivity: 89.19 %; specificity: 81.58 %; and area under the receiver operating characteristic curve: 0.9018). The ApEn of the right AG and the SVM-based decision value was positively correlated with the Hamilton Anxiety Scale (HAMA). LimitationsThis study used cross-sectional data and sample size was small. ConclusionPatients with GAD showed increased level of nonlinear dynamical complexity of ApEn in the right AG and decreased linear features of RSFC in the right IPG. Combining the linear and nonlinear features of brain signals may be used to effectively diagnose psychiatric disorders.

Locally Active Memristor with Variable Parameters and Its Oscillation Circuit

This paper designs a locally active memristor with two variable parameters based on Chua’s unfolding theorem. The dynamical behavior of the memristor is analyzed by employing pinched hysteresis loop, power-off plot (POP), DC V–I curve, small-signal analysis, and edge-of-chaos theory. It is found that the proposed memristor exhibits nonvolatile and bistable behaviors because of coexisting pinched hysteresis loops. And the variable parameters can realize the rotation of the coexisting pinched hysteresis loops, regulate the range of the locally active region and even transform the shape of the DC V–I curve into S-type or N-type. Furthermore, a simple oscillation circuit is constructed by connecting this locally active memristor with an inductor, a capacitor, a resistance, and a bias voltage. It is shown by analysis that the memristive circuit can generate complex nonlinear dynamics such as multiscroll attractor, initial condition-based dynamics switching, transient phenomenon with the same dynamical state but different offsets and amplitudes, and symmetric coexisting attractors. The measurement observed from the implementation circuit further verifies the numerical results of the oscillation circuit.

TASAC: A twin-actor reinforcement learning framework with a stochastic policy with an application to batch process control

Due to their complex nonlinear dynamics and batch-to-batch variability, batch processes pose a challenge for process control. Due to the absence of accurate models and resulting plant-model mismatch, these problems become harder to address for advanced model-based control strategies. Reinforcement Learning (RL), wherein an agent learns the policy by directly interacting with the environment, offers a potential alternative in this context. RL frameworks with actor–critic architecture have recently become popular for controlling systems where state and action spaces are continuous. The current study proposes a stochastic actor–critic RL algorithm, termed Twin Actor Soft Actor–Critic (TASAC), by incorporating an ensemble of actors in a maximum entropy framework to improve learning due to enhanced exploration. The efficacy of the proposed approach is showcased by applying the same for the control of batch transesterification.