Optimal resource allocation in micro-organisms under periodic nutrient fluctuations.

Although microorganisms often live in dynamic environments, most studies, both experimental and theoretical, are carried out under static conditions. In this work, we investigate the issue of optimal resource allocation in bacteria growing in periodic environments. We consider a dynamic model describing the microbial metabolism under varying conditions, involving a control variable quantifying the protein precursors allocation. Our objective is to determine the optimal strategies maximizing the long-term growth of cells under a piecewise-constant periodic environment. Firstly, we perform a theoretical analysis of the resulting optimal control problem (OCP), based on the application the Pontryagin's Maximum Principle (PMP). We determine that the structure of the optimal control must be bang-bang, with possibly some singular arcs corresponding to optimal equilibria of the system. If the control presents singular arcs, then these can only be reached and left through chattering arcs. We also use a direct optimization method, implemented in the BOCOP software, to solve the studied OCP. Our study reveals that the optimal solution over a large time horizon is related to the one over a single period of the varying environment with periodic constraints. Moreover, we observe that the maximal average growth rate attainable under periodic conditions can be higher than the one under a constant environment. We further extend our analysis to conduct a qualitative comparison between the predictions from our model and some recent biological experiments on E. coli. This analysis particularly highlights the mechanisms of action of the ppGpp signaling molecule, thus providing relevant explanations of the experimental observations. In conclusion, our study corroborates previous research indicating that this molecule plays a crucial role in the regulation of resource allocation of protein precursors in E. coli.

When preparation pays off.

Computational principles shed light on why movement is preceded by preparatory activity within the neural networks that control muscles.

Optimal Control of Underdamped Systems: An Analytic Approach.

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback-Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.

A mathematical insight to control the disease psoriasis using mesenchymal stem cell transplantation with a biologic inhibitor.

Psoriasis is a chronic, non-contagious, immune-mediated skin disorder. Inflammation of the skin's surface is characterised by scaly white, red, or silvery spots that occur due to the hyper-proliferation of keratinocytes in the epidermal layer. Primarily, pharmaceutical drugs or immune therapy are used to treat psoriasis. We are all aware that, certain therapeutic strategies can have some adverse effects, and over time, that hidden inflammation may manifest. This article introduces a mathematical model for psoriasis, formulated by employing a set of nonlinear ordinary differential equations (ODEs) that describe the densities of T-cells, dendritic cells (DCs), keratinocytes, and mesenchymal stromal cells (MSCs) as basic cell populations. A tumor necrosis factor- α ( T N F - α ) inhibitor has been imposed from the initial stage of the treatment regime, using the optimal control theoretic approach, and the numerical results have been observed. After 80 days of monitoring using only biologic T N F - α inhibitors, if this approach did not provide the intended outcomes (when severity arises), stem cells are administered a few times in a pulsed manner as a cell replacement technique in addition to this anti T N F - α medicine. We have observed the combined therapeutic benefit of stem cell replacement with a T N F - α inhibitor from a mathematical point of view. The theoretical analysis and the numerical results revealed that stem cell transplantation, along with a T N F - α inhibitor, is a promising psoriasis treatment option moving forward.

Efficiency-Oriented Model Predictive Control: A Novel MPC Strategy to Optimize the Global Process Performance.

Existing control strategies, such as Real-time Optimization (RTO), Dynamic Real-time Optimization (DRTO), and Economic Model Predictive Control (EMPC) cannot enable optimal operation and control behavior in an optimal fashion. This work proposes a novel control strategy, named the efficiency-oriented model predictive control (MPC), which can fully realize the potential of the optimization margin to improve the global process performance of the whole system. The ideas of optimization margin and optimization efficiency are first proposed to measure the superiority of the control strategy. Our new efficiency-oriented MPC innovatively uses a nested optimization structure to optimize the optimization margin directly online. To realize the computation, a Periodic Approximation technique is proposed, and an Efficiency-Oriented MPC Type I is constructed based on the Periodic Approximation. In order to alleviate the strict constraint of Efficiency-Oriented MPC Type I, the zone-control-based optimization concept is used to construct an Efficiency-Oriented MPC Type II. These two well-designed efficiency-oriented controllers were compared with other control strategies over a Continuous Stirred Tank Reactor (CSTR) application. The simulation results show that the proposed control strategy can generate superior closed-loop process performance, for example, and the Efficiency-Oriented MPC Type I can obtain 7.11% higher profits than those of other control strategies; the effectiveness of the efficiency-oriented MPC was, thereby, demonstrated.

A combined trade-off strategy of battery degradation, charge retention, and driveability for electric vehicles.

Electric vehicles are considered as an emerging solution to mitigate the environmental footprint of transportation sector. Therefore, researchers and automotive developers devote significant efforts to enhance the performance of electric vehicles to promote broader adoption of such technology. One of the critical challenges of the electric vehicle is limited battery lifetime and entailed range anxiety. In his context, development of counter-aging control strategies based on precise battery modeling is regarded as an emerging approach that has a significant potential to address battery degradation challenges. This paper presents a combined trade-off strategy to minimize battery degradation while maintaining acceptable driving performance and charge retention in electric vehicles. A battery aging model has been developed and integrated into a full vehicle model. An optimal control problem has been formulated to tackle the afore-mentioned challenges. Non-dominant sorting genetic algorithms have been implemented to yield the optimal solution through the Pareto-front of three contending objectives, based upon which an online simulation has been conducted considering three standard driving cycles. The results reveal the ability of the proposed strategy to prolong the life cycle of the battery and extend the driving range by 25 % and 8 % respectively with minimal influence of 0.6 % on the driveability.

When and why does motor preparation arise in recurrent neural network models of motor control?

During delayed ballistic reaches, motor areas consistently display movement-specific activity patterns prior to movement onset. It is unclear why these patterns arise: while they have been proposed to seed an initial neural state from which the movement unfolds, recent experiments have uncovered the presence and necessity of ongoing inputs during movement, which may lessen the need for careful initialization. Here, we modeled the motor cortex as an input-driven dynamical system, and we asked what the optimal way to control this system to perform fast delayed reaches is. We find that delay-period inputs consistently arise in an optimally controlled model of M1. By studying a variety of network architectures, we could dissect and predict the situations in which it is beneficial for a network to prepare. Finally, we show that optimal input-driven control of neural dynamics gives rise to multiple phases of preparation during reach sequences, providing a novel explanation for experimentally observed features of monkey M1 activity in double reaching.

Feasibility of predicting changes in gait biomechanics following muscle strength perturbations using optimal control in patients with transfemoral amputation.

Bone-anchored limbs (BALs) are socket prosthesis alternatives, directly fixing to residual bone via osseointegrated implant. There is a need to quantify multi-level effects of rehabilitation for transfemoral BAL users (i.e. changes in joint loading and movement patterns). Our primary objective was determining feasibility of using optimal control to predict gait biomechanics compared to ground-truth experimental data from transfemoral BAL users. A secondary objective was examining biomechanical effects from estimated changes in hip abductor muscle strength. We developed and validated a workflow for predicting gait biomechanics in four transfemoral BAL users and investigated the biomechanical effects of altered hip abductor strengths.

Enhanced Model Predictive Control Using State Variable Feedback for Steady-State Error Cancellation.

The rapid dynamic responses of predictive control algorithms are widely acknowledged. However, achieving accurate steady-state reference tracking hinges not just on a precise mathematical model of the system but also on its parameters. This document presents a predictive control scheme augmented with integral state feedback tailored to a photovoltaic (PV) application. In scenarios with uncertain system parameters, steady-state errors can particularly impact reactive power regulation, where the absence of an integral term in the loop exacerbates this issue. The robustness and sensitivity of both predictive control and the proposed enhanced predictive controller are thoroughly examined. Simulation and experimental results are included to validate the effectiveness of this approach.

Intelligent vehicle lateral control strategy research based on feedforward + predictive LQR algorithm with GA optimisation and PID compensation.

Targeting the lateral motion control problem in the intelligent vehicle autopilot structural system, this paper proposes a feedforward + predictive LQR algorithm for lateral motion control based on Genetic Algorithm (GA) parameter optimisation and PID steering angle compensation. Firstly, based on the vehicle dynamics tracking error model, the intelligent vehicle LQR lateral motion controller as well as the feedforward controller are designed, and upon which the predictive controller is added to eliminate the system lag.Subsequently, exploiting the advantage that the PID algorithm is not model-based, a PID steering angle compensation controller that can directly control and correct the lateral error is designed. Second, a LQR controller based on path tracking deviation is designed by using the parameter rectification method of genetic algorithm (GA), which optimizes the control parameters of the lateral motion controller and improves the adaptivity of the control accuracy. Finally, Based on the Carsim-Simulink co-simulation platform, the simulation validation and analysis of double lane change (DLC) test and circular condition test (CCT) are carried out, and the results indicate that compared with the other two LQR controllers, the optimised controllers improved more than 50% in lateral error and heading error control, and the vehicle sideslip angle and vehicle yaw rate are in the range of -0.05° to 0.05° and - 0.15 rad/s to 0.10 rad/s, and it showed improved performance in tracking accuracy and satisfied vehicle stability constrains.

Optimal control of bi-seasonal hand, foot and mouth disease in mainland China suggests transmission from children and isolating older infected individuals are critical.

Hand, foot and mouth disease (HFMD) is a Class C infectious disease that carries particularly high risk for preschool children and is a leading cause of childhood death in some countries. We mimic the periodic outbreak of HFMD over a 2-year period-with differing amplitudes-and propose a dynamic HFMD model that differentiates transmission between mature and immature individuals and uses two possible optimal-control strategies to minimize case numbers, total costs and deaths. We parameterized the model by fitting it to HFMD data in mainland China from January 2011 to December 2018, and the basic reproduction number was estimated as 0.9599. Sensitivity analysis demonstrates that transmission between immature and mature individuals contributes substantially to new infections. Increasing the isolation rates of infectious individuals-particularly mature infectious individuals-could greatly reduce the outbreak risk and potentially eradicate the disease in a relatively short time period. It follows that we have a reasonable chance of controlling HFMD if we can reduce transmission in children under 7 and isolate older infectious individuals.

Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime.

We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation scaling allows for a local approximation of the nonlinear dynamics by their linearized version. In addition, we identify a finite-dimensional subspace where exits take place with high probability. Using stochastic control and variational methods we show that our scheme performs well both in the zero noise limit and pre-asymptotically. Simulation studies for stochastically perturbed bistable dynamics illustrate the theoretical results.

Optimal control strategies for energy storage systems for HUB substation considering multiple distribution networks.

With the global consensus to achieve carbon neutral goals, power systems are experiencing a rapid increase in renewable energy sources and energy storage systems (ESS). Especially, recent development of hub substations (HS/S) equipped with ESS, applicable for resolving site constraints if implemented as mobile transformers, is expanding the development of ESS-equipped facilities. However, these units require centralized control strategies considering variability within integrated networks. While studies on electric vehicle charging considering the variability of renewable energy or load are widely studied, ESS management scheme for individual substations requires further optimization, especially considering the state of distributed sources at lower levels and transmission system operators. Thus, in this study, an optimal control approach for ESS located at the connection point of transmission and distribution systems, including further consideration of the loss in distribution lines and the constraints of renewable energy sources is presented. This study attempts to derive proactive control strategies for ESS in HS/S to operate with various distribution networks. By establishing control priorities for each source through optimal operation strategy, a suitable capacity of ESS and its economic benefits for distribution network management can be examined. Validation of the current analysis results is performed by utilizing MATPOWER. By adapting the operational range of design scenarios, diverse distribution systems can be tested against multiple configurations of connected devices.

Should all athletes use the same twisting strategy? The role of anthropometry in the personalisation of optimal acrobatic techniques.

Choosing the best acrobatic technique for each athlete remains a challenge for coaches. Predictive simulations may support coaches, but only a few athlete morphologies have been simulated yet. It is assumed that the optimal acrobatic techniques are somehow generalisable across athletes. However, anthropometry characteristics can influence the twist rotation outcome of an acrobatic technique. Our objective was to assess the differences in optimal techniques caused by the anthropometric differences between athletes. Anthropometry-specific techniques of double pike forward somersaults ending with 112 or 212 twists were generated using predictive simulations and the measurements of 18 acrobatic athletes presenting a wide range of anthropometry. We found that anthropometry had an impact on the optimal acrobatic techniques by modifying the amplitude of the strategies used or, more drastically, by modifying the strategies used. Some athletes had a morphological advantage for twist creation, which was measured using the combined twist potential, a metric introduced in the current study. This metric was very strongly correlated with the complexity of the techniques; models with an advantage for twist creation needed fewer/shorter limb movements to generate twists. This research shows that coaches should consider their athletes' anthropometry to offer them better guidance.

The MOEO algorithm for multi-objective optimization of the cancer immuno-chemotherapy.

In cancer treatment, chemotherapy has the disadvantage of killing both healthy and cancerous cells. Hence, the mixed-treatment of cancer such as chemo-immunotherapy is recommended. However, deriving the optimal dosage of each drug is a challenging issue. Although metaheuristic algorithms have received more attention in solving engineering problems due to their simplicity and flexibility, they have not consistently produced the best results for every problem. Thus, the need to introduce novel algorithms or extend the previous ones is felt for important optimization problems. Hence, in this paper, the multi-objective Equilibrium Optimizer algorithm, as an extension of the single-objective Equilibrium Optimizer algorithm, is recommended for cancer treatment problems. Then, the performance of the proposed algorithm is considered in both chemotherapy and mixed chemo-immunotherapy of cancer, considering the constraints of the tumor-immune dynamic system and the health level of the patients. For this purpose, two different patients with real clinical data are considered. The Pareto front obtained from the multi-objective optimization algorithm shows the points that can be selected for treatment under different criteria. Using the proposed multi-objective algorithm has reduced the total chemo-drug dose to 138.92 and 5.84 in the first patient, and 16.9 and 0.4384 in the second patient, for chemotherapy and chemo-immunotherapy, respectively. Comparing the results with previous studies demonstrates MOEO's superior performance in both chemotherapy and chemo-immunotherapy. However, it is shown that the proposed algorithm is more suitable for mixed-treatment approaches.

Smart waterborne disease control for a scalable population using biodynamic model in IoT network.

We propose a biodynamic model for managing waterborne diseases over an Internet of Things (IoT) network, leveraging the scalability of LoRa IoT technology to accommodate a growing human population. The model, based on fractional order derivatives (FOD), enables smart prediction and control of pathogens that cause waterborne diseases using IoT infrastructure. The human-pathogen-based biodynamic FOD model utilises epidemic parameters (SVIRT: susceptibility, vaccination, infection, recovery, and treatment) transmitted over the IoT network to predict pathogenic contamination in water reservoirs and dumpsites in Iji-Nike, Enugu, the study community in Nigeria. These pathogens contribute to person-to-person, water-to-person, and dumpsite-to-person transmission of disease vectors. Five control measures are proposed: potable water supply, treatment, vaccination, adequate sanitation, and health education campaigns. A stable disease-free equilibrium point is found when the effective reproduction number of the pathogens, R0eff<1 and unstable if R0eff>1. While other studies showed a 98.2% reduction in infections when using IoT alone, this paper demonstrates that combining the SVIRT epidemic control parameters (such as potable water supply and health education campaign) with IoT achieves a 99.89% reduction in infected human populations and a 99.56% reduction in pathogen populations in water reservoirs. Furthermore, integrating treatment with sanitation results in a 99.97% reduction in infected populations. Finally, combining these five control strategies nearly eliminates infection and pathogen populations, demonstrating the effectiveness of multifaceted approaches in public health and environmental management. This study provides a blueprint for governments to plan sustainable smart cities for a growing population, ensuring potable water free from pathogenic contamination,in line with the United Nations Sustainable Development Goals #6 (Clean Water and Sanitation) and #11 (Sustainable Cities and Communities).

New pure multi-order fractional optimal control problems with constraints: QP and LP methods.

Novel methods for finding the optimal controls of new types of fractional optimal control problems with Riemann-Liouville performance indices and systems comprised of subsystems with Caputo derivatives are introduced. Pure fractional quadratic optimal control problems are modeled as quadratic programming (QP) by using a new idea and a state-control parameterization method. After formulating each linear or nonlinear type, its QP model is derived by which the QP solver in MATLAB can be used to obtain the solutions. There is no need for such operations as defining costate variables, deriving optimality conditions, etc. New concepts such as fractional boundary constraints and Riemann-Liouville isoperimetric constraints, are introduced. Multiple problems in different scenarios are investigated and numerous graphs and numerical results are presented. Pure fractional linear control problems with Riemann-Liouville performance indices and fractional systems are modeled as linear programming (LP) without discretization for the first time. Using the LP solver in MATLAB, the optimal solutions of the fractional/integer linear control problems such as bang-bang (or On-Off) and minimum fuel optimal control systems are obtained. Fractional types of the real-world problems such as container cranes and drug scheduling of cancer chemotherapy, are studied.

Specification of the health production function and its behavioral implications.

The health production function of the canonical health-capital model is generalized to allow the state of health to affect the total and marginal products of health investment. If the total and marginal products of health investment are nonincreasing functions of the state of health, then the solution of the generalized model is locally qualitatively identical to that of the canonical model. Moreover, and in contrast to the canonical model, the generalized model is able to rationalize the cycling of the state of health and health investment observed in some individuals. The necessary conditions on the health production function for cyclical behavior are identified as well.

Learning a Tracking Controller for Rolling µbots.

Micron-scale robots (µbots) have recently shown great promise for emerging medical applications. Accurate control of µbots, while critical to their successful deployment, is challenging. In this work, we consider the problem of tracking a reference trajectory using a µbot in the presence of disturbances and uncertainty. The disturbances primarily come from Brownian motion and other environmental phenomena, while the uncertainty originates from errors in the model parameters. We model the µbot as an uncertain unicycle that is controlled by a global magnetic field. To compensate for disturbances and uncertainties, we develop a nonlinear mismatch controller. We define the model mismatch error as the difference between our model's predicted velocity and the actual velocity of the µbot. We employ a Gaussian Process to learn the model mismatch error as a function of the applied control input. Then we use a least-squares minimization to select a control action that minimizes the difference between the actual velocity of the µbot and a reference velocity. We demonstrate the online performance of our joint learning and control algorithm in simulation, where our approach accurately learns the model mismatch and improves tracking performance. We also validate our approach in an experiment and show that certain error metrics are reduced by up to 40%.

Nonlinear model predictive control of a conductance-based neuron model via data-driven forecasting.

Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control, which employs a dynamical model of the system to find optimal control inputs, has promise for dealing with the nonlinear dynamics, high levels of exogenous noise, and limited information about unmeasured states and parameters that are common in a wide range of neural systems. However, the challenge still remains of selecting the right model, constraining its parameters, and synchronizing to the neural system.Approach. As a proof of principle, we used recent advances in data-driven forecasting to construct a nonlinear machine-learning model of a Hodgkin-Huxley type neuron when only the membrane voltage is observable and there are an unknown number of intrinsic currents.Main Results. We show that this approach is able to learn the dynamics of different neuron types and can be used with model predictive control (MPC) to force the neuron to engage in arbitrary, researcher-defined spiking behaviors.Significance.To the best of our knowledge, this is the first application of nonlinear MPC of a conductance-based model where there is only realistically limited information about unobservable states and parameters.