Optimal Switching Time Research Articles

Optimal strategy for stabilizing protein folding intermediates.

To manipulate the protein concentration at a certain functional state through chemical stabilizers is crucial for protein-related studies. It not only plays a key role in protein structure analysis and protein folding kinetics, but also affects protein functionality to a large extent and thus has wide applications in medicine, food industry, etc. However, due to concerns about side effects or financial costs of stabilizers, identifying optimal strategies for enhancing protein stability with a minimal amount of stabilizers is of great importance. Here, we prove that either for the fixed terminal time (including both finite and infinite cases) or for the free one, the optimal control strategy for stabilizing the folding intermediates with a linear strategy for stabilizer addition belongs to the class of bang-bang controls. The corresponding optimal switching time is derived analytically, whose phase diagram with respect to several key parameters is explored in detail. The bang-bang control will be broken when nonlinear strategies for stabilizer addition are adopted. Moreover, the above theory is applied to the stabilization of erythropoietin by ten different kinds of chemicals, providing theoretical guidance for the selection and rational usage of stabilizers. Our current study on optimal strategies for protein stabilizers not only offers deep insights into the general picture of protein folding kinetics but also provides valuable theoretical guidance on treatments for protein-related diseases in medicine.

Robust Switching Time Optimization for Networked Switched Systems via Model Predictive Control.

This article presents a model predictive control (MPC) strategy to find the optimal switching time sequences of networked switched systems with uncertainties. First, based on predicted trajectories under exact discretization, a large-scale MPC problem is formulated; second, a two-level hierarchical optimization structure coupled with a local compensation mechanism is established to solve the formulated MPC problem, where the proposed hierarchical optimization structure is actually a recurrent neural network consisting of a coordination unit (CU) at the upper level and a series of local optimization units (LOUs) related to each subsystem at the lower level. Finally, a real-time switching time optimization algorithm is designed to calculate the optimal switching time sequences.

Optimal ventilation strategies for balancing carbon dioxide and suspended particulate matter concentrations in vehicle cabins

Maintaining safe levels of carbon dioxide (CO2) and particulate matter (PM) in vehicle cabins during driving is essential to ensure driver safety and minimize health risks. However, while the fresh-air ventilation mode reduces the CO2 level, it also allows the ingress of PM pollutants from the external environment and hence increases the PM concentration in the cabin. Thus, effective ventilation strategies are required to optimize the air quality by balancing the average levels of CO2 and suspended PM within the cabin. Accordingly, this study performed computational fluid dynamics simulations to explore the effects of different air-conditioning ventilation modes on the indoor air quality in the cabin of a commercial sports utility vehicle. The simulations commenced by examining the optimal switching times between the recirculation and fresh-air modes that yielded an average CO2 concentration of less than 1000 ppm for various numbers of occupants in the cabin. Further simulations were then performed to investigate the effect of the air filtration efficiency of the in-cabin filter on the PM concentration in the cabin under the optimal ventilation strategies determined for 1–5 occupants. The results indicated that, as the number of occupants increased, the required fresh-air mode usage time also increased. Furthermore, to mitigate the corresponding increase in the PM concentration, a higher filtration efficiency was required. Overall, the results showed that the optimal switching cycles achieved the required indoor air quality within the cabin by successfully balancing the CO2 and suspended PM concentrations.

The applicability of Zermelo's equation to indirect and direct optimization of commercial aircraft flights

This paper focuses on the applicability of Zermelo's equation within the context of 3D commercial aircraft trajectory optimization problems. The associated optimal control problem includes two singular controls, specifically aerodynamic path angle and throttle setting, and one regular control, specifically heading angle. Using Pontryagin's maximum principle and the direct adjoining method, we show that the optimal heading angle is defined by Zermelo's equation. The significance of the presented analysis is that Zermelo's equation holds for 3D commercial aircraft flights, even in the presence of standard state-inequality constraints and a more general objective function. With the help of Zermelo's equation, the control problem is initially analyzed for a 3D time-optimal climb-phase scenario, which is solved by an indirect approach. Through the analysis of the switching function, we demonstrate the dependency of the optimal aerodynamic path angle on the optimal heading angle. Next, by tackling a 3D time-fuel-optimal free-routing flight, solved by a direct approach, we show that Zermelo's equation can help reduce the overall dimension of the associated nonlinear programming. To successfully handle the initial guess in both indirect and direct problems, it is proposed a diminutive nonlinear programming technique as a fast and robust initializer. This simple-yet-effective initializer provides sufficient information about the optimal controls and state dynamics required for initializing a direct optimization, as well as the optimal switching times and co-states required for initializing an indirect optimization.

Optimal Switching Time Control Constrained by Immiscible Two-Phase Porous Media Flow Based on the Discontinuous Galerkin Method

Optimal Switching Time Control Constrained by Immiscible Two-Phase Porous Media Flow Based on the Discontinuous Galerkin Method

OptMSP: A toolbox for designing optimal multi-stage (bio)processes

One central goal of bioprocess engineering is to maximize the production of specific chemicals using microbial cell factories. Many bioprocesses are one-stage (batch) processes (OSPs), in which growth and product synthesis are coupled. However, OSPs often exhibit low volumetric productivities due to the competition for substrate for biomass and product synthesis implying trade-offs between biomass and product yields. Two-stage or, more generally, multi-stage processes (MSPs) offer the potential to tackle this trade-off for improved efficiency of bioprocesses, for example, by separating growth and production. MSPs have recently gained much attention, also because of a rapidly growing toolbox for the dynamic control of metabolic fluxes. Despite these promising advancements, computational tools specifically tailored for the optimal design of MSPs in the field of biotechnology are still lacking.Here, we present OptMSP, a new Python-based toolbox for identifying optimal MSPs maximizing a user-defined process metrics (such as volumetric productivity, yield, and titer or combinations thereof) under given constraints. In contrast to other methods, our framework starts with a set of well-defined modules representing relevant stages or sub-processes. Experimentally determined parameters (such as growth rates, substrate uptake and product formation rates) are used to build suitable ODE models describing the dynamic behavior of each module. OptMSP finds then the optimal combination of those modules, which, together with the optimal switching time points, maximize a given objective function. We demonstrate the applicability and relevance of the approach with three different case studies, including the example of lactate production by E. coli in a batch setup, where an aerobic growth phase can be combined with anaerobic production phases with or without growth and with or without enhanced ATP turnover.

Abstract PR003: Multi-drug adaptive therapy protocol in vitro: An exercise in optimization for neuroblastoma

Abstract From initiation, invasion, dissemination to local and distant progression, relapse, recurrence to metastasis – clinico-pathological development of cancer follows the ecological processes of a multi-species niche construction. Ecological interactions result in adaptive changes that are driven by Darwinian evolution. This can be observed in the heterogeneity of tumor cells and their differential response to therapy. Some tumor cells are sensitive to treatment and can be eliminated by therapy, while others are resistant and can survive and proliferate under therapy. Adaptive therapy is a novel approach that leverages the competitive dynamics between sensitive and resistant cells, by dynamically adjusting the therapy dose and schedule based on biomarkers of tumor burden. In this study, we propose a multi-drug adaptive therapy protocol that uses two drugs with orthogonal mechanisms of action, meaning that they target different pathways or processes in the cancer cells. We investigate how to optimize the switching time between the two drugs, based on the personalized response to therapy and the evolutionary trade-offs between resistance and fitness and describe a corresponding real-time in vitro protocol. We performed experiments using two human neuroblastoma cell lines, sknbe2c and lan1, which exhibit distinct resistance profiles to different therapies, have different genetic profiles and show different growth patterns. We chose the combination of cisplatin and vincristine as the drugs of interest, since they are part of the Rapid COJEC protocol, which is a standard multidrug regimen for treating high-risk neuroblastomas in children. We monitored the drug treatment effects using noninvasive real-time microscopy based on cellular holography, which allows us to capture the morphological and behavioral changes of the cells. We fitted the treatment response curves with a stochastic diffusion equation that incorporates evolutionary mechanisms such as speciation, cost-dependent predator-prey interaction and drift, to model the dynamics of drug resistance and sensitivity. Unlike conventional therapy, which follows a fixed schedule and dose, adaptive therapy uses biomarkers of tumor burden, such as imaging or circulating tumor cells, to guide the timing and intensity of treatment. We propose a stochastic model that predicts the optimal switching time between two drugs based on the personalized response to therapy, which is inferred from Bayesian updating of the model parameters. This results in a patient-specific response model that accounts for the uncertainty and variability in the data. Assuming that a reliable and sensitive measure of tumor burden is available, we demonstrate how our model can be used to design a customized multi-drug adaptive therapy protocol for each patient. We are currently testing the efficacy of our protocol over other conventional protocols, and we plan to translate it to patient derived xenograft mouse models of neuroblastoma in the future. Citation Format: Subhayan Chattopadhyay, Jenny Karlsson, David Gisselsson. Multi-drug adaptive therapy protocol in vitro: An exercise in optimization for neuroblastoma [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr PR003.

Dynamic Modeling Simulation of Regenerator for Glass Furnace Applications

The melting process in the glass industry is an energy-intensive process that uses fossil fuels to maintain melting temperatures between 1600°C and 1700°C. The process is carried out in the Glass Furnace. Obtained the high temperature also of flue gas is around 1350 °C – 1500 °C. Hence with the high temperature is potential to heat recovery in the form of combustion air pre-heating using a regenerator to increase the efficiency in Glass Furnace. This phenomenon gave rise to an idea to create a modelling mathematic to know the optimum process in Glass Furnace. Many studies on Glass furnace regenerator have been carried out but only for one cyclic of heat transfer in regenerator. Therefore, in this study, dynamic modeling of the regenerator will be made, namely a mathematical model that describes quantitatively the dynamic behavior during the process of reversing the direction between the regenerators, which will later explain the effect of air flow rate and the selection of the optimal transition time value for the demonstration, regenerator work and regenerator heat stability, by observing the dynamic behavior of the regenerator temperature profile using the FlexPDE software version 7. The simulation results show that the longer the switching time of regenerator is linier to inclining temperature in the regenerator with the optimum switching time (ST) at 10 minutes. The regenerator heat stability greatly influenced by air flow rate and heat propagation by heat transfer convection. However, the dimension selection of the regenerator plays a crucial role in heat utilization in glass furnaces.

Optimizing Fed-Batch Processes with Dynamic Control Flux Balance Analysis

Fed-batch processes are prevalent in biotechnological industries, but design of experiments often results in sub-optimal conditions due to incomplete solution space characterization. We employ a single-level dynamic control (DC) algorithm for dynamic flux balance analysis (dFBA), enhancing efficiency by reducing Karush-Kuhn-Tucker (KKT) condition constraints and adapting the algorithm for predicting optimal process length. In a growth-decoupled plasmid DNA production case study, we predict the optimal feeding profile and switching time between growth and production phase. Comparing our algorithm to its predecessor shows a speed-up of at least a factor of four. When the process length is part of the objective function the speed-up becomes considerably larger.

Toward constructing tax efficient withdrawal strategies for retirees with traditional 401(k)/IRAs, Roth 401(k)/IRAs, and taxable accounts

We construct an algorithm for U.S. retirees that computes individualized tax efficient annual withdrawals from tax-deferred, tax-exempt, and taxable accounts. Our algorithm applies a new approach using informa- tion from all years that generates an individualized strategy, in contrast to most previous approaches that chronologically generate a suboptimal strategy. Results equal or improve the chronological “na ̈ıve” with- drawal strategies advocated by many financial institutions, as well as the chronological “informed” strategies advanced by academics. Our approach allows us to determine the optimal switching times between tax- exempt and taxable account consumption, as well as between tax-deferred and taxable account consumption. It also allows us to understand the significant impact of an heir’s tax and withdrawal rate on a retiree’s opti- mal withdrawal strategy. Our model, which can work to optimize either portfolio longevity or the bequest to an heir, accommodates many salient tax code features, including dividends, different taxable lots, and required minimum distributions.

Path Planning and Energy Optimization in Optimal Control of Autonomous Wheel Loaders Using Reinforcement Learning

This paper proposes a novel solution based on reinforcement learning for optimal control of an autonomous Wheel Loader (WL). The solution considers the movement of a WL in a Short Loading Cycle (SLC) as a switched system with controlled subsystems such that the sequence of active modes is fixed. Therefore, the optimal control system solves two different levels of optimization. In the upper level, optimal switching times are sought. In the lower level, the control inputs to navigate the wheel loader and performing path planning are sought. For solving the problem, Approximate Dynamic Programming (ADP), which is the application of reinforcement learning to find near-optimal control solution, is used. Simulation results are provided to show the effectiveness of the solution. At last, challenges of using the proposed method and future works are summarized in Conclusion.

Optimal Control of Asymmetrical Multiagent Switching Systems for IoT

Asymmetrical multi-agent switching systems are hybrid systems with dynamic responses that are dependent on input direction and require multi-agent switching for IoT systems. In this research, a hybrid minimum principle is suggested to solve the optimal control problem of multi-agent switching in asymmetrical systems in order to accomplish intelligent switching between multi-agents for collaborative IoT systems with minimal communication overhead. The calculus of variations methodology is used to illustrate the essential conditions for optimality in Hamiltonian canonical form for asymmetrical multi-agent switching systems for IoT, and a comprehensive proof is provided. One analytical example indicates that the suggested hybrid minimum principle can solve the optimal control and switching times of the optimal control problem, demonstrating its validity for asymmetrical multi-agent switching systems.

Modified Respiratory Rate Oxygenation Index: An Early Warning Index for the Need of Intubation in COVID-19 Patients with High-Flow Nasal Cannula Therapy

BackgroundHigh-flow nasal cannula oxygen therapy (HFNC) is recommended for patients with COVID-19. However, the increasing use of HFNC brings a risk of delayed intubation. The optimal timing of switching from HFNC to invasive mechanical ventilation (IMV) remains unclear. An effective predictor is needed to assist in deciding on the timing of intubation. Respiratory rate and oxygenation (ROX) index, defined as (SpO2/FiO2) / respiratory rate, has already shown good diagnostic accuracy. Modified ROX (mROX) index, defined as (PaO2 /FiO2) / respiratory rate, might be better than the ROX index in predicting HFNC failure. ObjectiveThe aim was to evaluate the predictive value of mROX for HFNC failure in patients with COVID-19. MethodsSevere or critical patients with COVID-19 treated with HFNC were enrolled in two clinical centers. Laboratory indicators, respiratory parameters, and mROX index at 0 h and 2 h after initial HFNC were collected. Based on the need for IMV after HFNC initiation, the patients were divided into an HFNC failure group and an HFNC success group. The predictive value of mROX index for IMV was evaluated by the area under the receiver operating characteristic curve (AUROC) and logistic regression analysis. We performed Kaplan–Meier survival analysis using the log-rank test. ResultsSixty patients with COVID-19 (mean ± SD age, 62.8 ± 14.1 years; 42 patients were male) receiving HFNC were evaluated, including 18 critical and 42 severe cases. A total of 33 patients had hypertension; 14 had diabetes; 17 had chronic cardiac disease; 11 had chronic lung disease; 13 had chronic kidney disease; and 17 had a history of stroke. The AUROC of mROX index at 2 h was superior to that of other respiratory parameters to predict the need for IMV (0.959; p < 0.001). At the mROX index cutoff point of 4.45, predicting HFNC failure reached the optimal threshold, with specificity of 94% and sensitivity of 92%. Logistic regression analysis showed that 2-h mROX index < 4.45 was a protective factor for IMV (odd radio 0.18; 95% CI 0.05–0.64; p = 0.008). In the HFNC failure group, the median time from HFNC to IMV was 22.5 h. The 28-day mortality of the late intubation patients (≥ 22.5 h) was higher than that of the early intubation patients (< 22.5 h) (53.8% vs. 8.3%; p = 0.023). ConclusionsmROX at 2 h is a good early warning index of the need for IMV in patients with COVID-19 after HFNC initiation. Early intubation may lead to better survival in patients with 2-h mROX index < 4.45.

Performance Analysis of Beacon-Assisted Wireless Powered Communications With Spatially Random Sensors

In this work, we present the performance evaluation of a power beacon-assisted wireless-powered communication system in the presence of multiple co-channel interferers. We consider and compare three distinct interference modeling scenarios, namely the totally induced interference is approximated by the Gamma distribution, interferers are distributed according to a Poisson point process and interferers are distributed according to a binomial point process. Analytical expressions for the outage probability and the ergodic capacity of the considered system under each interference scenario are derived. Furthermore, optimization problems are formulated to determine the optimum switching time maximizing the achieved ergodic capacity. Numerical results accompanied with Monte Carlo simulations are presented to corroborate the proposed theoretical analysis.

Optimal standby activation in m‐out‐of‐n systems: A preventive approach

AbstractThis article investigates an optimal preventive standby activation policy for an ‐out‐of‐ redundant system. We assume that for such a system, which starts operating at time , a standby component will be activated at either the failure time of the system or at a predetermined time , whichever occurs first. We first obtain the system reliability function under this switching policy as a function of . Then, we investigate the optimal switching time so that the mean time to failure of the system is maximized. The results indicate that the existence of an optimal value of depends on the lifetime of the standby redundancy and its virtual age in the standby state. Some illustrative examples are presented to examine the theoretical outcomes.

Exploration of sensory-motor tradeoff behavior in Parkinson's disease.

While slowness of movement is an obligatory characteristic of Parkinson's disease (PD), there are conditions in which patients move uncharacteristically fast, attributed to deficient motor inhibition. Here we investigate deficient inhibition in an optimal sensory-motor integration framework, using a game in which subjects used a paddle to catch a virtual ball. Display of the ball was extinguished as soon as the catching movement started, segregating the task into a sensing and acting phase. We analyzed the behavior of 9 PD patients (ON medication) and 10 age-matched controls (HC). The switching times (between sensing and acting phase) were compared to the predicted optimal switching time, based on the individual estimates of sensory and motor uncertainties. The comparison showed that deviation from predicted optimal switching times were similar between groups. However, PD patients showed a weaker correlation between variability in switching time and sensory-motor uncertainty, indicating a reduced propensity to generate exploratory behavior for optimizing goal-directed movements. Analysis of the movement kinematics revealed that PD patients, compared to controls, used a lower peak velocity of the paddle and intercepted the ball with greater velocity. Adjusting the trial duration to the time for the paddle to stop moving, we found that PD patients spent a smaller proportion of the trial duration for observing the ball. Altogether, the results do not show the premature movement initiation and truncated sensory processing that we predicted to ensue from deficient inhibition in PD.

Fault tolerant time optimization for a class of time-varying switched infinite dimensional linear systems

This paper addresses the issue of finding the optimal switching times for the time-varying switched infinite dimensional linear system with discrete faults that lead to the deviation of the actual switching signal from the normal one. A robust fault tolerant time optimization scheme based on an equivalent time transformation and a min–max mechanism is proposed to obtain the upper bound of optimal values of cost functional of all possible discrete faults. For any detectable discrete fault, an active fault tolerant time optimization scheme equipped with a switching detection technique and a gradient descent algorithm is presented to minimize every post-fault cost functional, which reduces the conservation of the robust one.

Optimal Timing Fault Tolerant Control for Switched Stochastic Systems with Switched Drift Fault

In this article, an optimal timing fault tolerant control strategy is addressed for switched stochastic systems with unknown drift fault for each switching point. The proposed controllers in existing optimal timing control schemes are not directly aimed at the switched drift fault system, which affects the optimal control performance. A cost functional with system state information and fault variable is constructed. By solving the optimal switching time criterion, the switched stochastic system can accommodate switching drift fault. The variational technique is presented for the proposed cost function in deriving the gradient formula. Then, the optimal fault tolerant switching time is calculated by combining the Armijo step-size gradient descent algorithm. Finally, the effectiveness of the proposed controller design scheme is proved by the safe trajectory planning for a four wheel drive mobile robot and numerical example.

A class of hybrid LQG mean field games with state-invariant switching and stopping strategies

A novel framework is presented that combines Mean Field Game (MFG) theory and Hybrid Optimal Control (HOC) theory to obtain a unique ɛ-Nash equilibrium for a non-cooperative game with switching and stopping times. We consider the case where there exists one major agent with a significant influence on the system together with a large number of minor agents constituting two subpopulations, each agent with individually asymptotically negligible effect on the whole system. Each agent has stochastic linear dynamics with quadratic costs, and the agents are coupled in their dynamics and costs by the average state of minor agents (i.e. the empirical mean field). It is shown that for a class of Hybrid LQG MFGs, the optimal switching and stopping times are state-invariant and only depend on the dynamical parameters of each agent. Accordingly, a hybrid systems formulation of the game is presented via the indexing by discrete events: (i) the switching of the major agent between alternative dynamics or (ii) the termination of the agents’ trajectories in one or both of the subpopulations of minor agents. Optimal switchings and stopping time strategies together with best response control actions for, respectively, the major agent and all minor agents are established with respect to their individual cost criteria by an application of Hybrid LQG MFG theory.

Attitude Control of Rigid Bodies: An Energy-Optimal Geometric Switching Control Approach

In this article, the attitude control problem for a class of rigid body systems with switching submodes is investigated. To address such issue, an energy-optimal geometric switching control method is proposed for the first time. First, a switching Lie group method and a switching Lie group discrete variational integrator method based on the variational principle are developed. Then, continuous-time and discrete-time attitude switching dynamics models for rigid bodies are globally expressed on a special orthogonal matrix group (i.e., SO(3) group) to avoid the locality, singularity, and ambiguity caused by using the traditional Euler angle method, minimum representation method, or quaternion method. Second, the switching process of rigid bodies from initial attitude and angular velocity to desired attitude and angular velocity within a fixed maneuver time and the minimum energy consumption of rigid bodies with control saturation are solved. Furthermore, by solving the energy-optimal geometric control problem of attitude switching dynamics models, the global optimal geometric switching control and optimal switching time conditions under continuous-time and discrete-time are first derived. The obtained criteria ensure that the intrinsic geometric properties of attitude switching dynamics models will not be lost during the optimization process. Finally, some simulation results are presented to demonstrate the feasibility of the proposed techniques.