Optimal Control Framework Research Articles

Adaptive optimal backstepping control for strict-feedback nonlinear systems with time-varying partial output constraints

This paper investigates the optimal backstepping control strategy for strict-feedback nonlinear systems subject to input saturation and time-varying partial output constraints. Compared with the existing results on output constraints, the time-varying partial output constraint is a more general constraint that can start and end at any time during the system operation, or remain unconstrained, which can be called as output constraints occurring in a limited time interval (OCOLT). A special barrier function is embedded into the optimal performance index function to satisfy the OCOLT condition under the optimal control framework, and a shift function is introduced to address the function discontinuity caused by the OCOLT problem. Then, an auxiliary system and a disturbance observer are respectively constructed to handle the influence of the input saturation and compounded disturbances. Meanwhile, the simplified reinforcement learning algorithm, employing the identifier-critic-actor architecture, is developed to achieve the optimal control objective within the framework of the backstepping technology. Moreover, the proposed optimal control method ensures the semi-globally uniformly ultimately bounded of all signals within the closed-loop system. Finally, two simulation examples are given to further prove the effectiveness of the presented optimal control approach.

Coalitional Control Strategy for a Heterogeneous Platoon Application

In this work, we propose a coalitional control solution for a multi-agent networked system. The idea is to use a flexible communication topology, in which the communication links are enabled or disabled between sub-systems, depending on their shared task. The control methodology is designed in an optimal control framework, by computing an optimal state feedback gain matrix corresponding to each communication topology. The proposed control algorithm was validated in simulation, and tested in real-time experiments using a heterogeneous vehicle platoon consisting of four mobile robots. Both simulation and experimental results illustrate the efficacy of our proposed methodology.

Distributed Integral Convex Optimization-Based Current Control for Power Loss Optimization in Direct Current Microgrids

Due to the advantages of fewer energy conversion stages and a simple structure, direct current (DC) microgrids are being increasingly studied and applied. To minimize distribution loss in DC microgrids, a systematic optimal control framework is proposed in this paper. By considering conduction loss, switching loss, reverse recovery loss, and ohmic loss, the general loss model of a DC microgrid is formulated as a multi-variable convex function. To solve the objective function, a top-layer distributed integral convex optimization algorithm (DICOA) is designed to optimize the current-sharing coefficients by exchanging the gradients of loss functions. Then, the injection currents of distributed energy resources (DERs) are allocated by the distributed adaptive control in the secondary control layer and local voltage–current control in the primary layer. Based on the DICOA, a three-layer control strategy is constructed to achieve loss minimization. By adopting a peer-to-peer data-exchange strategy, the robustness and scalability of the proposed systematic control are enhanced. Finally, the proposed distribution current dispatch control is implemented and verified by simulations and experimental results under different operating scenarios, including power limitation, communication failure, and plug-in-and-out of DERs.

Gender differences in cycling motions: On objective functions for urban cycling

AbstractSocietal challenges such as climate change and the energy crisis are putting bicycles at the centre of many people's mobility considerations ‐ but not all. In addition to the need for improved infrastructure, stability and comfort when cycling also play a major role. Simulations offer the possibility to investigate the influence of biometric differences on comfort and stability more cost‐effectively than the measurement methods currently used for bike fitting. Bicycle dynamics and multibody simulation of cycling motions have been the subject of research for a long time. Often data‐driven models are used that follow pre‐established measurement data. Moreover, optimal control simulations for competitive sports are available, where for example, the travel distance during a given time is maximised. However, such models are usually based on the biometric data of an average 18–25 year old male, while the influence of gender differences on cycling motions are rarely explored. Yielding towards closing this gender data gap, we use a discrete mechanics and optimal control framework (DMOCC), which benefits from its structure preserving formulation and has been successfully used for biomechanical applications before. The implemented multibody model of a leg performing a cycling motion can be adapted to individual 3D scans via the geometry parameters and the bounds on the joint angles and torques, providing the possibility to investigate the influence of biometric diversity on the resulting motions. In this first approach, we discuss several possibilities to formulate appropriate objective functions for cycling. The final aim of this study is to supplement a given bike frame by software chosen adaptations so that it optimally fits to individual biometric conditions, thus increasing comfort, the sense of safety and performance, which ultimately enables greater participation in the mobility transition for women, children, and seniors.

Online accelerated data‐driven learning for optimal feedback control of discrete‐time partially uncertain systems

SummaryIn this paper, we develop an online learning algorithm for solving the Bellman equation for affine in the control discrete‐time nonlinear uncertain dynamical systems. To ensure accelerated learning of our algorithm in generating optimal control policies, we use an actor‐critic structure predicated on higher‐order tuner laws. More specifically, we construct a Nesterov‐like architecture involving momentum‐based learning laws leading to an accelerated convergence of the optimal control policy. The proposed online learning‐based optimal control framework guarantees uniform ultimate boundedness of the closed‐loop system under the assumption that the system is persistently excited. Finally, two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

Grid-tied solar and biomass hybridization for multi-family houses in Sweden: An optimal rule-based control framework through machine learning approach

Grid-tied solar and biomass hybridization for multi-family houses in Sweden: An optimal rule-based control framework through machine learning approach

Coordination and Optimization Control Framework for Vessels Platooning in Inland Waterborne Transportation System

Vessels sailing in a single platoon could reduce resistance from the perspective of the whole platoon and the individual vessel, and contribute to improving energy benefits. Moreover, transportation energy costs and traffic efficiency are essential indicators for measuring waterborne transportation systems. We attempt to minimize transportation energy costs by coordinating platoon formation using a distributed framework of controllers. A large-scale coordinated vessel platooning program is proposed to minimize transportation energy costs and optimize traffic efficiency while guaranteeing safety. The control framework covers routing, energy consumption-dependent cooperative platooning decision and speed optimization based on graph search algorithm, cluster analysis, optimal control approach and model predictive control. Firstly, a local scheduling strategy combined with the leader vessel selection algorithm is adopted. Furthermore, we used cluster analysis to create a series of mergeable vessel platooning sets. Then, we used the mathematical planning method and a two-step hybrid optimal control approach to calculate the improvement and optimization of each vessel platoon’s path and speed. Finally, the scalability of the scheduling strategy is elucidated. In a simulation of large scale inland waterborne network, savings surpassed 3.5% when six hundreds vessels participated in the system. These simulation results reveal that the scheduling strategy coordinating vessels into vessel platooning, which improves transportation efficiency as well as descends cost, comparing to a fixed origin route in the waterway network.

Toward a modeling, optimization, and predictive control framework for fed-batch metabolic cybergenetics.

Biotechnology offers many opportunities for the sustainable manufacturing of valuable products. The toolbox to optimize bioprocesses includes extracellular process elements such as the bioreactor design and mode of operation, medium formulation, culture conditions, feeding rates, and so on. However, these elements are frequently insufficient for achieving optimal process performance or precise product composition. One can use metabolic and genetic engineering methods for optimization at the intracellular level. Nevertheless, those are often of static nature, failing when applied to dynamic processes or if disturbances occur. Furthermore, many bioprocesses are optimized empirically and implemented with little-to-no feedback control to counteract disturbances. The concept of cybergenetics has opened new possibilities to optimize bioprocesses by enabling online modulation of the gene expression of metabolism-relevant proteins via external inputs (e.g., light intensity in optogenetics). Here, we fuse cybergenetics with model-based optimization and predictive control for optimizing dynamic bioprocesses. To do so, we propose to use dynamic constraint-based models that integrate the dynamics of metabolic reactions, resource allocation, and inducible gene expression. We formulate a model-based optimal control problem to find the optimal process inputs. Furthermore, we propose using model predictive control to address uncertainties via online feedback. We focus on fed-batch processes, where the substrate feeding rate is an additional optimization variable. As a simulation example, we show the optogenetic control of the ATPase enzyme complex for dynamic modulation of enforced ATP wasting to adjust product yield and productivity.

Automatic Continuous Thrust Control for Supersonic Transport Takeoff Noise Reduction

Advanced takeoff trajectories are proposed for supersonic transport noise reduction by capitalizing on excess engine thrust and improved aerodynamic efficiency at higher takeoff speeds. These novel trajectories use i) automatic continuous control of thrust, ii) increased takeoff speed, and iii) reduced cut-back altitude, compared to conventional pilot-initiated discrete thrust cut-back procedures currently used for subsonic transport. In this paper, we develop an optimal control framework to assess the attributes of effective takeoff trajectories for supersonic transport that yield minimum noise levels. We quantify the noise reduction potential of advanced takeoff trajectories for the eight-passenger, 55-metric-ton, Mach-1.4 NASA Supersonic Technology Concept Airplane. For the aircraft examined, these advanced takeoff trajectories enable a cumulative certification noise reduction of 10.6 EPNdB, which is insufficient to meet current subsonic transport noise limits.

The effect of governance structures on optimal control of two-patch epidemic models

Infectious diseases continue to pose a significant threat to the health of humans globally. While the spread of pathogens transcends geographical boundaries, the management of infectious diseases typically occurs within distinct spatial units, determined by geopolitical boundaries. The allocation of management resources within and across regions (the “governance structure”) can affect epidemiological outcomes considerably, and policy-makers are often confronted with a choice between applying control measures uniformly or differentially across regions. Here, we investigate the extent to which uniform and non-uniform governance structures affect the costs of an infectious disease outbreak in two-patch systems using an optimal control framework. A uniform policy implements control measures with the same time varying rate functions across both patches, while these measures are allowed to differ between the patches in a non-uniform policy. We compare results from two systems of differential equations representing transmission of cholera and Ebola, respectively, to understand the interplay between transmission mode, governance structure and the optimal control of outbreaks. In our case studies, the governance structure has a meaningful impact on the allocation of resources and burden of cases, although the difference in total costs is minimal. Understanding how governance structure affects both the optimal control functions and epidemiological outcomes is crucial for the effective management of infectious diseases going forward.

A numerical scheme to solve Fokker–Planck control collective-motion problem

A numerical scheme to solve the optimal control problem, governed by Fokker–Planck (FP) equation, is presented. In particular, a bilinear optimal control framework is considered for the evolution of the probability density function (PDF), corresponding to collective (stochastic) motion. A FP optimality system is described and a Chang–Cooper (CC) discretization scheme is employed on staggered grids to numerically solve this optimality system. This CC scheme preserves non-negativity, conservation and second-order accuracy to the PDF. Analysis of the forward time Chang–Cooper (FT-CC) scheme is provided. For the time discretization, we use the Euler first-order time differencing scheme. Furthermore, a gradient update procedure combined with a projection step is investigated to solve the optimal control problem. Numerical results validate the proposed staggered-grid FT-CC scheme for the proposed control framework in stochastic motion.

Optimal Control Framework for Alkane Separation in Semicontinuous Distillation

Optimal Control Framework for Alkane Separation in Semicontinuous Distillation

An economic model predictive control-based flexible power point tracking strategy for photovoltaic power generation

In a high solar-power-penetration power grid, photovoltaic (PV) power generation requires to run in a flexible power point tracking (FPPT) mode. However, traditional hierarchical control-based FPPT strategy ignores the dynamic economic performance of PV power generation. To address this issue, an advanced FPPT strategy based on economic model predictive control (EMPC) is proposed to achieve higher dynamic economic performance. This strategy integrates the PV voltage reference calculation, PV voltage control, and pulse width modulation into one optimal control framework, utilizing the economic indices of the PV power generation system (PVPGS) as the cost function to achieve its economic optimization and power tracking. Due to the strong nonlinearity in the PVPGS, the EMPC optimization problem is non-convex, leading to a local optimum. A mixed integer nonlinear programming algorithm is developed, which utilizes a finite number of converter switching states for obtaining the global optimum. Simulations demonstrate that the EMPC-based FPPT strategy enhances the dynamic economic performance compared to the hierarchical control-based FPPT strategy.

The Real-Time Optimal Attitude Control of Tunnel Boring Machine Based on Reinforcement Learning

Efficient control of tunnel boring machine (TBM) tunneling along the designed tunnel axis in an unknown variable geological environment is a difficult and significant task. At present, the TBM attitude during tunneling is mostly manually controlled based on the deviation between the tunneling axis and the designed tunnel axis and their experiences. The tunneling axis from manual control is often the snakelike motion around the designed tunnel axis, even exceeding the deviation limit, for which this paper analyzed three reasons, the unknown geological environment, the hysteresis of TBM position response, and the unsolved overall optimization of tunneling axis. For these reasons, this paper proposed a real-time optimal control framework of TBM attitude based on reinforcement learning, which contains the geological information predictive model, TBM attitude and position (TBMAP) predictive model, and optimal attitude control policy (OACP). This framework can predict the current geological information in real-time and provide the corresponding real-time optimal attitude control that simultaneously considers the hysteresis of TBM position response and the overall optimization of the tunneling axis. This attitude control framework can be directly deployed to TBM without increasing costs and excessive modifications to the equipment. To verify the effectiveness of this attitude control framework, the Xinjiang Yiner Water Supply Phase II Project, using the TBM method, was adopted as a case study. The results revealed that the accuracy of geological environment recognition reached 94%, and OACP can significantly reduce the accumulated deviation of the tunneling axis from the designed tunnel axis by over 80% compared with the manual control and easily provide real-time decision support for attitude control in actual engineering.

Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: An application to the Italian scenario.

In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory represents a useful mathematical tool to plan the vaccination campaign aimed at eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a given time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Compared to other recent works, our model incorporates all stages of the COVID-19 disease, including death or recovery, without accounting for additional specific compartments that would increase computational complexity and that are not relevant for our purposes. Moreover, we introduce an optimal control framework where the model is the state problem while the vaccine doses administered are the control variables. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, proves that the presented framework can be a valuable tool to support the planning of vaccination campaigns. Indeed, in each considered scenario, our optimization framework guarantees noticeable improvements in terms of reducing deceased, infected or hospitalized individuals with respect to the baseline vaccination policy.

A Dimensionality-Reducible Operational Optimal Control for Wastewater Treatment Process.

Operational optimal control (OOC) is an essential component of wastewater treatment process (WWTP). The control variables usually are high-dimensional, nonlinear, and strongly coupled, which can easily fail traditional optimization control methods. Mathematically, these operational variables usually are in the unknown low-dimensional space embedded in the high-dimensional space. Therefore, the OOC problem of WWTP can be resolved as an optimization challenge involving low-dimensional space, and the unknown low-dimensional space is presented in the form of a set of controlled variables in a high-dimensional space, which is normal in real-world industries. Here, a dimension-reducible data-driven optimization control framework for WWTP is proposed. Considering the difficulty in elucidating the whole space of set points, a neural network is designed to approximate the constraint relationship between control variables. The search process is based on optimization methods in low-dimensional space embedded into Euclidean spaces. Furthermore, the convergence of the process is ensured via mathematical analysis. Finally, the experimental simulation of wastewater treatment revealed that this approach is effective for an optimal solution in control systems.

Leveraging an epidemic–economic mathematical model to assess human responses to COVID-19 policies and disease progression

It is imperative that resources are channelled towards programs that are efficient and cost effective in combating the spread of COVID-19, the disease caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). This study proposed and analyzed control strategies for that purpose. We developed a mathematical disease model within an optimal control framework that allows us to investigate the best approach for curbing COVID-19 epidemic. We address the following research question: what is the role of community compliance as a measure for COVID-19 control? Analyzing the impact of community compliance of recommended guidelines by health authorities—examples, social distancing, face mask use, and sanitizing—coupled with efforts by health authorities in areas of vaccine provision and effective quarantine—showed that the best intervention in addition to implementing vaccination programs and effective quarantine measures, is the active incorporation of individuals’ collective behaviours, and that resources should also be directed towards community campaigns on the importance of face mask use, social distancing, and frequent sanitizing, and any other collective activities. We also demonstrated that collective behavioral response of individuals influences the disease dynamics; implying that recommended health policy should be contextualized.

A Unified Framework for Data-Driven Optimal Control of Connected Vehicles in Mixed Traffic

This paper presents a unified approach to the problem of learning-based optimal control of connected human-driven and autonomous vehicles in mixed-traffic environments including both the freeway and ring road settings. The stabilizability of a string of connected vehicles including multiple autonomous vehicles (AVs) and heterogeneous human-driven vehicles (HDVs) is studied by a model reduction technique and the Popov-Belevitch-Hautus (PBH) test. For this problem setup, a linear quadratic regulator (LQR) problem is formulated and a solution based on adaptive dynamic programming (ADP) techniques is proposed without a priori knowledge on model parameters. To start the learning process, an initial stabilizing control law is obtained using the small-gain theorem for the ring road case. It is shown that the obtained stabilizing control law can achieve general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{p}$</tex-math></inline-formula> string stability under appropriate conditions. Besides, to minimize the impact of external disturbance, a linear quadratic zero-sum game is introduced and solved by an iterative learning-based algorithm. Finally, the simulation results verify the theoretical analysis and the proposed methods achieve desirable performance for control of a mixed-vehicular network.

Complex objective optimization in fuzzy environments

Multi-objective optimization can be used to address possible conflicting relationships between multiple objectives. However, some objectives have a fuzzy temporal relationship between them, making it difficult to give a common method to portray the fuzzy temporal relationship. To fill this gap, we propose the concept of complex objectives, which can be described by fuzzy temporal logic that includes both temporal and logical operators. Furthermore, we investigated the optimal control problems of complex objectives and developed a fuzzy system called possibilistic decision systems (PDSs) to establish a framework for optimal control. In PDSs, states of fuzzy systems are determined by a family of variables, and transitions induced by actions between fuzzy states of systems are also fuzzy uncertain and determined by a possibility degree. Importantly, we proved that memoryless strategies are sufficient for optimal control of complex objectives. Finally, the theory presented in this paper is illustrated by a mobile robot simulation.

An inverse problem of reconstructing the refractive index interrain parabolic equations ∗ ∗ Supported by National Natural Science Foundation of China (Nos. 61663018, 11961042), and NSF of Gansu Province of China (No. 22JR5RA341).

This work deals with an inverse problem of identifying the refractive index in terrain parabolic equations, which has important applications in radio systems and other applied scientific fields. Unlike other inverse coefficient problems arising in the real field, the underlying mathematical model is discussed in the complex field which may lead to many mathematical tools not available, and the corresponding theoretical analysis rather difficult. Based on the optimal control framework, the recognition problem is transformed into an optimization problem, and the existence and necessary condition of the minimizer for the cost functional are deduced. The local uniqueness and stability of the minimizer are derived from the necessary condition. Finally, a gradient descent iterative scheme is designed to solve the numerical solution of the inverse problem. The validity of the proposed algorithm is illustrated by some typical numerical examples.