Optimal Control Perspective Research Articles

Organ registration from partial surface data in augmented surgery from an optimal control perspective

We address the problem of organ registration in augmented surgery, where the deformation of the patient’s organ is reconstructed in real-time from a partial observation of its surface. Physics-based registration methods rely on adding artificial forces to drive the registration, which may result in implausible displacement fields. In this paper, we look at this inverse problem through the lens of optimal control, in an attempt to reconstruct a physically consistent surface load. The resulting optimization problem features an elastic model, a least-squares data attachment term based on orthogonal projections, and an admissible set of surface loads defined prior to reconstruction in the mechanical model. After a discussion about the existence of solutions, we analyse the necessary optimality conditions and use them to derive a suitable optimization algorithm. We implement an adjoint method and we test our approach on multiple examples, including the so-called Sparse Data Challenge . We obtain very promising results, that illustrate the feasibility of our approach with linear and nonlinear models.

An Optimal Control Perspective on Classical and Quantum Physical Systems

This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels.

Simulating Interaction Movements via Model Predictive Control

We present a Model Predictive Control (MPC) framework to simulate movement in interaction with computers, focusing on mid-air pointing as an example. Starting from understanding interaction from an Optimal Feedback Control (OFC) perspective, we assume that users aim at minimizing an internalized cost function, subject to the constraints imposed by the human body and the interactive system. Unlike previous approaches used in HCI, MPC can compute optimal controls for nonlinear systems. This allows to use state-of-the-art biomechanical models and handle nonlinearities that occur in almost any interactive system. Instead of torque actuation, our model employs second-order muscles acting directly at the joints. We compare three different cost functions and evaluate the simulation against user movements in a pointing study. Our results show that the combination of distance, control, and joint acceleration cost matches individual users’ movements best, and predicts movements with an accuracy that is within the between-user variance. To aid HCI researchers and designers in applying our approach for different users, interaction techniques, or tasks, we make our SimMPC framework, including CFAT, a tool to identify maximum voluntary torques in joint-actuated models, publicly available, and give step-by-step instructions.

The role of storage degradation in energy management problems: An optimal control perspective

The energy management problem of grid-connected storage systems is becoming crucial due to massive integration of renewable energy sources. However, in these problems, the storage degradations are often overlooked while designing the optimal control policy. The key reason behind that is the degradation cost, which occurs at each (dis)charging storage cycle, is hard to evaluate, and it is highly dependent on the grid demand. Thus, integrating them in the energy management problem is a challenge. In this article, we address this challenge, and propose an optimal control update, which solves the energy management problem of a power grid considering the storage degradation cost. We first adopt a multi-storage setup, where each storage system has a constant efficiency function and finite storage capacity (not necessarily the same), and then evaluate necessary optimal conditions based on Pontryagin’s minimum principle. We show that these conditions can further be leveraged to obtain an explicit optimal control update for a family of homogeneous storage systems. Moreover, we derive explicit control updates for the energy management problems, where the storage degradation costs obey either the additive or the multiplicative degradation cost models. Several numerical experiments are performed on the Israel electric grid to demonstrate the covered concepts and the effectiveness of the proposed approach.

An Offline Closed-Form Optimal Predictive Power Management Strategy for Plug-In Hybrid Electric Vehicles

This article develops an optimal predictive power management strategy (OP-PMS) for plug-in hybrid electric vehicles (PHEVs) to manage the remaining battery level throughout a defined journey. Apart from using the battery before charging it again at the destination, this approach also supports transit through an Ultra Low Emission Zone (ULEZ), where a PHEV needs to operate in pure electric mode to avoid emissions. This type of PHEV power management strategy (PMS) design problem is a noncausal control problem, where the power demand of the remaining driving cycle and the final battery energy level targets influence the current power management action. Rather than solving the whole optimization problem online, this article presents a simplification that leads to a closed-form analytic solution with parameters that can be computed offline. This article makes three key contributions. First, a novel input-linearization method is developed, which converts the OP-PMS into a convex quadratic programming (QP) problem that captures the essential model nonlinearities using an input transformation and a quadratic cost function. Second, the influence of future power demands and final targets on current energy management policy is explicitly quantified from a dynamic optimal control perspective. Third, the noncausal convex QP is approximated with a closed-form analytic solution that is calculated offline. This leads to a real-time implementable OP-PMS with coefficients that can be precalculated and stored in the engine control unit. To demonstrate the viability of this approach, numerical examples are provided based on a generic PHEV model to verify the efficacy of the proposed OP-PMS.

An optimal control perspective on the dynamic allocation problem for linear systems*

In this paper the problem of dynamic control allocation for input redundant, continuous-time linear systems is studied in the context of optimal control theory. Providing a new framework for the subject and relying on a well-established theoretical setting, an equivalent problem formulation is given and its solution is determined and discussed, also highlighting its simpler structure with respect to the one provided by approaches purely in the context of control allocation alone.

Controlling eutrophication by means of water recirculation: An optimal control perspective

In this work, the artificial recirculation of water is presented and analyzed, from the perspective of the optimal control of partial differential equations, as a tool to prevent eutrophication effects in large waterbodies. A novel formulation of the environmental problem, based on the coupling of nonlinear models for hydrodynamics, water temperature and concentrations of the different species involved in the eutrophication processes, is introduced. After a complete and rigorous analysis of the existence of optimal solutions, a full numerical algorithm for their computation is proposed. Finally, some numerical results for a realistic scenario are shown, in order to prove the efficiency of our approach.

Dynamic incentives for inhibiting private sectors' opportunistic effort diversion in infrastructure PPP projects: an optimal control perspective

PurposeAn optimal control model is built considering the private sector's opportunistic effort diversion and reciprocal effort improvement, while a numerical study is conducted to draw some managerial implications.Design/methodology/approachIn infrastructure PPP projects, private sectors may opportunistically divert part of their effort from the current projects to other projects to allocate their limited human resources. Nevertheless, this effort diversion can be inhibited by dynamic incentives since the private sectors reciprocally exert greater effort into the current projects when receiving the dynamic incentives. This article investigates how the government specifies the output standard that the private sector should meet and offers dynamic incentives to mitigate the private sector's opportunistic effort diversion.FindingsThe output standard for the private sector to acquire the dynamic incentives should be specified as the output level corresponding to the private sector's optimal long-run stationary equilibrium (OLSE) effort level, which decreases with its reciprocal preference level but increases with its effort-diverting level. The optimal dynamic incentives comprise an initial incentive and a periodic OLSE incentive, which declines with the reciprocal preference level but improves with the effort-diverting level. Besides, the numerical study reveals that the government should distinguish whether the bidders have high effort-diverting levels and, if so, should focus on their reciprocal preference levels and decline the bidders with low reciprocal preference to avoid utility loss.Originality/valueThis article provides a theoretical model combining opportunistic behavior with reciprocal preference through an optimal control lens, thus embedding the problem of incentive design into a broader socioeconomic framework.

To Procrastinate or Not to Procrastinate: A Retrospective Study of the Optimal Timing of Containing the Global Spread of the COVID-19 Pandemic.

As global public health is under threat by the 2019-nCoV and a potential new wave of large-scale epidemic outbreak and spread is looming, an imminent question to ask is what the optimal strategy of epidemic prevention and control (P&C) measures would be, especially in terms of the timing of enforcing aggressive policy response so as to maximize health efficacy and to contain pandemic spread. Based on the current global pandemic statistic data, here we developed a logistic probability function configured SEIR model to analyse the COVID-19 outbreak and estimate its transmission pattern under different “anticipate- or delay-to-activate” policy response scenarios in containing the pandemic. We found that the potential positive effects of stringent pandemic P&C measures would be almost canceled out in case of significantly delayed action, whereas a partially procrastinatory wait-and-see control policy may still be able to contribute to containing the degree of epidemic spread although its effectiveness may be significantly compromised compared to a scenario of early intervention coupled with stringent P&C measures. A laissez-faire policy adopted by the government and health authority to tackling the uncertainly of COVID19-type pandemic development during the early stage of the outbreak turns out to be a high risk strategy from optimal control perspective, as significant damages would be produced as a consequence.

An Optimal Control Perspective on Weather and Climate Modification

Intentionally altering natural atmospheric processes using various techniques and technologies for changing weather patterns is one of the appropriate human responses to climate change and can be considered a rather drastic adaptation measure. A fundamental understanding of the human ability to modify weather conditions requires collaborative research in various scientific fields, including, but not limited to, atmospheric sciences and different branches of mathematics. This article being theoretical and methodological in nature, generalizes and, to some extent, summarizes our previous and current research in the field of climate and weather modification and control. By analyzing the deliberate change in weather and climate from an optimal control and dynamical systems perspective, we get the ability to consider the modification of natural atmospheric processes as a dynamic optimization problem with an emphasis on the optimal control problem. Within this conceptual and unified theoretical framework for developing and synthesizing an optimal control for natural weather phenomena, the atmospheric process in question represents a closed-loop dynamical system described by an appropriate mathematical model or, in other words, by a set of differential equations. In this context, the human control actions can be described by variations of the model parameters selected on the basis of sensitivity analysis as control variables. Application of the proposed approach to the problem of weather and climate modification is illustrated using a low-order conceptual model of the Earth’s climate system. For the sake of convenient interpretation, we provide some weather and climate basics, as well as we give a brief glance at control theory and sensitivity analysis of dynamical systems.

From Pulses to Circuits and Back Again: A Quantum Optimal Control Perspective on Variational Quantum Algorithms

The last decade has witnessed remarkable progress in the development of quantum technologies. Although fault-tolerant devices likely remain years away, the noisy intermediate-scale quantum devices of today may be leveraged for other purposes. Leading candidates are variational quantum algorithms (VQAs), which have been developed for applications including chemistry, optimization, and machine learning, but whose implementations on quantum devices have yet to demonstrate improvements over classical capabilities. In this Perspective, we propose a variety of ways that the performance of VQAs could be informed by quantum optimal control theory. A major theme throughout is the need for sufficient control resources in VQA implementations; we discuss different ways this need can manifest, outline a variety of open questions, and look to the future.Received 11 September 2020DOI:https://doi.org/10.1103/PRXQuantum.2.010101Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum controlQuantum information processingQuantum Information

Optimal Control Perspective on Parkinson's Disease: Increased Delay Between State Estimator and Controller Produces Tremor.

Parkinson's disease produces tremor in a large subset of patients despite generally inhibiting movement. The pathophysiology of parkinsonian tremor is unclear, leading to uncertainty in how and why treatments reduce tremor with varying effectiveness. Models for parkinsonian tremor attempt to explain the underlying principles of tremor generation in the central nervous system, often focusing on neural activity of specific substructures. In contrast, control system approaches to modeling the human motor system provide qualitative results that help inform conclusions from clinical studies. This article uses an optimal control approach to investigate the hypothesis that an increased delay in the central nervous system-unaccounted by delay compensation mechanisms-produces parkinsonian tremor. This hypothesis is motivated by the excessive inhibition projected from the basal ganglia to the thalamus in Parkinson's disease. The thalamus relays signals from the cerebellum to the primary motor cortex: previous mapping of optimal control components indicates this prospective delay exists between the estimator (cerebellum) and controller (primary motor cortex). Simulations demonstrate realistic tremor in a neuromuscular model of the wrist. In addition, changes to effort sensitivity in the optimal controller may account for some clinical features of parkinsonian tremor, including the characteristics of re-emergent tremor and the time-varying amplitude and frequency of tremor. Contextualization of the optimal control model with physiological models and clinical observations provides insight into the potential role of the basal ganglia and cerebello-thalamo-cortical circuit and how treatments like dopaminergic medications and deep brain stimulation reduce tremor.

A neural network approach for improving airfoil active flutter suppression under control-input constraints

This study deals with improving airfoil active flutter suppression under control-input constraints from the optimal control perspective by proposing a novel optimal neural-network control. The proposed approach uses a modified value function approximation dynamically tuned by an extended Kalman filter to solve the Hamilton–Jacobi–Bellman equality online for continuously improved optimal control to address optimality in parameter-varying nonlinear systems. Control-input constraints are integrated into the controller synthesis by introducing a generalized nonquadratic cost function for control inputs. The feasibility of using a performance index involving the nonquadratic control-input cost with the modified value function approximation is examined through the Lyapunov stability analysis. Wind tunnel experiments were conducted for controller validation, where an optimal controller synthesized offline via linear parameter-varying technique was used as a benchmark and compared. It is shown, both theoretically and experimentally, that the proposed method can effectively improve airfoil active flutter suppression under control-input constraints.

Studying the Impact of Vaccination Strategy and Key Parameters on Infectious Disease Models

In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international spread of the infectious diseases. The relationship between epidemiology, mathematical modeling and computational tools lets us to build and test theories on the development and fighting with a disease. This study is motivated by the study of epidemiological models applied to infectious diseases in an optimal control perspective. We use the numerical methods to display the solutions of the optimal control problems to find the effect of vaccination on these models. Finally, global sensitivity analysis LHS Monte Carlo method using Partial Rank Correlation Coefficient (PRCC) has been performed to investigate the key parameters in model equations. This present work will advance the understanding about the spread of infectious diseases and lead to novel conceptual understanding for spread of them.

Motion-Communication Co-Optimization With Cooperative Load Transfer in Mobile Robotics: An Optimal Control Perspective

This paper considers the co-optimization of motion and communication in mobile robotic networks operating under energy constraints. More specifically, we consider a team of robots tasked with collectively transmitting a given amount of data to a remote station, while operating in realistic communication environments that experience path loss, shadowing, and multipath fading. We are interested in designing the load distribution, paths, and transmission power/rate schedules of the robots in a way that minimizes the total energy required for motion and communication. We use realistic models to quantify the motion and transmission power. We then show how this multiagent problem can be efficiently solved using an optimal control framework and mathematically characterize properties of the optimal solution. We further extend the problem to an online adaptation setting, where the robots need to keep adjusting their communication and motion decisions (e.g., paths, loads to transfer, and transmission rates/power) as more information on the channel quality becomes available during the operation. We show how this problem can be effectively solved in a distributed manner and prove that this online distributed approach provides performance guarantees. Extensive simulations with real channel parameters demonstrate the efficacy of the proposed approach and validate the theoretical results.

Fundamentals of energy efficient driving for combustion engine and electric vehicles: An optimal control perspective

This paper formulates energy efficient driving of gasoline and electric powered vehicles as optimal control problems of various complexity. We show minimizing aerodynamic drag can maximize utilization of energy available at the wheel and requires low and constant speeds. By employing optimal control theory we show periods of maximal acceleration, maximal braking, and coasting often accompany constant speed cruising to satisfy boundary conditions on the states (bang-singular-bang optimal control). In the case of gasoline engine vehicles, analytical optimal control derivations show that pulse and glide operation of the engine while cruising can further reduce fuel use (chattering optimal control). For electric vehicles (EV), quadratic rather than linear dependence of energy use on control input results in different eco-driving patterns from gasoline engine vehicles. For EVs, analytical solution to the two point boundary value optimal control problem could be obtained after model simplification which is compared to numerical solution based on a more accurate model. We also evaluate optimal control solution in the presence of state constraints for EVs. Several simulation case studies are presented to showcase the energy efficiency gains with proposed eco driving strategies.

Energy-Efficiency Improvement Potential of Electric Vehicles Considering Transmission Temperature

This study presents an integrated energy and transmission thermal management system to quantify the impact of a cold-start on the energy consumption of electric vehicles (EVs) from optimal control perspective. In addition, it provides insights into reducing this cold effect from design point of view. The cold-start conditions in an EV refer to a low transmission temperature, which increases the frictional power losses caused by viscosity effects in the transmission. These losses are eventually compensated by the battery, leading to excess energy usage. A detailed EV model, especially the transmission part with transient thermodynamics based on experiment data, is developed, and the integrated energy and thermal controller aims to maximize the energy efficiency. Numerical results show that a cold-start influences the energy-saving potential, up to 2.9%. Through analysis of temperature-dependent transmission behavior and energy losses of the EV, design considerations of reducing the cold impact, thus improving energy efficiency, can be derived.

A new continuous time optimal control model for manpower planning with promotion from inside the system

The aim of this paper is to face the manpower planning problem from a continuous time optimal control perspective. A new continuous-time manpower planning model is proposed in which the promotions occur inside the system. The proposed model contains four main sections: applicants, newcomers, experienced employees and supervisors (or managers). Each of these sections has a target value which we try to attain them by applying appropriate control variables, such as lay off, degradation, promotion and retirement. To attain the targets, we formulated an optimal control problem using a linear system transition equation with a quadratic cost functional. Finally, the proposed model is applied for a real-world organization as a case study.

Metamorphoses of Functional Shapes in Sobolev Spaces

In this paper, we describe in detail a model of geometric-functional variability between fshapes. These objects were introduced for the first time by Charlier et al. (J Found Comput Math, 2015. arXiv:1404.6039 ) and are basically the combination of classical deformable manifolds with additional scalar signal map. Building on the aforementioned work, this paper’s contributions are several. We first extend the original $$L^2$$ model in order to represent signals of higher regularity on their geometrical support with more regular Hilbert norms (typically Sobolev). We describe the bundle structure of such fshape spaces with their adequate geodesic distances, encompassing in one common framework usual shape comparison and image metamorphoses. We then propose a formulation of matching between any two fshapes from the optimal control perspective, study existence of optimal controls and derive Hamiltonian equations and conservation laws describing the dynamics of geodesics. Secondly, we tackle the discrete counterpart of these problems and equations through appropriate finite elements interpolation schemes on triangular meshes. At last, we show a few results of metamorphosis matchings on several synthetic and real data examples in order to highlight the key specificities of the approach.

Adaptive nonlinear optimal control for active suppression of airfoil flutter via a novel neural-network-based controller

This paper proposes a novel adaptive nonlinear controller based on neural-networks (NNs) for active suppression of airfoil flutter (ASAF) from the optimal control perspective. Optimal control laws for locally nonlinear systems are synthesized in real time by solving the Hamilton–Jacobi–Bellman equation online with a proposed new form of NN-based value function approximation (VFA) and an extended Kalman filter. A systematic procedure based on linear matrix inequalities is further proposed for designing a scheduled parameter matrix that generalizes the new form of VFA to globally nonlinear systems to suit ASAF applications. Un-modeled dynamics are captured using an NN identifier. Comparisons drawn with a linear-parameter-varying optimal controller in wind-tunnel experiments confirm the effectiveness and validity of the proposed control scheme.