Principle For Optimal Control Research Articles

Применение принципа Понтрягина для оптимального отключения энергетического ядерного реактора

The theory of optimal control is based on two approaches, the dynamic programming method (Bellman equation) and Pontryagin maximum principle. Pontryagin maximum principle is applied in the physics of nuclear reactors when optimizing various transient processes. The mathematical justification of this theory is based on the elements of convex analysis, which is not used by physicists and engineers, so the physical issues are less studied in scientific literature. The subject of the study is a nuclear power reactor of the WWER type. The problem of minimizing its shutdown time, bypassing the iodine pit is solved and it is possible to start up the reactor at any moment after its shutdown. Analytical and numerical methods are used. The paper considers an example of applying the maximum principle for optimal control of the process of shutting down a nuclear reactor bypassing the iodine pit. A physical mathematical model of the Pontryagin principle is formulated. The process of optimal control of reactor shutdown for large and small reactivity margins is justified and calculated. Pontryagin principle does not contain an algorithm to find an optimization process; the stages of the process must be selected based on physical considerations, but these stages must satisfy the specified principle. Based on the Pontryagin principle, the results of the study make it possible to draw up a step-by-step action plan when shutting down a WWER-type reactor with any value of the reactivity margin and its switching is possible at any time after the transition process, which avoids downtime. The proposed plan can be used both in mathematical modeling of transient processes in a reactor and in reactor control systems to improve its controllability and, consequently, to improve safety.

Realistic 3D human saccades generated by a 6-DOF biomimetic robotic eye under optimal control.

We recently developed a biomimetic robotic eye with six independent tendons, each controlled by their own rotatory motor, and with insertions on the eye ball that faithfully mimic the biomechanics of the human eye. We constructed an accurate physical computational model of this system, and learned to control its nonlinear dynamics by optimising a cost that penalised saccade inaccuracy, movement duration, and total energy expenditure of the motors. To speed up the calculations, the physical simulator was approximated by a recurrent neural network (NARX). We showed that the system can produce realistic eye movements that closely resemble human saccades in all directions: their nonlinear main-sequence dynamics (amplitude-peak eye velocity and duration relationships), cross-coupling of the horizontal and vertical movement components leading to approximately straight saccade trajectories, and the 3D kinematics that restrict 3D eye orientations to a plane (Listing's law). Interestingly, the control algorithm had organised the motors into appropriate agonist-antagonist muscle pairs, and the motor signals for the eye resembled the well-known pulse-step characteristics that have been reported for monkey motoneuronal activity. We here fully analyse the eye-movement properties produced by the computational model across the entire oculomotor range and the underlying control signals. We argue that our system may shed new light on the neural control signals and their couplings within the final neural pathways of the primate oculomotor system, and that an optimal control principle may account for a wide variety of oculomotor behaviours. The generated data are publicly available at https://data.ru.nl/collections/di/dcn/DSC_626870_0003_600.

Research on an Intelligent Vehicle Trajectory Tracking Method Based on Optimal Control Theory

This study aims to explore an intelligent vehicle trajectory tracking control method based on optimal control theory. Considering the limitations of existing control strategies in dealing with signal delays and communication lags, a control strategy combining an anthropomorphic forward-looking reference path and longitudinal velocity closure is proposed to improve the accuracy and stability of intelligent vehicle trajectory tracking. Firstly, according to the vehicle dynamic error tracking model, a linear quadratic regulator (LQR) transverse controller is designed based on the optimal control principle, and a feedforward control strategy is added to reduce the system steady-state error. Secondly, an anthropomorphic look-ahead prediction model is established to mimic human driving behavior to compensate for the signal lag. The double proportional–integral–derivative (DPID) control algorithm is used to track the longitudinal speed reference value. Finally, a joint simulation is conducted based on MatLab/Simulink2021b and CarSim2019.0 software, and the effectiveness of the control strategy proposed in this paper is verified by constructing a semi-physical experimental platform and carrying out a hardware-in-the-loop test. The simulation and test results show that the control strategy can significantly improve the accuracy and stability of vehicle path tracking, which provides a new idea for future intelligent vehicle control system design.

Enhancing stance robustness and jump height in bipedal muscle-actuated systems: a bioinspired morphological development approach.

Recognizing humans' unmatched robustness, adaptability, and learning abilities across anthropomorphic movements compared to robots, we find inspiration in the simultaneous development of both morphology and cognition observed in humans. We utilize optimal control principles to train a muscle-actuated human model for both balance and squat jump tasks in simulation. Morphological development is introduced through abrupt transitions from a 4 year-old to a 12 year-old morphology, ultimately shifting to an adult morphology. We create two versions of the 4 year-old and 12 year-old models- one emulating human ontogenetic development and another uniformly scaling segment lengths and related parameters. Our results show that both morphological development strategies outperform the non-development path, showcasing enhanced robustness to perturbations in the balance task and increased jump height in the squat jump task. Our findings challenge existing research as they reveal that starting with initial robot designs that do not inherently facilitate learning and incorporating abrupt changes in their morphology can still lead to improved results, provided these morphological adaptations draw inspiration from biological principles.

Derivation of Dirac equation from the stochastic optimal control principles of quantum mechanics.

In this paper, we present a stochastic approach to relativistic quantum mechanics. We formulate the three fundamental principles of this theory and derive the Dirac equations based on them. This approach enables us to bring more insight into the nature of Dirac's spinors. Furthermore, we provide a physical interpretation of the stochastic optimal control theory of quantum mechanics.

The maximum principle for optimal control of mean‐field FBSDE driving by Teugels martingales with terminal state constraints

AbstractThis article studies the problem of optimal control with state constraints for mean‐field type stochastic systems, which is governed by a fully coupled forward‐backward stochastic differential equation with Teugels martingales. In this system, the coefficients contain not only the state processes but also its expectation value, and the cost function is of mean‐field type as well. We use an equivalent backward formulation to deal with the terminal state constraint, and then we obtain a stochastic maximum principle by Ekeland's variational principle. In addition, we discuss a stochastic linear‐quadratic control problem with state constraints.

Deep L1 Stochastic Optimal Control Policies for Planetary Soft Landing

In this paper, a novel deep-learning-based solution is introduced to the Powered Descent Guidance problem, grounded in principles of nonlinear Stochastic Optimal Control (SOC) and Feynman–Kac theory. Our algorithm solves the problem by framing it as an L1-SOC problem for minimum fuel consumption. Additionally, it can handle practically useful control constraints and nonlinear dynamics and enforces state constraints as soft constraints. This is achieved by building off of recent work on deep forward-backward stochastic differential equations and differentiable neural-network layers for nonconvex optimization based on stochastic search. In contrast to previous approaches, our algorithm does not require convexification of the constraints or linearization of the dynamics and is empirically shown to be robust to stochastic disturbances and the initial conditions of the spacecraft. After training offline, our control policy can be activated once the spacecraft is within a prespecified radius of the landing zone and at a prespecified altitude, in other words, the base of an inverted cone with the tip at the landing zone. We demonstrate empirically that our controller can successfully and safely land all trajectories initialized in the vicinity of the base of this cone as well as with randomization in the starting velocities and spacecraft mass while minimizing fuel consumption.

The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion

The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion

Separation Principle for Partially-Observed Linear-Quadratic Optimal Control for Mean-Field Type Stochastic Systems

Separation Principle for Partially-Observed Linear-Quadratic Optimal Control for Mean-Field Type Stochastic Systems

Optimal robust reinsurance contracts with investment strategy under variance premium principle

This paper investigates the optimal robust proportional reinsurance contracts with investment in a liquid financial market under variance premium principle in a principal-agent framework. The surplus process of the insurer (agent) is assumed to follow an approximating compound Poisson risk process. Both the insurer and reinsurer (principal) are allowed to invest in a risk-free asset and a risky asset whose price process is governed by the constant elasticity of variance model. The insurer and reinsurer aim to maximize the expected exponential utility of terminal wealth. The reinsurer is ambiguity-averse and has deterministic ambiguity aversion preferences against the diffusion risk caused by the financial market and the approximated diffusion risk which comes from the claim process. The reinsurance price is described by the reinsurer's safety loading which can be decided by the optimal strategies of the insurer and the reinsurer. By utilizing stochastic optimal control principle and HJB (or HJBI) equations, the optimal (robust) proportional reinsurance-investment strategies and the corresponding value functions are obtained explicitly. Numerical examples are provided.

A maximum principle for progressive optimal control of mean‐field forward–backward stochastic system involving random jumps and impulse controls

AbstractIn this paper, we study an optimal control problem of a mean‐field forward–backward stochastic system with random jumps in progressive structure, where both regular and singular controls are considered in our formula. In virtue of the variational technology, the related stochastic maximum principle (SMP) has been obtained, and it is essentially different from that in the classical predictable structure. Specifically, there are three parts in our SMP, that is, continuous part, jump part, and impulse part, and they are, respectively, used to characterize the characteristics of the optimal controls at continuous time, jump time, and impulse time. This shows that the progressive structure can more accurately describe the characteristics of the optimal control at the jump time. We also give two linear–quadratic examples to show the significance of our results.

On pointwise second‐order maximum principle for optimal stochastic controls of general mean‐field type

AbstractIn this paper, we establish a second‐order stochastic maximum principle for optimal stochastic control of stochastic differential equations of general mean‐field type. The coefficients of the system are nonlinear and depend on the state process as well as of its probability law. The control variable is allowed to enter into both drift and diffusion terms. We establish a set of second‐order necessary conditions for the optimal control in integral form. The control domain is assumed to be convex. The proof of our main result is based on the first‐ and second‐order derivatives with respect to the probability law and by using a convex perturbation with some appropriate estimates.

Maximum Principle for Optimal Control of Stochastic Evolution Equations with Recursive Utilities

Maximum Principle for Optimal Control of Stochastic Evolution Equations with Recursive Utilities

The effects of public health measures on severe dengue cases: An optimal control approach

Dengue fever is the most important viral mosquito-borne disease worldwide, with approximately 3.9 billion people at risk of acquiring dengue infection. Measures against mosquito bite combined with vector control programs to reduce mosquito population have been used in endemic countries for several years. Most recently, vaccines have become an important ally to prevent and control disease transmission. Economic costs of dengue control programs vary from region to region and therefore designing an optimal control strategy must be evaluated at different epidemiological contexts. Using a multi-strain vector-host mathematical model, we investigate the impact of different control measures to reduce dengue prevalence. A detailed sensitivity analysis to identify the key parameters influencing disease transmission is followed by an exploratory analysis of the possible solutions for the optimal control problem considering preventive measures to avoid mosquito bites, reduce mosquito population and vaccinate human hosts. The proposed cost functional includes a weighted sum of several efforts (not necessarily quantified as economic costs) for the controls which are evaluated alone and combined. The control system is analyzed using the Pontryagin‘s Principle for optimal control where different strategies are compared. Our results have shown that the simultaneous use of intervention measures are highly effective to reduce disease cases, however, the use of a single control measure can be as effective as the use of two or more controls combined. A careful evaluation of the epidemiological scenario is advised before designing strategies for disease prevention and control, allowing an optimal allocation of the public health resources.

The Global Maximum Principle for Progressive Optimal Control of Partially Observed Forward-Backward Stochastic Systems with Random Jumps

This paper is concerned with a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enters into all the coefficients. In our model, the observation equation is not only driven by a Brownian motion but also a Poisson random measure, which also has correlated noises with the state equation. The partially observed global maximum principle is proved. To show its applications, a partially observed linear quadratic progressive optimal control problem of forward-backward stochastic differential equations with random jumps is investigated by the maximum principle and stochastic filtering. State estimate feedback representation of the optimal control is given in a more explicit form by introducing some ordinary differential equations.

Analytical review of approaches to control over longitudinal and lateral dynamics of an autonomous vehicle

Introduction (problem statement and relevance). One of the major tasks when autonomous vehicle motion implementing is control over the vehicle actuating mechanisms to complete the requests from the controllers responsible for the motion trajectory planning. Currently, the longitudinal dynamics control is performed by controlling the torque on the wheels from the power unit and braking system, while the lateral control is performed through steering control. The paper considers the existing approaches to motion control for vehicles of diff erent automation levels and diff erent types of controllers with their advantages and disadvantages.The purpose of the study is to conduct the analytical review of the approaches being used to control longitudinal and lateral dynamics of an autonomous vehicle, to compare the regularities and logic of the solutions being used and the vehicle theory, and to specify the main issues and problems of autonomous vehicle dynamics control.Methodology and research methods. Analytical research method: analysis of domestic and foreign technical literature suggesting the approaches to control autonomous vehicle actuating mechanisms.Scientifi c novelty and results. Analysis of the approaches when forming the algorithms to control autonomous vehicle actuating mechanisms has been performed and the regularities and logic of solutions being used and the vehicle theory have been compared. As a result of the analysis, a conclusion has been made that there are no approaches of controller synthesis to control actuating mechanisms of a highly automated vehicle, the structure of which is theoretically substantiated when solving the control problem taking into account the vehicle theory, optimal control principles and adaptive control principles.Practical signifi cance. The research results can be used when setting the task to develop lower level control systems using the quality functional where the controller synthesis is made following the results of solving the control task based on the vehicle theory, optimal control principles and adaptive control principles, and the controller structure is theoretically substantiated.

Optimal Charging Scheduling of Electric Vehicles: The Co-Charging Case

A <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">co-charging</i> parking system is a charging system in which the chargers are automated, i.e., they can automatically connect to or disconnect from vehicles presented in the parking. This system makes it possible to have less chargers than the number of parking places. This paper studies an optimal scheduling problem aiming at charging all vehicles to required battery level while minimizing the total charging cost. We formulate this scheduling problem as a non-linear optimal control problem with mixed integer constraints and mixed discrete and continuous time. The problem is solved using a Branch and Bound Strategy coupled with Pontryagin Maximum Principle (PMP) and Interior Point Methods (IPMs) for optimal control. The presented method is tested on numerous configurations and shows promising results both in term of precision and in term of convergence rate.

Integrable Systems: In the Footprints of the Greats

In his 1842 lectures on dynamics C.G. Jacobi summarized difficulties with differential equations by saying that the main problem in the integration of differential equations appears in the choice of right variables. Since there is no general rule for finding the right choice, it is better to introduce special variables first, and then investigate the problems that naturally lend themselves to these variables. This paper follows Jacobi’s prophetic observations by introducing certain “meta” variational problems on semi-simple reductive groups G having a compact subgroup K. We then use the Maximum Principle of optimal control to generate the Hamiltonians whose solutions project onto the extremal curves of these problems. We show that there is a particular sub-class of these Hamiltonians that admit a spectral representation on the Lie algebra of G. As a consequence, the spectral invariants associated with the spectral curve produce a large number of integrals of motion, all in involution with each other, that often meet the Liouville complete integrability criteria. We then show that the classical integrals of motion associated, with the Kowalewski top, the two-body problem of Kepler, and Jacobi’s geodesic problem on the ellipsoid can be all derived from the aforementioned Hamiltonian systems. We also introduce a rolling geodesic problem that admits a spectral representation on symmetric Riemannian spaces and we then show the relevance of the corresponding integrals on the nature of the curves whose elastic energy is minimal.

Optimization of the operating mode of a squirrel-cage induction motor

THE PURPOSE. The presented work aims to optimize the operating mode of an asynchronous motor (AM) with a short-circuited rotor. To implement energy-efficient modes of operation of AM, operating in the resources of a rational electric drive, it is necessary to determine the numerical values of the parameters of the AM equivalent circuit, the currents flowing through the circuit element. There is no significance to this important definition of squirrel-cage currents, in accordance with the identification of the allocation of squirrel-cage rotor currents, which requires a solution along with the determination of the parameters of the IM equivalent circuit.METHODS. To analyze the work of AM in technical and educational formulations, equivalent circuits are presented, which turn into circuits with serial and analytical connections of active and inductive connections. For the established and transient operating modes of AM, it is important to determine the stator and rotor currents, their active and reactive components. In this regard, it is proposed to present the IM equivalent circuit in the form of conductivities connected in parallel, which will allow determining the components of IM currents without complex mathematical models. The replacement circuit of AM consisting of a series and parallel connection of active and inductive resistances has been converted into a circuit consisting of conductances. When converting the AM equivalent circuit, no additional dependencies and coefficients were introduced, and all assumptions that are accepted for IM equivalent circuits refer to the circuit under consideration. RESULTS. It was decided to use the equivalent circuit of one phase of AM, expressed in terms of the conductivities of the stator and rotor. According to the found dependences of conductivities, for the proposed equivalent circuit, the corresponding currents and powers of the AM phase are determined. Formulate the basic principle of optimal frequency control of AM, according to the criterion of energy saving. As an indicator of the efficiency of AM operation in steady-state operating modes, the minimum value of the total losses of the engine, the value of which is determined by the ratio of the product of the active conductivity of the rotor circuit q2s and the active conductivity of the phase q to the square of total conductivity y.CONCLUSION. Based on the results of the analysis of the characteristics of an asynchronous motor, the following conclusion was drawn: the motor will operate with minimal losses if the amplitude of the supply voltage is changed so that the slip of the asynchronous motor is equal to the critical value sξ for a given frequency. For the investigated engine AIR100S4, the critical value is sξ=0.0613 at a network frequency of 50 Hz. The method proposed in the work allows to reduce the loss of active power by 3-5% in the motor windings.

Применение оптимального управления при определении режима обработки материалов концентрированными потоками энергии: краткий обзор

The analysis of approaches and ways of determining the processing mode (mechanical, local thermal, welding, thermal cutting, etc.) is given. It is shown that the task of determining the processing mode is the reverse, characterized by a violation of the causal relationship inherent in the real thermal process. Methods and principles of optimal control theory are more effective methods for solving inverse problems. The first problems of optimal control of thermal processes of processing materials with concentrated energy flows were posed and solved in 1976 at the Baykov Institute of Metallurgy of the USSR Academy of Sciences as one-dimensional problems of thermal conductivity. Two- and three-dimensional optimal control problems were posed later and solved using the same methods of the theory of optimal control of systems with distributed parameters. The application of the principles of optimal control and the capabilities of modern computer technology make it possible to reduce the number of field experiments in determining the processing mode and increase the efficiency of the technological processes being developed.