Optimal Control Procedure Research Articles

Analysis of a Dry Friction Force Law for the Covariant Optimal Control of Mechanical Systems with Revolute Joints

This contribution shows a geometric optimal control procedure to solve the trajectory generation problem for the navigation (generic motion) of mechanical systems with revolute joints. The mechanical system is analyzed as a nonlinear Lagrangian system affected by dry friction at the joint level. Rayleigh’s dissipation function is used to model this dissipative effect of joint-level friction, and regarded as a potential. Rayleigh’s potential is an invariant scalar quantity from which friction forces derive and are represented by a smooth model that approaches the traditional Coulomb’s law in our proposal. For the optimal control procedure, an invariant cost function is formed with the motion equations and a Riemannian metric. The goal is to minimize the consumed energy per unit time of the system. Covariant control equations are obtained by applying Pontryagin’s principle, and time-integrated using a Finite Elements Method-based solver. The obtained solution is an optimal trajectory that is then applied to a mechanical system using a proportional–derivative plus feedforward controller to guarantee the trajectory tracking control problem. Simulations and experiments confirm that including joint-level friction forces at the modeling stage of the optimal control procedure increases performance, compared with scenarios where the friction is not taken into account, or when friction compensation is performed at the feedback level during motion control.

Optimal control of entanglement in atom pairs with dipole-dipole interaction by quantum phase space formalism

We investigate the entanglement in a two-particle system with continuous degree of freedom constituted by trapped neutral atoms interacting via tunable dipole-dipole interaction. We describe the system in the quantum Wigner phase space representation. The atom entanglement is measured in terms of violation of the non separability condition or of some Bell inequalities. By an optimal control procedure, we design the control parameters that steer the system toward a maximally entangled state. We estimate the robustness of the control by considering the presence of an external source of noise weakly interacting with the atoms.

Optimal Suppression of Oscillations in the Problem of a Spin-Up of a Two-Mass System

We consider a controlled mechanical system of many bodies, consisting of a load-bearing disk that rotates around its axis fixed in space, and a carried disk attached to it using weightless elastic elements. The presented bodies are in the same plane. The problem of minimizing the amplitude of radial oscillations is studied. To solve this problem over a sufficiently large interval, two numerical methods are used: the method of successive approximations in the control space and Newton’s method. The properties of the phase trajectories of the system are studied depending on the initial states of the disks. Various disk spin-up modes are detected. Using the smoothing procedure for optimal control, a continuous control is constructed that reduces the amplitude of radial oscillations.

Stochastic Optimal Control for Multivariable Dynamical Systems Using Expectation Maximization.

Trajectory optimization is a fundamental stochastic optimal control (SOC) problem. This article deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic models. Exact/complete solutions to these kind of control problems have been deemed analytically intractable in literature because they come under the category of partially observable Markov decision processes (MDPs). Therefore, effective solutions with reasonable approximations are widely sought for. We propose a reformulation of stochastic control in a reinforcement learning setting. This type of formulation assimilates the benefits of conventional optimal control procedure, with the advantages of maximum likelihood approaches. Finally, an iterative trajectory optimization paradigm called as SOC-expectation maximization (SOC-EM) is put forth. This trajectory optimization procedure exhibits better performance in terms of reduction in cumulative cost-to-go which is proven both theoretically and empirically. Furthermore, we also provide novel theoretical work which is related to uniqueness of control parameter estimates. Analysis of the control covariance matrix is presented, which handles stochasticity through efficiently balancing exploration and exploitation.

Energy-maximising tracking control for a nonlinear heaving point absorber system commanded by second order sliding modes

Energy-maximising control has proven to be of fundamental aid in the pathway towards commercialisation of wave energy conversion technology. The WEC control problem is based upon the design of a suitable control law capable of maximising energy extraction from the wave resource, while effectively minimising any risk of component damage. A particularly well-established family of WEC controllers is based upon a composite structure, where an optimal velocity reference is generated via direct optimal control procedures, followed by a suitable tracking control strategy. This paper presents the design and synthesis of a second order sliding mode controller to attain a reference tracking for a wave energy system. The presented approach can inherently handle parameter uncertainty in the model, which is ubiquitous within hydrodynamic modelling procedures. Furthermore, the proposed sliding mode controller has relatively mild computational requirements, and finite-time convergence to the designed surface, hence being an ideal candidate for real-time energy-maximising control of WEC systems.

Self-Driven Reverse Thermal Engines Under Monotonous and Oscillatory Optimal Operation

Abstract The complex time-dependent heat and electromagnetic energy transfer in a new type of reverse thermal engine is analyzed. The reverse thermal engine consists of a cold body, a Peltier element and an electric circuit containing an inductor with controllable inductance. This system allows cooling a body below the ambient temperature. The inductor acts as an accumulator of magnetic energy, receiving electrical work from the Peltier element during some time intervals and supplying the Peltier element with electrical work during other time intervals. The system is named self-driven reverse thermal engine since one of its subsystems (the inductor) receives and releases work. The new type of engine has features which make it different from classical reverse thermal engines: it cannot operate in steady state and it operates for a finite time interval. Instead of usual indicators of performance such as the coefficient of performance, other performance indicators should be used, such as the minimum cooled body temperature and the interval of time needed to reach a given cooled body temperature. Significant cooling effects do not necessarily need high inductance values. The operation of the new engine has been optimized by using direct optimal control procedures. The open-source program package BOCOP has been used to transform the optimal control problem into a non-linear dynamic problem. The minimum temperature reached by the cooled body depends on its mass. There exists, however, a global minimum temperature, for a specified optimum mass of the cooled body. The minimum temperature decreases by increasing the value of the Seebeck coefficient and by decreasing the thermal conductance. Thermal damped oscillations may arise under special circumstances. This implies a very small difference between the initial temperatures of the cold and cooled bodies and a specific range of variation for the conductance of the Peltier element.

An Iterative Procedure for Optimal Control of Bilinear Systems

An Iterative Procedure for Optimal Control of Bilinear Systems

ОРГАНИЗАЦИЯ МАТЕРИАЛЬНОГО ПОТОКА В УСЛОВИЯХ ЦИФРОВОЙ ЭКОНОМИКИ: МЕСТО И РОЛЬ ТЕХНОЛОГИИ ЦИФРОВОГО ДВОЙНИКА

The article provides an overview of theoretical studies and modern trends in the development of the concept of “digital economy” and analyzes the technical and economic foundations of such changes, and also identifies the directions of further development of such studies. The difference between engineering and technical and economic approaches to the problem of production management is actualized. It is concluded that the problems of production and supply chains in the digital economy require an integrated, technical and economic approach. It is also concluded that the theory of material flow (logistics) should be based on the knowledge in the field of economic theory, with the active use of the concept of SCM 4.0. The characteristic of the modern stage is given - the rejection of traditional, hierarchical models of building organizations in favor of “streaming” ones. The urgency of digitalizing supply chain models is argued. At the same time, the important role of combining the knowledge of different specialists in the implementation of the function of organizing material flows is shown. The importance of Industry 4.0 in improving the rational use of resources, predictability, transparency and quality of the economy is shown. The features of the modern economy, technical and economic methods and technologies of SCM 4.0 are correlated. In conclusion, the article considers the concept of “digital twin” of supply chain processes, which correlates with the methods of simulation. Simulation and digital twin are here optimization procedures, optimal control, important and promising technical procedures of Industry 4.0. Basing on the study of Western and Russian science literature, the characteristics and properties of “digital twins”, their importance for the management of production and other processes in the supply chain, and directions for further research of this phenomenon are highlighted.

Personalized medicine for in vitro fertilization procedure using modeling and optimal control

In vitro fertilization (IVF) is the most common technique in assisted reproductive technology and in most cases the last resort for infertility treatment. It has four basic stages: superovulation, egg retrieval, fertilization, and embryo transfer. Superovulation is a drug-induced method to enable multiple ovulation per menstrual cycle and key component towards a successful IVF cycle. Although there are the general guidelines for dosage, the dose is not optimized for each patient, and complications, such as overstimulation, can occur. To overcome the shortcomings of this general system, a mathematical procedure is developed which can provide a customized model of this stage regarding the size distribution of eggs (follicles/ oocytes) obtained per cycle as a function of the chemical interactions of the drugs used and the conditions imposed on the patient during the cycle, which provide a basis for predicting the possible outcome. Uncertainty and risk are modeled and included in optimal drug dosage decisions. This paper describes the theory, model, and the optimal control procedure for improving outcomes of IVF treatment for one of the four protocols used in real practice. The validation of the procedure is performed using clinical data from the patients previously undergone IVF cycles. Customized patient-specific model parameters are obtained by using initial two-day data for each patient. Subsequently, this model is used to predict the FSD for the remaining days of the cycle. This procedure was conducted for 49 patients. The results of the customized models are found to be closely matching with the observed FSD. These results thus validate the modeling approach and consequently its use for predicting the customized optimal drug dosage for each patient. Using the customized model and the optimized dosage, the FSD at the end of the cycle was determined. A small double-blind clinical trial was also conducted in India. The results from the trial show that the dosage predicted by using the model is 40% less than the suggestion made by the IVF clinicians. The testing and monitoring requirements for patients using optimized drug dosage is reduced by 72%. Work on the other three protocols and for patients in the USA is started and is showing promising results.

Helicopter Landing Trajectory Optimization after Tail Rotor Control Failure in Different Collective Pitch

This paper studies helicopter optimal landing and control procedure after tail rotor control failure (TRCF) in different collective pitch. The optimal control problem of landing after tail rotor control failure was solved numerically by direct multiple shooting method and sequential quadratic programming. A sample helicopter optimal landing procedures after tail rotor control failure in large collective pitch and small collective pitch were investigated respectively. As can be seen from the results, when the tail rotor is stuck at large collective pitch, the tail rotor provides a large lateral force, which facilitates landing with small forward speed and descent rate in a large power state. The pilot can maintain stability of heading by side slipping. When the tail rotor is stuck at small collective pitch, the tail rotor provides a small lateral force, which is favorable for flying near economic speed, but difficult for a safe landing. A normal landing maneuver will cause a high yaw rate at touchdown, which is dangerous. Therefore, autorotation is preferred during touchdown because the landing is more secure with small yaw rate. The trajectory optimization method of helicopter safe landing after tail rotor control failure can provide a reference for flight test.

Optimal Control of Jebba Hydropower Operating Head by a Dynamic Programming

Nigeria with a generating potential of roughly 12,522 MW only supplies less than 20% of the national demand. This necessitates an optimal use of the Jebba Hydroelectric Power Plant whose optimal generation depends on the operating head. This paper presents the solution to an optimal control problem involving the operating head of the plant. An optimal control problem consisting of a model of the system dynamics, performance index and system constraints was solved using a dynamic programming approach. The control procedure was built on the integration of the nonlinear dynamical model by an Adams-Moulton technique with Adams-Bashfort as predator and Runge-Kutta as a starter. The numerical solution, coupled with dynamic programming was employed in developing an optimal control procedure for the regulation of the operating head. Result presented shows the potential of the control procedure in determining the amount of inflow required to restore the operating head to a nominal level whenever there is a disturbance.

Vibration suppression of a boron nitride nanotube under a moving nanoparticle using a classical optimal control procedure

The current research investigates the vibration of single-walled boron nitride nanotube (SWBNNT) induced by a moving nanoparticle. In order to decrease the forced vibration of SWBNNT under a moving nanoparticle, a linear classical optimal control procedure is used to manipulate the movement of a nanoparticle as a drug material inside a nano-structure with consideration of various size-dependent procedures based on Rayleigh beam model. The Pasternak substrate is utilized to model the elastic medium. Hamilton, Galerkin and Newmark methods are also employed to solve the motion equations. Different size-dependent beam theories have been considered, such as the classical beam theory, nonlocal beam theory, strain gradient beam theory and nonlocal strain gradient beam theory, in order to reveal small-scale effects. The effects of the small length scale considered herein, the velocity of a moving nanoparticle, electrical potential field, the number of vibration modes and actuators and also resultant control force on the vibration behavior of the SWBNNT are investigated in detail.

Solution to a Zero-Sum Differential Game with Fractional Dynamics via Approximations

The paper deals with a zero-sum differential game in which the dynamical system is described by a fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ The goal of the first (second) player is to minimize (maximize) the value of a given quality index. The main contribution of the paper is the proof of the fact that this differential game has the value, i.e., the lower and upper game values coincide. The proof is based on the appropriate approximation of the game by a zero-sum differential game in which the dynamical system is described by a first order functional differential equation of a retarded type. It is shown that the values of the approximating differential games have a limit, and this limit is the value of the original game. Moreover, the optimal players' feedback control procedures are proposed that use the optimally controlled approximating system as a guide.

Enhanced passive control of dual‐mode systems under extreme seismic loading: An optimal control approach

Passive protective measures suffer from limited displacement capacities. When the capacity is reached under extreme loading, harsh impacts occur, resulting in spikes in acceleration. Supplemental damping increases the effective displacement capacity at the expense of increasing accelerations, even in the absence of impact, and at the same time altering the normal operation of systems. In this study, a dual-mode system is studied, which improves the performance of these systems under extreme events, without affecting the normal operation, by applying the control action only at some reserved capacity regions. An innovative solution is sought that can more effectively utilize the available displacement capacity while simultaneously seeking to control the sustained accelerations without any prior assumption on force–displacement or force–velocity relationship. Optimal control is used to determine the best possible control force trajectories to achieve both performance objectives. Open-loop solutions are found by solving the Euler–Lagrange equations with the constrained control force. Because finding the solution to this problem requires the knowledge of the future loading, these solutions are not immediately implementable. Therefore, a piecewise optimal control with unknown fixed final times on each excursion is proposed on the reserved capacity regions only, which can be used to find the best control action mechanism that can guide the design of novel dual-mode systems with impact-mitigation mechanisms. Finally, by utilizing the designed curves obtained from the proposed optimal control procedure, a Kelvin–Voigt device is tuned for illustrative purposes. The performance of the system equipped with a tuned Kelvin–Voigt device under an maximum considered earthquake-level event is evaluated, and it is compared with the piecewise optimal solution and a suboptimal solution using the linear quadratic regulator.

Forming an automated technology to manage freight transportation along a direction

The study investigated the process of rolling stock movement along a direction and took into consideration possible risks during transportation of freight. It revealed the main reasons, which cause effects of the first and last mile. They include, namely, the lack of the required number of technically sound rolling stock on scheduled time and significant difficulties with the passage of trains, specifically through port and border stations. The study formalized the technological process of transportation of freight along a direction in the form of an optimization mathematical model of the process of movement of freight wagons. The objective function of the model represented total operation costs. Its basis was the Lebesgue-Stieltjes integral, which took into consideration the effect of the first and last mile. The model also took into consideration possible risks, which arise in the process of wagon operation. It is expedient to refer the built optimization model to the problems of stochastic programming. The analysis of statistical data showed that the time required for wagons to move from an initial station of a route to a port station and the time required for movement of wagons from a port station directly to a port conform to normal distribution. The presence of a positive correlation between these two values gave reason to consider the corresponding parameters within a single probabilistic field. This approach made possible to determine probability of untimely arrival of wagons to a port more accurately and, accordingly, to determine a value of financial risk. The modeling proved that there was an extremum of the objective function of the minimum type, which made possible to form a procedure for optimal control of transport parameters. Thus, the generated model is universal in nature. It gives possibility to manage the transportation process with the lowest operational costs for the railway in the presence of feedback. Calculations showed a decrease in railway costs approximately by 10 % comparing with the costs calculated according to the existing method of determination of the actual cost of transportation of freight. The optimization model is the basis for formation of an automated technology for the management of freight traffic. We propose to implement it in the form of a system of decision support for the dispatcher staff

Vibrational control scrutiny of physically affected SWCNT acted upon by a moving nanoparticle in the framework of nonlocal–strain gradient theory

The possibility of moving drug materials into the intelligent nano-materials such as nanotubes such as set of DNA or RNA molecules to change the behavior of cells is an important problem in the nano-medicine science. This paper deals with vibrational control of magnetically thermally affected single-walled carbon nanotube (SWCNT) under a moving nanoparticle using the nonlocal–strain gradient theory based on the Rayleigh beam model. The elastic medium is modeled as Pasternak substrate. A gain matrix with time-varying behaviors and displacement–velocity feedback in the framework of linear classical optimal control procedure is used to suppress the vibration responses of the SWCNT. Hamilton, Galerkin and Newmark time integration principles are jointly utilized to ascertain the equations of motion. The influences of the nonlocal and material length-scale parameters, the velocity of nanoparticle and physical fields on the vibration behavior of the SWCNT are explored. Likewise, a specified control algorithm in suppressing the vibrational behavior of SWCNT under the effect of moving nanoparticle is examined.

Power system stabilization using an optimal hybrid control strategy with a PID controller

ABSTRACTAs a power system turns out to be all the more heavily loaded and more unpredictable, maintaining stability becomes a difficult issue. In this paper, we propose an optimal control procedure for power system adjustment utilizing a proportional-integral-derivative (PID) controller in a coordinated power system. In modern applications, the most generally utilized controller is the PID controller, which necessitates productive techniques to control the distinctive parameters of the plant. The proposed strategy uses the particle swarm optimization algorithm-based way to deal with producing the optimal tuning parameters. This paper investigates the execution of the power system and dynamic execution of the controller is compared with the conventional controller with approval of the adequacy of the proposed mixture controller. Experimental results demonstrate that the proposed system has upgraded the system stability of the power system all the more adequately existing systems.

On the Numerical Solution of Differential Games for Neutral-Type Linear Systems

The paper deals with a zero-sum differential game, in which the dynamics of a conflict-controlled system is described by linear functional differential equations of neutral type and the quality index is the sum of two terms: the first term evaluates the history of motion of the system realized up to the terminal time, and the second term is an integral–quadratic evaluation of the corresponding control realizations of the players. To calculate the value and construct optimal control laws in this differential game, we propose an approach based on solving a suitable auxiliary differential game, in which the motion of a conflict-controlled system is described by ordinary differential equations and the quality index evaluates the motion at the terminal time only. To find the value and the saddle point in the auxiliary differential game, we apply the so-called method of upper convex hulls, which leads to an effective solution in the case under consideration due to the specific structure of the quality index and the geometric constraints on the control actions of the players. The efficiency of the approach is illustrated by an example, and the results of numerical simulations are presented. The constructed optimal control laws are compared with the optimal control procedures with finitedimensional approximating guides, which were developed by the authors earlier.

A Gravitational Search Algorithm-Based Single-Center of Mass Flocking Control for Tracking Single and Multiple Dynamic Targets for Parabolic Trajectories in Mobile Sensor Networks

Developing optimal flocking control procedure is an essential problem in mobile sensor networks (MSNs). Furthermore, finding the parameters such that the sensors can reach to the target in an appropriate time is an important issue. This paper offers an optimization approach based on metaheuristic methods for flocking control in MSNs to follow a target. We develop a non-differentiable optimization technique based on the gravitational search algorithm (GSA). Finding flocking parameters using swarm behaviors is the main contributing of this paper to minimize the cost function. The cost function displays the average of Euclidean distance of the center of mass (COM) away from the moving target. One of the benefits of using GSA is its application in multiple targets tracking with satisfying results. Simulation results indicate that this scheme outperforms existing ones and demonstrate the ability of this approach in comparison with the previous methods.

Feedback Traffic Control at Highway Work Zones using Variable Speed Limits

This paper presents a novel real-time merging traffic control approach for throughput maximization at highway work zones using Variable Speed Limits (VSL). A Proportional-Integral (PI) feedback regulator is employed for control which is simpler and potentially more robust compared to heuristic or optimal control procedures. Practical VSL implementation aspects have been taken into account. The proposed concept is demonstrated and evaluated using a validated microscopic traffic flow model for a real motorway work zone in Germany. Remarkable improvements can be observed for all performance indexes considered and for all replications simulated. Investigations have been carried out for different compliance rates, different set points utilized by the feedback regulator, as well as for different values of the lower admissible bound of the VSL. The proposed approach is deemed suitable for field implementation.