Conditions For Optimal Control Research Articles

Characterizing Temporal Ecophysiology for Herbicide Management of Huisache (Acacia farnesiana [L.] Willd.)

Huisache (Vachellia farnesiana [L.] Wight & Arn.) is a woody species native to the western hemisphere that can invade a variety of native rangeland habitats around the world. In South Texas, it is native yet increasing in density and range while displacing more desirable forage plants, and because it resprouts prolifically it has been difficult to control. We therefore attempted to characterize optimal timing and environmental conditions for herbicide control. We collected weather data in four huisache-invaded pastures along the Texas Coastal Bend and recorded the average huisache phenological stage at those pastures each month. We also analyzed root crown total nonstructural carbohydrate (TNC) and huisache mortality resulting from herbicide treatment each month between April 2012 and November 2014. Huisache mortality and TNC data were analyzed using a randomized complete block analysis of variance, with post hoc tests to separate means; Akaike's information criterion determined best-fit models for mortality data. Root crown TNC increased during May, August, and December, indicating downward translocation and the potential for increased mortality of treated plants. Actual mortality was greatest during the months of May, September, October, and November. The best fit model for mortality was a sixth-order polynomial function of mortality versus month; when month was removed as a model factor, the best fit model was a quadratic function of soil temperature (peaking at ≈24.5°C), combined with a quadratic function of phenology (highest at full canopy stage). These results indicate that huisache is best treated with chemicals when soil temperature is near 24.5°C and during the full canopy stage. In the coastal plains of South Texas these variables coincide with two windows of optimal mortality for huisache treatment: May and September−November.

Optimal control problems governed by 1-D Kobayashi–Warren–Carter type systems

This paper is devoted to the study of a class of optimal control problems governed by 1–D Kobayashi–Warren–Carter type systems, which are based on a phase-field model of grain boundary motion, proposed by [Kobayashi et al, Physica D, 140, 141–150, 2000]. The class consists of an optimal control problem for a physically realistic state-system of Kobayashi–Warren–Carter type, and its regularized approximating problems. The results of this paper are stated in three Main Theorems 1–3. The first Main Theorem 1 is concerned with the solvability and continuous dependence for the state-systems. Meanwhile, the second Main Theorem 2 is concerned with the solvability of optimal control problems, and some semi-continuous association in the class of our optimal control problems. Finally, in the third Main Theorem 3, we derive the first order necessary optimality conditions for optimal controls of the regularized approximating problems. By taking the approximating limit, we also derive the optimality conditions for the optimal controls for the physically realistic problem.

Solvability and optimal controls of non-instantaneous impulsive stochastic fractional differential equation of order q ∈ (1,2)

In this article, we study the stochastic fractional optimal control problem for a system governed by a class of non-instantaneous impulsive stochastic fractional differential equation in the infinite-dimensional spaces. We utilize the fractional calculus, stochastic analysis theory and a suitable fixed point approach to present the solvability of the stochastic fractional system. Then, the existence of optimal state-control pairs of the Lagrange problem is derived without uniqueness of solutions of the stochastic system. Finally, the main results are validated with the aid of an example.

Center-Articulated Hydrostatic Cotton Harvesting Rover Using Visual-Servoing Control and a Finite State Machine

Multiple small rovers can repeatedly pick cotton as bolls begin to open until the end of the season. Several of these rovers can move between rows of cotton, and when bolls are detected, use a manipulator to pick the bolls. To develop such a multi-agent cotton-harvesting system, each cotton-harvesting rover would need to accomplish three motions: the rover must move forward/backward, turn left/right, and the robotic manipulator must move to harvest cotton bolls. Controlling these actions can involve several complex states and transitions. However, using the robot operating system (ROS)-independent finite state machine (SMACH), adaptive and optimal control can be achieved. SMACH provides task level capability for deploying multiple tasks to the rover and manipulator. In this study, a center-articulated hydrostatic cotton-harvesting rover, using a stereo camera to locate end-effector and pick cotton bolls, was developed. The robot harvested the bolls by using a 2D manipulator that moves linearly horizontally and vertically perpendicular to the direction of the rover’s movement. We demonstrate preliminary results in an environment simulating direct sunlight, as well as in an actual cotton field. This study contributes to cotton engineering by presenting a robotic system that operates in the real field. The designed robot demonstrates that it is possible to use a Cartesian manipulator for the robotic harvesting of cotton; however, to reach commercial viability, the speed of harvest and successful removal of bolls (Action Success Ratio (ASR)) must be improved.

Probabilistic State Forecasting and Optimal Voltage Control in Distribution Grids under Uncertainty

Nowadays, the uncertainty in distribution systems rises, notably due to an increasing share of solar panels and electric vehicles whose power production and consumption are characterized by a high volatility. This poses challenges to distribution system operators to ensure stable and secure operation of their grid. Hence, an optimal integration of these distributed energy resources in real-time control schemes inevitably relies on appropriate forecasts of the near-future system state. This paper investigates the short-term probabilistic state prediction of low-voltage grids for operation purposes. The performance of two quantile forecasting algorithms is evaluated for different levels of distributed energy resources penetration and availability of measurements. Quantile forecasts are finally integrated into the framework of an optimization problem that aims at minimizing the costs associated with overvoltages by suitable solar power curtailment. The advantages of quantile forecasts considering different imbalance prices are demonstrated.

Model predictive air path control for a two-stage turbocharged spark-ignition engine with low pressure exhaust gas recirculation

Innovative air path concepts for turbocharged spark-ignition engines with exhaust gas recirculation impose high demands on the control due to nonlinearities and cross-couplings. This contribution investigates the control of the air and exhaust gas recirculation paths of a two-stage turbocharged spark-ignition engine with low pressure exhaust gas recirculation. Using exhaust gas recirculation at high loads, the in-cylinder temperature can be lowered, reducing the knock tendency, while at the same time preventing the need for the enrichment of the air/fuel ratio. Air and exhaust gas recirculation paths are cross-coupled and show different delay times. To tackle these challenges, a data-based two-stage model predictive controller is proposed: The target selector accounts for the overactuated system structure, while the dynamic controller adjusts the charging pressure and exhaust gas recirculation rate. The prediction model setup is based on a small amount of dyno-run measurement data. To ensure real-time capability, the model is kept as simple as possible. This allows for fast turnaround times of the algorithm, while maintaining the necessary accuracy in steady-state and transient operation. This study focuses on a two-stage control concept based on a target selector for optimal stationary control inputs and the dynamic controller considering the dynamic behavior of the air and exhaust gas recirculation paths. Subsequently, the control concept for the two-stage turbocharged spark-ignition engine with low pressure exhaust gas recirculation is validated via experimental tests under real-driving conditions on an automotive test track, using a prototype test vehicle. Results show that boost pressure as well as exhaust gas recirculation rate setpoints are met without overshoot and control deviation with settling times being close to the boundaries set by the hardware.

Guiding a supersonic controlled object in a multi-position air basing radar

The possibility of control of a guided supersonic aviation unmanned interceptor on a moving target in an autonomous airborne multi-position radar station has been investigated. To obtain the coordinate information, the algorithm of difference-range finding and difference range-Doppler spatial measurements is selected using a limited number of transmitting positions that do not provide an unambiguous determination of the coordinates and speed of the object with high accuracy. The paper proposes various approaches to eliminate a priori uncertainty regarding the estimated coordinates in a limited set of measuring radio engineering positions.An analytical method is considered for constructing an optimal state control device for a nonlinear multidimensional and multiply connected dynamic object, taking into account the constraints, which allows one to obtain finite computational relations in a closed algebraic form. The control device was synthesized using measurements in the Cartesian and spherical coordinate systems, several varieties of the combined method of pointing a controlled object to an instant meeting point were obtained. The given guidance algorithms are a generalization of the method of proportional navigation widely used in practice and its modifications. A distinctive feature of the synthesized algorithms is the natural accounting for the nonlinear, multidimensional, and multiply connected structure of the control object, as well as the parameters of unsteady perturbations (acceleration of gravity, projections of the longitudinal acceleration of the object and acceleration of the target’s maneuver) that act in the guidance process.The unified kinematic differential equations that describe the dynamics of the control object, are obtained, and they can be used to synthesize a controller that operates according to switched or smoothly matched non-stationary optimality criteria (target functions, target integral manifolds). The developed algorithms can be used in the design of autonomous homing and telecontrol systems, implemented in hardware and software both on board an unmanned aerial or artillery interceptor, and as a part of autonomous multiposition airborne radar stations.

Ergodic control of diffusions with compound Poisson jumps under a general structural hypothesis

We study the ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process. This extends the results of Arapostathis et al. (2019) to running costs that are not near-monotone. This generality is needed in applications such as optimal scheduling of large-scale parallel server networks.We provide a full characterizations of optimality via the Hamilton–Jacobi–Bellman (HJB) equation, for which we additionally exhibit regularity of solutions under mild hypotheses. In addition, we show that optimal stationary Markov controls are a.s. pathwise optimal. Lastly, we show that one can fix a stable control outside a compact set and obtain near-optimal solutions by solving the HJB on a sufficiently large bounded domain. This is useful for constructing asymptotically optimal scheduling policies for multiclass parallel server networks.

Analysis and Simulation of a Fractional Order Optimal Control Model for HBV

In this paper, we propose a fractional optimal control model of anti-HBV infection based on saturation incidence and logistic proliferation of uninfected cells for the first time. We derive the basic reproduction number R0 and the cytotoxic T lymphocyte immune response reproductive number R1 and give the stable analysis based on R0 and R1. We analyse the optimal control condition and give two optimal control strategies about entecavir monotherapy and combination therapy of traditional Chinese medicine and entecavir with different fractional orders by simulation. The simulation shows that combination therapy may be a good choice in anti-HBV infection therapy. We also compare the objective function values of the optimal control strategies with other constant control strategies; the comparison shows that the optimal therapy can get similar or better treatment effect with less drug dose and side effects.

Numerical modeling of ethanol-fueled solid oxide fuel cells with a Ni-BaZr0.1Ce0.7 Y0.1Yb0.1O3–δ external reformer

A numerical model is developed to evaluate ethanol-fueled solid oxide fuel cells (E-SOFCs) with a Ni-BaZr0.1Ce0.7Y0.1Yb0.1O3–δ (Ni-BZCYYb) external reformer owing to its high hydrophilia, carbon deposition resistance, and catalytic properties. This model is validated by the ethanol conversion and product selectivity with the introduction of the steam for adjusting the water-carbon ratio. The simulated E-SOFCs provide a suitable porosity and thickness for the Ni-BZCYYb external reformer, and the optimal control conditions are that the porosity is around 0.4, and the thickness is more than 4 mm for the best reforming effect, which can decrease the concentration polarization loss and improve cell performance. The carbon deposition boundaries and the equilibrium composition can be predicted by the thermodynamic equilibria calculation for E-SOFCs. The proposed model can give the optimization of the geometry design and operating conditions to avoid carbon deposition and improve the electrochemical performance of E-SOFCs.

OBTAINING COAL ADSORBENTS BASED ON LOCAL WOOD WASTE, RESEARCH OF THEIR PHYSICO-CHEMICAL AND ADSORPTION PROPERTIES

The article presents the results of a study of porous carbon materials obtained by thermal and steam activation of wood waste. Regardless of the type of feedstock, carbon materials with high physicochemical properties were obtained as a result of activation. Based on the results of theoretical and experimental studies, the conditions for optimal process control were determined, which made it possible to control the technological properties of the obtained sorbents. It has been established that the adsorption properties of the sorbent are determined by the porous structure and chemical nature of the surface.

Optimal leader-following consensus of fractional opinion formation models

This paper deals with a control strategy enforcing consensus in a fractional opinion formation model with leadership, where the interaction rates between followers and the influence rate of the leader are functions of deviations of opinions between agents. The fractional-order derivative determines the impact of the memory during the opinion evolution. The problem of leader-following consensus control is cast in the framework of nonlinear optimal control theory. We study a finite horizon optimal control problem, in which deviations of opinions between agents and with respect to the leader are penalized along with the control that is applied only to the leader. The existence conditions for optimal consensus control are proved and necessary optimality conditions for the considered problem are derived. The results of the paper are illustrated by some examples.

RETRACTED ARTICLE: Existence of global solutions to a quasilinear Schr\xf6dinger equation with general nonlinear optimal control conditions

In this article, we study a modified maximum principle approach under condition on the weight of the delay term in the feedback and the weight of the term without delay. On that basis, we prove the existence of global solutions for a quasilinear Schrödinger equation in an unbounded domain with a general nonlinear nonlinear optimal control condition in the weakly nonlinear internal feedback. The equation includes many special cases such as classical Schrödinger equations, fractional Schrödinger equations, and relativistic Schrödinger equations, etc. Our results are established by means of the fixed point theory associated with the Schrödinger operator in suitable b-metric spaces. Moreover, we establish general stability estimates by using some properties of Schrödinger convex functions.

Global Convergence of Policy Gradient Algorithms for Indefinite Least Squares Stationary Optimal Control

We consider policy gradient algorithms for the indefinite least squares stationary optimal control, e.g., linear-quadratic-regulator (LQR) with indefinite state and input penalization matrices. Such a setup has important applications in control design with conflicting objectives, such as linear quadratic dynamic games. We show the global convergence of gradient, natural gradient and quasi-Newton policies for this class of indefinite least squares problems.

Design and experiment of electronic seeding system based on response surface method

ABSTRACT A new electronic seeding device was designed for large-sized seeds, such as soybean, corn, and peanuts, that supports an independent electronic-controlled seeding process. The developed seeding device consists of a programmable logic controller, pulse generator, stepper motor, and stepper motor driver. Based on the Box–Behnken Design model, the effects of different factors on the plant spacing control were analyzed, and the control parameters of the seeding system were optimized by correlation analysis. Through performance tests, the results of the research showed that the coefficient of variation of plant spacing was found to be affected by the interaction between shaft speed and belt speed, in which the belt speed was dominant. And the optimal control conditions by using Box–Behnken Design model are as follows: the seed shaft speed was 0.60 r/s, the soybean hundred-grain weight was 22 g, and the belt speed was 1.5 m/s. The results of the experiments showed that the socket-roller seeding device successfully completed the seeding test, and its performance index was in accord with the applicable standards for single grain precision seeding equipment.

Generalized multiple dependent state optimal control charts under ranked set sampling for monitoring process mean

AbstractThis paper proposes two optimal control charts by using the generalized multiple dependent state (GMDS) plan to monitor the process mean. These charts make advantageous use of the ranked set sampling schemes and integrate them with the GMDS plan to improve the shift detection ability of the Shewhart‐type control charts. The proposed control charts have two pairs of control limits, inner and outer, which enables them to consider the current and previous sample information while making a decision about the process state. The run‐length profiles of the proposed charts are obtained through extensive Monte Carlo simulations. The individual and overall mean shift detection abilities of the proposed charts are compared with various competing control charts by using out‐of‐control average run length ( ) and the average extra quadratic loss ( ) as performance metrics. The comparison establishes the complete dominance of the proposed charting strategy. In the end, the practical implementation of the proposed charts is demonstrated by using a real data set related to the cement manufacturing industry.

Optimization of Constrained Stochastic Linear-Quadratic Control on an Infinite Horizon: A Direct-Comparison Based Approach

In this paper we study the optimization of the discrete-time stochastic linear-quadratic (LQ) control problem with conic control constraints on an infinite horizon, considering multiplicative noises. Stochastic control systems can be formulated as Markov Decision Problems (MDPs) with continuous state spaces and therefore we can apply the direct-comparison based optimization approach to solve the problem. We first derive the performance difference formula for the LQ problem by utilizing the state separation property of the system structure. Based on this, we successfully derive the optimality conditions and the stationary optimal feedback control. By introducing the optimization, we establish a general framework for infinite horizon stochastic control problems. The direct-comparison based approach is applicable to both linear and nonlinear systems. Our work provides a new perspective in LQ control problems; based on this approach, learning based algorithms can be developed without identifying all of the system parameters.

Separating two species of microalgae in photobioreactors in minimal time

This paper proposes a strategy to separate two strains of microalgae in minimal time. The control is the dilution rate of the continuous photobioreactor. The microalgae dynamics is described by the Droop’s model, taking into account the internal quota storage of the cells. Using Pontryagin’s principle, we develop a dilution-based control strategy that leads to the most efficient species separation in minimal time. A numerical optimal synthesis –based on direct optimization methods– is performed throughout the paper, in order to determine the structure of the optimal feedback-control law, which is bang-singular. Our numerical study reveals that singular arcs play a key role in the optimization problem since they allow the optimal solution to be close to an associated static optimal control problem. A resulting turnpike-like behavior, which characterizes the optimal solution, is highlighted throughout this work.

On continuous-time constrained stochastic linear–quadratic control

This paper studies a class of continuous-time scalar-state stochastic Linear–Quadratic (LQ) optimal control problems with the linear control constraints. Using the state separation theorem induced from its special structure, we derive the analytical solution for this class of problems. The revealed optimal control policy is a piece-wise affine function of system state. This control policy can be computed efficiently by solving two Riccati equations off-line. Under some mild conditions, the stationary optimal control policy can be also achieved for this class of problems over an infinite horizon. Examples are presented to shed light on the theoretical results established.

Singular optimal control problems with recursive utilities of mean‐field type

AbstractIn this paper a second‐order necessary condition for singular optimal controls with recursive utilities of mean‐field control systems is investigated. For our mean‐field singular control problem, the second‐order adjoint system is not a single mean‐field backward stochastic differential equation (BSDE), but a matrix‐valued system, which consists of three classical BSDEs. Based on this observation, a new second‐order expansion of cost functional is proved and also the stochastic maximum principle. Our method is appropriate for a large class of mean‐field singular optimal control problems.