Control Variable Constraints Research Articles

An Analytical Reentry Solution Based Online Time-Coordinated A* Path Planning Method for Hypersonic Gliding Vehicles Considering No-Fly-Zone Constraint

To meet the time-coordinated requirement of hypersonic gliding vehicles to reach a single target simultaneously in the presence of no-fly-zone constraints, this paper proposes a time-coordinated A* path planning method considering multiple constraints. The path planning method is designed based on an analytical steady gliding path model and the framework of the A* algorithm. Firstly, an analytical steady gliding path model is designed based on a quadratic function-type altitude-velocity profile. It can derive the control commands explicitly according to the desired terminal altitude and velocity, thus establishing a mapping between the terminal states and the control commands. Secondly, the node extension method of the A* algorithm is improved based on the mapping. Taking the terminal states as new design variables, a feasible path-node set is produced by a one-step integration using the control commands derived according to different terminal states. This node extension method ensures the feasibility of the path nodes while satisfying terminal constraints. Next, the path evaluation function of the A* algorithm is modified by introducing a heuristic switching term to select the most proper node as a waypoint, aiming to minimize the arrival time deviation. Meanwhile, introducing the penalty items into the path evaluation function satisfies the no-fly-zone constraints, process constraints, and control variable constraints. Finally, an online time-coordinated method is proposed to determine a commonly desired arrival time for several hypersonic gliding vehicles. It eliminates the need to specify the arrival time in advance and improves the capability to deal with sudden threats, increasing the path planning method’s online application capability. The proposed method can achieve online time-coordinated multi-constraint path planning for several hypersonic gliding vehicles, whose effectiveness and superiority are verified by simulations.

Aerocapture Optimization Method with Lift–Drag Joint Modulation Suitable for Variable Structure Spacecraft

Aerocapture, the action of delivering a vehicle from a hyperbolic orbit to a planetary orbit by using the aerodynamic force, could potentially lower fuel consumption. By controlling the direction and size of the aerodynamic force, the vehicle can accurately enter the target orbit. This paper focuses on a preliminary study of the optimal trajectory for aerocapture on the basis of a novel flight control option, which considers lift and drag joint modulation so as to suit variable structure spacecraft. In the preliminary evaluation of such a flight control option, the aerocapture corridors under lift modulation and drag modulation and the influence of the ballistic coefficient on aerocapture were analyzed, demonstrating that joint modulation can achieve complementary advantages compared with pure lift modulation and drag modulation. Based on this flight control option, optimal aerocapture trajectories with different path constraints, target orbital constraints and control variable constraints were found. It bears noting that both the bank angle and the reference area were taken as control variables for lift modulation and drag modulation, respectively, during the atmospheric flight in the process of designing the optimal trajectories. The optimal results indicate that the flight control option with lift and drag joint modulation can greatly broaden the necessary conditions for aerocapture and extend the target orbital range.

Parallel solution of optimal control problems using the graphics processing unit

AbstractThis paper presents an indirect method for solving optimal control problems (OCPs) using graphics processing unit (GPU). The OCPs considered here include control variable inequality constraints (CVICs), state variable inequality constraints (SVICs), and parameters. The necessary conditions of the minimum for the OCPs are written as a boundary value problem with index‐1 differential algebraic equations (BVP‐DAEs). The complementarity conditions associated with those inequality constraints are approximated using Kanzow's smoothed Fisher‐Burmeister formula. The numerical solution for solving the BVP‐DAEs is based on the multiple shooting technique and the DAEs are solved using a single step linearly implicit Runge–Kutta (Rosenbrock–Wanner, ROW) method. A Newton's continuation method is performed to solve the BVP‐DAEs system and the descent direction is found by solving a sparse bordered almost block diagonal (BABD) linear system with a structured orthogonal factorization algorithm. Parallel computing techniques are used to accelerate the code which is implemented using Python and CUDA on GPU. Numerical examples are presented to illustrate the efficiency of the code. The GPU based parallel implementation is shown to be significantly faster than the implementation using central processing unit (CPU) alone.

Optimal Solution of Reactive Power Dispatch in Transmission System to Minimize Power Losses Using Sine-Cosine Algorithm

Optimal reactive power dispatch (ORPD) has a crucial impact to enhance safety, reliability, and economical operation of the electric power system. ORPD is a non-linear, non-convex and mixed variable problem, which has been solved by many researchers via different meta-heuristic algorithms during the last decade. In this work, a novel algorithm named sine-cosine algorithm (SCA) is utilized to solve ORPD problem by considering both dependent and independent control variable constraints. SCA has been tested and validated on standard 14, 30 and 57-bus power systems. To validate the superiority of proposed algorithm, the outcomes obtained through SCA are compared with recent published results attained through particle swarm optimization (PSO), modified Gaussian barebones teaching–learning based optimization (BBTLBO), ant bee colony optimization (ABCO), whale optimization algorithm (WOA) and backtracking search algorithms (BSA). The results attained using SCA show the improvement in the power losses minimization. Thus, with standard 14-bus system, the power losses are minimized from 0.04% to 4.78%. While, using standard 30-bus, the power losses are minimized from 0.4% to 3.4% and with standard 57-bus, power losses are reduced from 0.9% to 1.99%. Furthermore, a comparative analysis with 30 independent runs on the above-mentioned bus systems is performed to examine the functioning of the proposed method in terms of probability density function (PDF) and cumulative density function (CDF). For such analysis, well-known meta-heuristic algorithms such as PSO, WOA, differential evolution (DE) are compared with proposed SCA in solving the ORPD problem. The results of this analysis clearly show that proposed algorithm is robust, effective, and computationally easy in solving the ORPD problem compared to the existing meta-heuristic algorithms.

Robust spline-line energy management guidance algorithm with multiple constraints and uncertainties for solid rocket ascending

For the solid rocket with depletion shutdown system, effective energy management is significant to meet terminal constraints by exhausting excess energy. Several traditional energy management algorithms cannot satisfy the altitude constraint and path constraints are not sufficiently considered. The velocity adjustment capability of these algorithms is limited and the uncertainties are not considered. Based on the on-line programming of velocity capability curve, Spline-Line Energy Management (SLEM) guidance algorithm is proposed. It introduces lateral maneuvers to further consume the available velocity on the basis of longitudinal energy management. After expressing the constraints as several algebraic equations, the closed-loop guidance problem is converted to solving a system of nonlinear equations about the curve parameters in real time. The advantage is that the altitude constraint can be satisfied theoretically. The overload and control variable change rate and amplitude constraints are also considered during the flight by constructing the feasible boundary of velocity capability curve. To improve the robustness, it is further extended by estimating the actual uncertainties. The effectiveness and advantages of SLEM are demonstrated by simulations and comparisons with other energy management algorithms. Simulation results show that the proposed approach can satisfy multiple constraints with high precision under the condition of uncertainties.

A path planning model of a tiltrotor for approaching an aircraft carrier during landing

A path planning model concerning a tiltrotor approaching an aircraft carrier is established in this study. In the model, the characteristic of the tiltrotor, the landing task, and the environment of the carrier are taken into account. First, the motion equations and the maneuverability of the tiltrotor in each flight mode are presented, and the constraints of control variables and flight envelope are given. The returning flight of the tiltrotor is divided into three phases corresponding to the three flight modes of the tiltrotor, and the constraints in each phase and the goal are set. Considering the flight safety of the tiltrotor, the environment of the carrier is described as flyable space and no-fly zones, and the no-fly zones are set taking the influences of turbulence and wind field induced by the moving aircraft carrier into account. The path planning issue is formulated into an optimization problem under the constraints of control variables and state variables. According to the characteristic of the established model, a pigeon inspired optimization (PIO)-based path planning algorithm is developed integrating the “step-by-step” and “one effort” path search strategies. Simulation results demonstrate that the tiltrotor can reach the target point with a reasonable landing path. Comparison among different algorithms is also conducted to verify that the PIO algorithm is capable of solving this online path planning problem.

The Optimal Power Flow Solution by Optimal Location of STATCOM Device using AHP Method

Optimum power flow is a useful tool for planning and operating the electrical system and maintains the economy and safety of the modern electrical system. Teaching, Learning-based Algorithm is one of the new Metaheuristic algorithms which can influence both teachers and students by expediting the interaction among them in sharing the necessary knowledge. The proposed TLBO is designed here to solve the problem of an optimum power flow with STATCOM FACTS device. The optimal location of STATCOM FACTS device on the weak bus is obtained by Analytical Hierarchy Process (AHP) method. The main objective of this study is to reduce fuel cost of generation, reduce active and reactive power loss, improve voltage deviation and enhance voltage stability index within the given control variable constraints. The proposed TLBO algorithm with STATCOM device is evaluated on the standard IEEE-57 bus system. From the simulation result, it shows that the Teaching Learning-based algorithm gives the optimal solution as compared to the recent algorithm mentioned in the literature with some IEEE-57 bus test system.

The multi-objective optimization of combustion system operations based on deep data-driven models

Advancing methods for modeling combustion systems and optimizing their operations is beneficial to improve the combustion performance. This paper develops a deep data-driven framework for the optimization of combustion system operations. First, a deep belief network based method is developed to model both of the combustion efficiency and the NOx emission. Next, a multi-objective optimization model is developed by integrating the deep belief network based models, the considered operational constraints, and the control variable constraints. Two objectives, maximizing the combustion efficiency and minimizing the NOx emission, are considered in the optimization. Due to the nonlinearity and complexity of the optimization model, traditional exact solution methods are not applicable to solve it. A recently presented swarm intelligence method, the JAYA algorithm, is applied to obtain the optimal solutions of the developed optimization model. Advantages of using JAYA are proved by benchmarking against well-known computational intelligence methods. The feasibility and effectiveness of the developed framework for optimizing the combustion process using industrial data is validated by computational experiments. Results demonstrate the potential of further improving both of the combustion efficiency and NOx emission by optimizing control settings of the combustion system.

Flexible‐regulation resources planning for distribution networks with a high penetration of renewable energy

Aimed at the status of distribution networks with a high penetration of renewable energy starved of flexible-regulation resources for improving their ability to absorb renewable-energy sources, this study puts forward flexibility-supply and flexibility-demand indexes for distribution networks and establishes a bi-level programming model for the distribution of flexible-regulation resources within the system-flexibility-balance constraints. The lower-level planning model seeks the lowest annual operating cost, lowest annual network loss, and lowest annual abandonment of wind and solar sources; in addition to the traditional power balances and constraints of various control variables and state variables, the requirement to balance constraints involving the flexibility of the system's supply and demand is even more crucial. The upper-level model aims to minimise the annual investment and operational costs. Combining the models, a double-layer iterative optimisation algorithm for flexible-regulation-resource allocation is proposed. Simulation results for an actual distribution network show that the proposed bi-level programming model can increase the capacity to absorb renewable energy and reduce system losses with the lowest investment and operational cost.

Optimal Control of Aerosol Emissions into the Stratosphere to Stabilize the Earth’s Climate

The problem of the optimal control of aerosol emissions into the stratosphere to stabilize the Earth’s climate is considered based on the zero-dimensional energy balance model. The global surface-temperature deviation from the undisturbed value is the state variable, and the albedo of the artificial aerosol layer, whose time variations are functionally related to the change in the total mass of aerosol particles and, consequently, the rate of their emissions, is the control variable. The problem is solved with and without consideration for the system phase path and control variable constraints for the given performance measure (objective function). Unlike previous studies, the aerosol emission scenarios are not set a priori, but represent a rigorous solution of the optimal control problem, ensuring the minimization of the objective function. The method is illustrated using the RCP8.5 scenario of growing concentration of greenhouse gases in the atmosphere. The approach considered in this paper can be easily extended to the cases of applying other known methods of climate engineering to manipulate the climate.

Gain‐scheduled constrained state feedback control of DC–DC buck power converter

A gain-scheduled constrained state feedback controller (SFC) for a SiC MOSFET direct current (DC)-DC buck power converter with a non-synchronous control strategy is presented. First, the synthesis process of a gain-scheduled SFC for a control system with a state-dependent parameter is proposed. Next, constraints of important states and control variables are a posteriori introduced into control algorithm to provide satisfactory dynamic behaviour and safe operation of the plant. The boundary values of control signals which provide permissible values of the future state-space variables are derived from the models of power converters that take into account two modes of operation (i.e. charging and discharging mode). The novelty of the proposed approach lies in efficient control algorithm that utilises the gain-scheduled SFC with the parameter-dependent constraint handling method. The designed control algorithm is extensively tested through simulation and experiments at a switching frequency of 36 kHz. The proposed solution is further compared with a conventional cascade control structure based on two proportional integral controllers for voltage and current loops as well as with a non-constrained state feedback control structure to illustrate its performance and low computational complexity.

Optimal reactive power dispatch using backtracking search algorithm

Optimal reactive power dispatch (ORPD) problem has a mounting effectuation on secure and economical operation of electrical power systems. It is well-known as a non-linear, multimodal and mixed-variable problem which has been solved using various computation intelligence-based techniques in the last decades. In this paper, as a new approach, backtracking search algorithm (BSA) is applied to solve the ORPD problem to minimise the power losses and/or improve the voltage profile under control and dependent variable constraints. The BSA is a new evolutionary algorithm for solving real-valued numerical optimisation problems. It has a simple structure and single control parameter. It memorises a population from a randomly chosen previous generation for use in generating the search-direction matrix. This grants BSA the advantage of experiences gained from previous generations to generate the offsprings. The proposed BSA is applied to the IEEE standard 30-bus system, and a real power system at West Delta Network as a part of the Unified Egyptian Network. Simulation results show the capability of the proposed BSA for solving the ORPD problem.

A Hierarchical Reliability Control Method for a Space Manipulator Based on the Strategy of Autonomous Decision-Making

In order to maintain and enhance the operational reliability of a robotic manipulator deployed in space, an operational reliability system control method is presented in this paper. First, a method to divide factors affecting the operational reliability is proposed, which divides the operational reliability factors into task-related factors and cost-related factors. Then the models describing the relationships between the two kinds of factors and control variables are established. Based on this, a multivariable and multiconstraint optimization model is constructed. Second, a hierarchical system control model which incorporates the operational reliability factors is constructed. The control process of the space manipulator is divided into three layers: task planning, path planning, and motion control. Operational reliability related performance parameters are measured and used as the system’s feedback. Taking the factors affecting the operational reliability into consideration, the system can autonomously decide which control layer of the system should be optimized and how to optimize it using a control level adjustment decision module. The operational reliability factors affect these three control levels in the form of control variable constraints. Simulation results demonstrate that the proposed method can achieve a greater probability of meeting the task accuracy requirements, while extending the expected lifetime of the space manipulator.

Methods to Deal with Control Variable Path Constraints in Dynamic Optimization Problems

Methods to Deal with Control Variable Path Constraints in Dynamic Optimization Problems

Methods to Deal with Control Variable Path Constraints in Dynamic Optimization Problems

Many researchers have reported their methods to handle state variable path constraints in dynamic optimization problems. However, very few of them mentioned the techniques to handle control variable path constraints specifically. This paper firstly introduces two methods to deal with control variable path constraints, then presents a novel smoothed quadratic penalty function method that can solve dynamic optimization problems with both control and state variable path constraints at the same time. The control variable parameterization strategy is used to solve the resulting problems. Two separate cases are considered where testing of case1 demonstrates the characteristics of the three methods, while testing of Case 2 indicates the effectiveness and the superiority of the proposed smoothed penalty function method.

Parallel indirect solution of optimal control problems

SUMMARY This paper presents an algorithm for the indirect solution of optimal control problems that contain mixed state and control variable inequality constraints. The necessary conditions for optimality lead to an inequality constrained two-point BVP with index-1 differential-algebraic equations (BVP-DAEs). These BVP-DAEs are solved using a multiple shooting method where the DAEs are approximated using a single-step linearly implicit Runge–Kutta (Rosenbrock–Wanner) method. An interior-point Newton method is used to solve the residual equations associated with the multiple shooting discretization. The elements of the residual equations, and the Jacobian of the residual equations, are constructed in parallel. The search direction for the interior-point method is computed by solving a sparse bordered almost block diagonal (BABD) linear system. Here, a parallel-structured orthogonal factorization algorithm is used to solve the BABD system. Examples are presented to illustrate the efficiency of the parallel algorithm. It is shown that an American National Standards Institute C implementation of the parallel algorithm achieves significant speedup with the increase in the number of processors used. Copyright © 2013 John Wiley & Sons, Ltd.

An ant colony optimization algorithm-based emergency control strategy for voltage collapse mitigation

Abstract This paper presents optimal preventive control actions using ant colony optimization (ACO) algorithm to mitigate the occurrence of voltage collapse in stressed power systems. The proposed objective functions are: minimizing the transmission line losses as optimal reactive power dispatch (ORPD) problem, maximizing the preventive control actions by minimizing the voltage deviation of load buses with respect to the specified bus voltages and minimizing the reactive power generation at generation buses based on control variables under voltage collapse, control and dependent variable constraints using proposed sensitivity parameters of reactive power that dependent on a modification of Fast Decoupled Power Flow (FDPF) model. The proposed preventive actions are checked for different emergency conditions while all system constraints are kept within their permissible limits. The ACO algorithm has been applied to IEEE standard 30-bus test system. The results show the capability of the proposed ACO algorithm for preparing the maximal preventive control actions to remove different emergency effects.

하이브리드 이륜차의 동력원 용량 매칭 및 연비평가

Recently, most of the countries started to regulate the emission of vehicle because of the global warming. The engine scooter is also one of the factor which cause the pollution. The hybrid system of a vehicle has many advantages such as fuel saving and emission reduction. The purpose of this study is to choose optimal size of engine, motor and battery for hybrid scooter system using Dynamic programming. The dynamic programming is an effective method to find an optimal solution for the complicated nonlinear system, which contains various constraints of control variables. The power source size of hybrid scooter was chosen through the backward simulator using dynamic programming. From the analysis, we choose the optimal size of each power source. To verify the optimal size of the power source, the Forward simulation was carried out. As a result, the fuel efficiency of hybrid scooter has significantly increased in comparison with that of engine scooter.

An Input-Output Optimal Control Model under Uncertain Influence and its Solution

An input-output optimal control model is established under uncertain influence in environment. The objective function, terminal constraint of state variables and bound constraints of control variables are considered with fuzziness. The direct consumption coefficient matrix and investment coefficient matrix are regarded as stochastic variables. Membership function and chance constrained programming are applied to convert the uncertain model to a definite one. Penalty function and Particle Swarm Optimization are used to solve the model. The calculation results of an example demonstrate that the uncertain model has more practical value to decision makers compared to a definite one.

Optimal reactive power dispatch using ant colony optimization algorithm

This paper proposed a procedure to solve the optimal reactive power dispatch (ORPD) problem using ant colony optimization (ACO) algorithm. The objective of the ORPD problem is to minimize the transmission power losses under control and dependent variable constraints. Proposed sensitivity parameters of reactive power at generation and switchable sources are derived based on a modified model of fast decoupled power flow. The proposed ACO-based algorithm is applied to the IEEE standard 14-bus, 30-bus systems, and a real power system at West Delta Network as a part of the Unified Egyptian Network. The obtained simulation results are compared with those of conventional linear programming, genetic algorithm, and particle swarm optimization technique. Simulation results show the capability of the proposed ACO-based algorithm for solving the ORPD problem, especially with increasing the system size.