SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.

Trust-region based instantaneous optimal semi-active control of long-span spatially extended structures with MRF-04K damper

In the field of civil engineering, magnetorheological fluid （MRF） damper-based semi-active control systems have received considerable attention for use in protecting structures from natural hazards such as strong earthquakes and high winds. In this paper, the MRF damper-based semi-active control system is applied to a long-span spatially extended structure and its feasibility is discussed. Meanwhile, a _trust-region method based instantaneous optimal semi-active control algorithm （TIOC） is proposed to improve the performance of the semi-active control system in a multiple damper situation. The proposed TIOC describes the control process as a bounded constraint optimization problem, in which an optimal semi- active control force vector is solved by the trust-region method in every control step to minimize the structural responses. A numerical example of a railway station roof structure installed with MRF-04K dampers is presented. First, a modified Bouc- Wen model is utilized to describe the behavior of the selected MRF-04K damper. Then, two semi-active control systems, including the well-known clipped-optimal controller and the proposed TIOC controller, are considered. Based on the characteristics of the long-span spatially extended structure, the performance of the control system is evaluated under uniform earthquake excitation and travelling-wave excitation with different apparent velocities. The simulation results indicate that the MR fluid damper-based semi-active control systems have the potential to mitigate the responses of full-scale long-span spatially extended structures under earthquake hazards. The superiority of the proposed TIOC controller is demonstrated by comparing its control effectiveness with the clipped-optimal controller for several different cases.

Stabilization of linear time-varying systems with state and input constraints using convex optimization

The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.

An Intelligent Approach in Design Optimzation Based on Determining Constraints Compatibility

Based on monotonicity analysis and computer symbolic manipulating technique,a procedure for determining constraints compatibility in design optimization hasbeen proposed in this paper. By using the proposed method relationshipsbetween constrains can be determined and the optimization is greatly simplifid.The method is code with intelligent production systems.

Centralized-local PV voltage control considering opportunity constraint of short-term fluctuation

This study proposes a two-stage photovoltaic(PV)voltage control strategy for centralized control that ignores short-term load fluctuations.In the first stage,a deterministic power flow model optimizes the 15-minute active cycle of the inverter and reactive outputs to reduce network loss and light rejection.In the second stage,the local control stabilizes the fluctuations and tracks the system state of the first stage.The uncertain interval model establishes a chance constraint model for the inverter voltage-reactive power local control.Second-order cone optimization and sensitivity theories were employed to solve the models.The effectiveness of the model was confirmed using a modified IEEE 33 bus example.The intraday control outcome for distributed power generation considering the effects of fluctuation uncertainty,PV penetration rate,and inverter capacity is analyzed.

Joint Optimization of Channel Allocation,Link Assignment and Power Control for Device-to-Device Communication Underlaying Cellular Network

Device-to-Device(D2D) communication has been proposed to facilitate cellular network with system capacity(SC) and quality of service(QoS).We consider the design of link assignment(LA),channel allocation(CA)and power control(PC) in D2D-aided content delivery scenario for both user fairness(UF)and system throughput(ST) under QoS requirement.Due to the complexity of the problem,we decompose it into two components:CA is formulated from graph perspective to mitigate severe co-channel interference,which turns out to be the Max K-cut problem;LA and PC are jointly optimized to utilize the gain achieved from CA for supreme performance,and specifically,genetic algorithm(GA) is adopted to optimize LA,but when deriving the fitness of each chromosome,PC optimization will be involved.Thanks to numerical results,we elucidate the efficacy of our scheme.

Optimization of Line Configuration and Balancing for Flexible Machining Lines

Line configuration and balancing is to select the type of line and allot a given set of operations as well as machines to a sequence of workstations to realize high-efficiency production. Most of the current researches for machining line configuration and balancing problems are related to dedicated transfer lines with dedicated machine workstations. With growing trends towards great product variety and fluctuations in market demand, dedicated transfer lines are being replaced with flexible machining line composed of identical CNC machines. This paper deals with the line configuration and balancing problem for flexible machining lines. The objective is to assign operations to workstations and find the sequence of execution, specify the number of machines in each workstation while minimizing the line cycle time and total number of machines. This problem is subject to precedence, clustering, accessibility and capacity constraints among the features, operations, setups and workstations. The mathematical model and heuristic algorithm based on feature group strategy and polychromatic sets theory are presented to find an optimal solution. The feature group strategy and polychromatic sets theory are used to establish constraint model. A heuristic operations sequencing and assignment algorithm is given. An industrial case study is carried out, and multiple optimal solutions in different line configurations are obtained. The case studying results show that the solutions with shorter cycle time and higher line balancing rate demonstrate the feasibility and effectiveness of the proposed algorithm. This research proposes a heuristic line configuration and balancing algorithm based on feature group strategy and polychromatic sets theory which is able to provide better solutions while achieving an improvement in computing time.

Robust design and optimization for autonomous PV-wind hybrid power systems

This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.

A modified normalized input-output minimization (Mod-NIOM) method for seismic wave propagation modeling

A new method for wave propagation modeling is introduced in this paper. By using the constraint optimization （Lagrange multiplier） method, the sum of weighted squared Fourier amplitudes is minimized when subjected to a constraint. The sum of the maximum amplitudes obtained from all output models is normalized to unity and is taken as a constraint. In this method, all the actual time histories are considered as outputs and dealt with equally. Independently of the combinations of time histories （or the first time history selected） during the analysis, the method captures the relationship of actual time histories by showing clear peaks. This paper describes the formulation of the models and illustrates the advantage of this method over the normalized input-output minimization （NIOM） method. The Mod-NIOM is then used to analyze the time histories of the Hyogoken-nanbu earthquake recorded at the Port Island vertical array site in Kobe, which suffered from liquefaction caused by the strong motions during the main shock. This method showed good correlations between the observed time histories at the site even though the surface time history was greatly modified by the liquefaction.

Cooperative Multi-Agent Reinforcement Learning with Constraint-Reduced DCOP

Cooperative multi-agent reinforcement learning（ MARL） is an important topic in the field of artificial intelligence,in which distributed constraint optimization（ DCOP） algorithms have been widely used to coordinate the actions of multiple agents. However,dense communication among agents affects the practicability of DCOP algorithms. In this paper,we propose a novel DCOP algorithm dealing with the previous DCOP algorithms＇ communication problem by reducing constraints.The contributions of this paper are primarily threefold：（1） It is proved that removing constraints can effectively reduce the communication burden of DCOP algorithms.（2） An criterion is provided to identify insignificant constraints whose elimination doesn＇t have a great impact on the performance of the whole system.（3） A constraint-reduced DCOP algorithm is proposed by adopting a variant of spectral clustering algorithm to detect and eliminate the insignificant constraints. Our algorithm reduces the communication burdern of the benchmark DCOP algorithm while keeping its overall performance unaffected. The performance of constraint-reduced DCOP algorithm is evaluated on four configurations of cooperative sensor networks. The effectiveness of communication reduction is also verified by comparisons between the constraint-reduced DCOP and the benchmark DCOP.

Guignard’s Constraint Qualification (GCQ) and Multiobjective Optimisation Problems

Investigation of optimality conditions has been one of the most interesting topics in the theory of multiobjective optimisation problems (MOP). To derive necessary optimality conditions of MOP, we consider assumptions called constraints qualifications. It is recognised that Guignard Constraint Qualification (GCQ) is the most efficient and general assumption for scalar objective optimisation problems;however, GCQ does not ensure Karush-Kuhn Tucker (KKT) necessary conditions for multiobjective optimisation problems. In this paper, we investigate the reasons behind that GCQ are not allowed to derive KKT conditions in multiobjective optimisation problems. Furthermore, we propose additional assumptions that allow one to use GCQ to derive necessary conditions for multiobjective optimisation problems. Finally, we also include sufficient conditions for multiobjective optimisation problems.

Effects of Memory Foam on Optimizing Shoulder Fatigue of Wearable Exoskeleton

Wearable exoskeleton is a wearable device to enhance human ability,however,it is too heavy because of some constraints,such as material,structure and energy storage battery. Thus it brings fatigue to people after a long period of wearing. The research aims at optimizing shoulder fatigue and improving wearing comfort by means of changing the device-body contact material. After analyzing the current wearable exoskeletons ' weight, a standard load was set and a wearable exoskeleton was designed that could switch the weight. The experiment chose movement stability and change of cumulative pressure upon shoulder as the indexes of fatigue. The indexes were measured and analyzed before and after changing the contact material to memory foam with the standard load. The results showed promotion in action stability and obvious decrease in cumulative pressure upon shoulder.The experiment proves that the using of memory foam in wearable exoskeleton has evident effects on optimizing shoulder fatigue with load,promoting movement stability and wearing comfort.

A review on applications of heuristic optimization algorithms for optimal power flow in modern power systems

Optimal power flow(OPF)is one of the key tools for optimal operation and planning of modern power systems.Due to the high complexity with continuous and discrete control variables,modern heuristic optimization algorithms(HOAs)have been widely employed for the solution of OPF.This paper provides an overview of the latest applications of advanced HOAs in OPF problems.The most frequently applied HOAs for solving the OPF problem in recent years are covered and briefly introduced,including genetic algorithm(GA),differential evolution(DE),particle swarm optimization(PSO),and evolutionary programming(EP),etc.

Optimal guidance of extended trajectory shaping

To control missile＇s miss distance as well as terminal impact angle, by involving the timeto-go-nth power in the cost function, an extended optimal guidance law against a constant maneuvering target or a stationary target is proposed using the linear quadratic optimal control theory.An extended trajectory shaping guidance（ETSG） law is then proposed under the assumption that the missile-target relative velocity is constant and the line of sight angle is small. For a lag-free ETSG system, closed-form solutions for the missile＇s acceleration command are derived by the method of Schwartz inequality and linear simulations are performed to verify the closed-form results. Normalized adjoint systems for miss distance and terminal impact angle error are presented independently for stationary targets and constant maneuvering targets, respectively. Detailed discussions about the terminal misses and impact angle errors induced by terminal impact angle constraint, initial heading error, seeker zero position errors and target maneuvering, are performed.

AN ANT COLONY ALGORITHM FOR YARD TRUCK SCHEDULING AND YARD LOCATION ASSIGNMENT PROBLEMS WITH PRECEDENCE CONSTRAINTS

This paper examines the yard truck scheduling,the yard location assignment for discharging containers,and the quay crane scheduling in container terminals.Taking into account the practical situation,we paid special attention to the loading and discharging precedence relationships between containers in the quay crane operations.A Mixed Integer Program（MIP） model is constructed,and a two-stage heuristic algorithm is proposed.In the first stage an Ant Colony Optimization（ACO） algorithm is employed to generate the yard location assignment for discharging containers.In the second stage,the integration of the yard truck scheduling and the quay crane scheduling is a flexible job shop problem,and an efficient greedy algorithm and a local search algorithm are proposed. Extensive numerical experiments are conducted to test the performance of the proposed algorithms.

Stiffeners layout design of thin-walled structures with constraints on multi-fastener joint loads

The purpose of this paper is to present an extended topology optimization method for the stiffeners layout design of aircraft assembled structures. Multi-fastener joint loads and manufacturing constraints are considered simultaneously. On one hand, the joint loads are calculated and constrained within a limited value to avoid the failure of fasteners. On the other hand, the manufacturing constraints of the material distribution in the machining directions of stiffeners are implemented by an improved piecewise interpolation based on a beveled cut-surface. It is proven that the objective function is strictly continuous and differentiable with respect to the piecewise interpolation. The effects of the extended method with two different constraints are highlighted by typical numerical examples. Compared with the standard topology optimization, the final designs have clearly shown the layout of stiffeners and the joint loads have been perfectly constrained to a satisfying level.

Differences and relations of objectives, constraints, and decision parameters in the optimization of individual heat exchangers and thermal systems

Performance improvement of heat exchangers and the corresponding thermal systems benefits energy conservation, which is a multi-parameters, multi-objectives and multi-levels optimization problem. However, the optimized results of heat exchangers with improper decision parameters or objectives do not contribute and even against thermal system performance improvement. After deducing the inherent overall relations between the decision parameters and designing requirements for a typical heat exchanger network and by applying the Lagrange multiplier method, several different optimization equation sets are derived, the solutions of which offer the optimal decision parameters corresponding to different specific optimization objectives, respectively. Comparison of the optimized results clarifies that it should take the whole system, rather than individual heat exchangers, into account to optimize the fluid heat capacity rates and the heat transfer areas to minimize the total heat transfer area, the total heat capacity rate or the total entropy generation rate, while increasing the heat transfer coefficients of individual heat exchangers with different given heat capacity rates benefits the system performance. Besides, different objectives result in different optimization results due to their different intentions, and thus the optimization objectives should be chosen reasonably based on practical applications, where the inherent overall physical constraints of decision parameters are necessary and essential to be built in advance.

A car-following model based on the optimized velocity and its security analysis

An enhanced optimal velocity model(EOVM)that considers driving safety is established to alleviate traffic congestion and ensure driving safety.Time headway is introduced as a criterion for determining whether the car is safe.When the time headway is less discussed to ensure the model's safety and maintain the following state.A stability analysis of the model was carried out to determine than the minimum time headway(TH_(min))or more than the most comfortable time headway(TH_(com)),the acceleration constraints are the stability conditions of the model.The EOVM is compared with the optimal velocity model(OVM)and fuzzy car-following model using the real dataset.Experiments show that the EOVM model has the smallest error in average,maximum and median with the real dataset.To confirm the model's safety,design fleet simulation experiments were conducted for three actual scenarios of starting,stopping and uniform process.

A predictive chance constraint rebalancing approach to mobility-on-demand services

This paper considers the problem of supply-demand imbalances in Mobility-on-Demand(MoD)services.These imbalances occur due to uneven stochastic travel demand and can be mitigated by proactively rebalancing empty vehicles to areas where the demand is high.To achieve this,we propose a method that takes into account uncertainties of predicted travel demand while minimizing pick-up time and rebalance mileage for autonomous MoD ride-hailing.More precisely,first travel demand is predicted using Gaussian Process Regression(GPR)which provides uncertainty bounds on the prediction.We then formulate a stochastic model predictive control(MPC)for the autonomous ride-hailing service and integrate the demand predictions with uncertainty bounds.In order to guarantee constraint satisfaction in the optimization under estimated stochastic demand prediction,we employ a probabilistic constraining method with user-defined confidence interval,using Chance Constrained MPC(CCMPC).The benefits of the proposed method are twofold.First,travel demand uncertainty prediction from data can naturally be embedded into the MoD optimization framework,allowing us to keep the imbalance at each station below a certain threshold with a user-defined probability.Second,CCMPC can be relaxed into a Mixed-Integer-Linear-Program(MILP)and the MILP can be solved as a corresponding Linear-Program,which always admits an integral solution.Our transportation simulations show that by tuning the confidence bound on the chance constraint,close to optimal oracle performance can be achieved,with a median customer wait time reduction of 4%compared to using only the mean prediction of the GPR.

Model predictive control with an on-line identification model of a supply chain unit

A model predictive controller was designed in this study for a single supply chain unit.A demand model was described using an autoregressive integrated moving average(ARIMA) model,one that is identified on-line to forecast the future demand.Feedback was used to modify the demand prediction,and profit was chosen as the control objective.To imitate reality,the purchase price was assumed to be a piecewise linear form,whereby the control objective became a nonlinear problem.In addition,a genetic algorithm was introduced to solve the problem.Constraints were put on the predictive inventory to control the inventory fluctuation,that is,the bullwhip effect was controllable.The model predictive control(MPC) method was compared with the order-up-to-level(OUL) method in simulations.The results revealed that using the MPC method can result in more profit and make the bullwhip effect controllable.