Feasibility Constraints Research Articles

Dynamic Launch Trajectory Planning of a Cable-Suspended Translational Parallel Robot Using Point-to-Point Motions

In the last decade, cable-suspended parallel robots have attracted significant interest due to their large workspaces and high dynamic performances. However, a significant drawback is that cables must always be in tension to control the motion. Using launch motions to reach a target can enlarge the workspace of such robots. For a spatial translational cable robot suspended by six pairwise-parallel cables, an analytical method for planning point-to-point dynamic trajectories is proposed. Using a second-order Bézier curve trajectory, the mechanism starts from a static condition, passes through intermediate points, and finally launches an object towards a target. According to the kinematic constraint conditions on the position, the velocity and acceleration of the end-effector at a prescribed point, the parametric expressions for a dynamically-feasible trajectory can be determined. The feasibility of the trajectory is analyzed under the constraint that cable tensions must be positive at all times. By changing the position of the end point of the trajectory and the total motion time, the kinematic conditions on the position and velocity as well as the feasibility constraint can be satisfied. Finally, our point-to-point dynamic launch trajectories are verified by simulations and experiments.

Cooperation and Coordination Transportation for Nonholonomic Mobile Manipulators: A Distributed Model Predictive Control Approach

This article addresses the problem of cooperation and coordination transportation for decoupling nonholonomic mobile manipulators (NMMs) in a workspace with obstacles. We propose a distributed model predictive control (MPC) approach for a team of NMMs to transport a target object while satisfying significant constraints and limitations, such as the feasible state and control input constraints, parameter synchronization constraints, and obstacles within the workspace. First, under the framework of the decoupling dynamics, an auxiliary dynamics model for task-space end-effectors and null-space mobile bases is obtained by the nonlinear feedback technique based on the Euler–Lagrange description of the NMMs. Using the modified virtual structure method, the cooperation and coordination transportation problem for NMMs is simplified as two independent synchronization tracking control problems for task-space end-effectors and null-space mobile bases. A distributed constrained optimization problem is established by taking the parameter synchronization and system constraints into the cost function. A general projection neural network (GPNN) approach is employed to solve the optimization problem and obtain the optimal control input. Moreover, a sufficient condition that guarantees the stability of the closed-loop system is further developed. Simulation results show that the proposed cooperation and coordination transportation strategy is feasible and effective.

Fixed-Time Path-Following Control of an Autonomous Vehicle With Path-Dependent Performance and Feasibility Constraints

Constrained operations for autonomous vehicles have been extensively studied in the literature over the recent years. However, to the best of the authors’ knowledge, all of the existing works address only constant or time-varying constraint functions. In this work, we study <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">path-dependent</i> constraint requirements, which explicitly depend on the path parameter, instead of depending on the time variable directly. This approach is more practical in reality, where the constraint requirements are often shaped by the environment boundaries. From the system users’ perspectives, it is also much easier to define constraint functions based on the path parameter. A modified version of the universal barrier function is used in the analysis of path-dependent constraint requirements. We show that under the proposed novel control scheme, the vehicle’s line-of-sight distance and angle error terms can converge into small sets near the equilibrium with a fixed-time convergence rate, while the path-dependent constraint requirements are satisfied at all time. A simulation and an experiment study further demonstrate the efficacy of the proposed scheme.

Long Duration Stochastic MPC With Mission-Wide Probabilistic Constraints Using Waysets

A stochastic Model Predictive Control (MPC) formulation is presented for systems operating for a finite time subject to constraints on the Mission-Wide Probability of Safety (MWPS). For linear discrete-time systems subject to unknown disturbances, the goal is to formulate an MPC controller to achieve a desired probability of mission success, where the entire closed-loop state and input trajectories stay within the state and input constraint sets and the final state reaches the desired terminal set. To enable longer missions under greater uncertainty, a wayset-based approach is proposed that allows for the prediction horizon of the MPC to be significantly shorter than the length of the mission. Using a scenario-based approach to stochastic MPC, the use of constrained zonotopes makes the computation of these waysets efficient and practical. Numerical results demonstrate the utility of the waysets for increasing the feasibility of MWPS constraints to longer missions and that the percentage of successful missions asymptotically converges above the desired probability.

Output feedback attitude control for rigid spacecraft under attitude constraints

&lt;p style='text-indent:20px;'&gt;An output feedback control law is proposed in this paper for spacecraft attitude reorientation task. Although attitude maneuver has been widely investigated and obtained significant results, it is still challenging when considering attitude pointing constraints and lacking the information of angular velocity. Firstly, potential function is introduced to tackle attitude pointing constraints. Then, by jointly designing sign function and potential function, the anti-unwinding performance can also be achieved. Furthermore, the relevant information of angular velocity is obtained by utilizing first-order passive filter with the attitude error quaternion. Moreover, by properly selecting candidate Lyapunov function, the feasibility of attitude constraints can be rigorously proved under the proposed control law, while the stability of the system can be guaranteed without signal of angular velocity and information of inertia matrix. A numerical example is carried out to demonstrate the effectiveness of the proposed method.&lt;/p&gt;

Offline Uncertainty Sampling in Data-driven Stochastic MPC

In this work, we exploit an offline-sampling based strategy for the constrained data-driven predictive control of an unknown linear system subject to random measurement noise. The strategy uses only past measured, potentially noisy data in a non-parametric system representation and does not require any prior model identification. The approximation of chance constraints using uncertainty sampling leads to efficient constraint tightening. Under mild assumptions, robust recursive feasibility and closed-loop constraint satisfaction is shown. In a simulation example, we provide evidence for the improved control performance of the proposed control scheme in comparison to a purely robust data-driven predictive control approach.

FEASIBLE AND OPTIMAL TRAJECTORIES GENERATION FOR AUTONOMOUS DRIVING VEHICLES, 11-24.

Real-time feasible and optimal trajectory generation subject tothe vehicle physical constraints, the surrounding obstacles, andthe environmental conditions is one of the most important partsof autonomous driving vehicles.

Zeroth-order Gradient Tracking for Distributed Constrained Optimization

Distributed optimization is an important and practical problem that arose from machine learning, smart grid, and multi-robot systems. In this paper, we propose a zeroth-order gradient tracking method to solve a class of constrained distributed optimization problems with nonidentical feasible sets. We design a more general pseudo-gradient estimation scheme, which includes the existing coordinate descent, discretized gradient descent, and spherical smoothing methods as its special cases. Moreover, we propose pseudo-gradient tracking with projection dynamics to deal with nonidentical feasible set constraints and achieve the optimal solution. We show the proposed algorithm achieves the optimal solution with an O(lnT/√T) convergence rate. Finally, we present an example to demonstrate the effectiveness of the proposed algorithm.

Adapting ecosystem restoration for sustainable development in a changing world

Adapting ecosystem restoration for sustainable development in a changing world

Transmission Expansion Planning Considering a High Share of Wind Power to Maximize Available Transfer Capability

To have an effective transmission network and support free trading, the open and non-discriminatory access to transmission services for all market participants under all conditions is of significant concern. To this end, a sufficient value of available transfer capability (ATC) is required, which can significantly affect the electricity market efficiency. This paper constructs a methodology for reinforcing an existing transmission network considering wind power investment to enhance ATC. In this regard, a bi-level structure is adopted whose upper level is the joint transmission expansion planning (TEP) and wind power investment subject to the technical power grid limitations. After solving the upper level, a security-constrained economic dispatch (SC-ED) is formulated to acquire the optimal generation scheduling. Then, the lower level is designed to calculate the ATC. To solve this problem, the SC-ED is first replaced by its primal and dual feasibility constraints and strong duality equality. Then, these constraints are added to the upper level. The lower level is also replaced by its corresponding constraints. Consequently, a bilinear single-level optimization problem is extracted, which is further solved by employing Konno’s cutting plane algorithm. The experimental results on the IEEE 24-bus RTS show the proposed method’s effectiveness. It is indicated that the ATC can be improved by 27.2 % using the formulated model at the expense of more investment cost resulting in less load shedding and less wind curtailment.

Low-Light Image Enhancement via Self-Reinforced Retinex Projection Model

Low-light image enhancement aims to improve the quality of images captured under low-lightening conditions, which is a fundamental problem in computer vision and multimedia areas. Although many efforts have been invested over the years, existing illumination-based models tend to generate unnatural-looking results (e.g., over-exposure). It is because that the widely-adopted illumination adjustment (e.g., Gamma Correction) breaks down the favorable smoothness property of the original illumination derived from the well-designed illumination estimation model. To settle this issue, a great-efficiency and high-quality Self-Reinforced Retinex Projection (SRRP) model is developed in this paper, which contains optimization modules of both illumination and reflectance layers. Specifically, we construct a new fidelity term with the self-reinforced function for the illumination optimization to eliminate the dependence of the illumination adjustment to obtain a desired illumination with the excellent smoothing property. By introducing a flexible feasible constraint, we obtain a reflectance optimization module with projection. Owing to its flexibility, we can extend our model to an enhanced version by integrating a data-driven denoising mechanism as the projection, which is able to effectively handle the generated noises/artifacts in the enhanced procedure. In the experimental part, on one side, we make ample comparative assessments on multiple benchmarks with considerable state-of-the-art methods. These evaluations fully verify the outstanding performance of our method, in terms of the qualitative and quantitative analyses and execution efficiency. On the other side, we also conduct extensive analytical experiments to indicate the effectiveness and advantages of our proposed model.

Minimally Disruptive Cooperative Lane-Change Maneuvers

A lane-change maneuver on a congested highway could be severely disruptive or even infeasible without the cooperation of neighboring cars. However, cooperation with other vehicles does not guarantee that the performed maneuver will not have a negative impact on traffic flow unless it is explicitly considered in the cooperative controller design. In this letter, we present a socially compliant framework for cooperative lane-change maneuvers for an arbitrary number of CAVs on highways that aims to interrupt traffic flow as minimally as possible. Moreover, we explicitly impose feasibility constraints in the optimization formulation by using reachability set theory, leading to a unified design that removes the need for an iterative procedure used in prior work. We quantitatively evaluate the effectiveness of our framework and compare it against previously offered approaches in terms of maneuver time and incurred throughput disruption.

Stackelberg packing games

Stackelberg pricing games are pricing problems over a set of items. One player, the leader, sets prices for the items and the second player, the follower, buys a subset of items at minimal total cost subject to feasibility constraints. The constraints are determined by an optimization problem. For example, the Stackelberg shortest path game is used to optimize the income from road tolls (cf. [21]). The items are edges in a network graph and the follower buys a subset of edges forming a path.The Stackelberg pricing games studied in the literature are formulated on top of covering problems. In this paper, we introduce pricing games based on packing problems. We are interested in the complexity of computing leader-optimal prices depending on different types of follower-constraints. We show that optimal prices can be computed in polynomial time if the follower-constraints are determined by the well-known interval scheduling problem. This problem is equivalent to the independent set problem on interval graphs. In case the follower-constraints are based on the independent set problem on perfect graphs or on the bipartite matching problem, we prove APX-hardness for the pricing problem.On a more general note, we prove Σ2p-completeness if the follower-constraints are given by a packing problem that is NP-complete, i.e., the leader's pricing problem is hard even if she has an NP-oracle at hand.

MPC Trajectory Feasibility Constraints for Self-Powered Control Systems

A self-powered control system derives the energy to power its operation entirely from the dynamics of the plant in which it is embedded. Each actuator is a transducer capable of injecting energy into, as well as removing energy from, the plant. Removed energy is stored for reuse in rechargeable energy storage subsystems. Control inputs are physically constrained by the requirement that the system does not exhaust these energy storage subsystems. This article analyzes model-predictive control (MPC) trajectory feasibility for self-powered control systems. Specifically, we examine the case in which the MPC algorithm formulates a discrete-time zero-order-hold control trajectory, for which the energy constraints are approximately enforced by using response information only at discrete sample times. It is shown that continuous-time control feasibility can be ensured by conservatively overbounding the transmission loss model. The analysis is conducted both for the case in which future disturbances are known deterministically and the case in which they are uncertain but bounded. The methodology is demonstrated on an example pertaining to vibration control.

DNN-based policies for stochastic AC OPF

A prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these uncertainties by computing dispatch decisions and control policies that maintain feasibility under uncertainty. Most SOPF formulations consider simple control policies such as affine policies that are mathematically simple and resemble many policies used in current practice. Motivated by the efficacy of machine learning (ML) algorithms and the potential benefits of general control policies for cost and constraint enforcement, we put forth a deep neural network (DNN)-based policy that predicts the generator dispatch decisions in real time in response to uncertainty. The weights of the DNN are learnt using stochastic primal–dual updates that solve the SOPF without the need for prior generation of training labels and can explicitly account for the feasibility constraints in the SOPF. The advantages of the DNN policy over simpler policies and their efficacy in enforcing safety limits and producing near optimal solutions are demonstrated in the context of a chance constrained formulation on a number of test cases.

Dynamic optimization of state-dependent switched systems with free switching sequences

Without necessarily assuming that switching sequences are fixed, a dynamic optimization method is proposed for optimal control of state-dependent switched systems. First, a parameterization method is developed to parameterize the switching instants and control vectors to facilitate the calculation of the gradient information, and then the original problem becomes a finite-dimensional mixed discrete–continuous nonlinear program as the switching sequence is discrete and the other variables are continuous. Secondly, the mixed discrete–continuous nonlinear program is transformed into an equivalent problem that contains only continuous variables by relaxing 0 and 1 discrete variables into continuous variables between 0 and 1 and adding proper linear and quadratic constraints. Thirdly, the formulas to compute the gradients of the objective function with respect to all the arguments are derived by solving the variational systems and a two-point boundary value differential algebraic equations (DAEs). Fourthly, an algorithm is proposed to locate a feasible point satisfying the Karush–Kuhn–Tucker (KKT) conditions to a specified tolerance of dynamic optimization of switched systems (DOSS) while guaranteeing feasibility of inequality path constraints, and the finite convergence of the algorithm is proved. Finally, the performance of the algorithm is analyzed via a numerical example.

The paired mail carrier problem

Often traditional mail carrier models assume that one carrier is assigned to each truck. This carrier drives the truck according to a delivery route, gets out of the truck at a stop, and services customers using a walking loop. We introduce the Paired Mail Carrier Problem (PMCP), which allows for two mail carriers per truck. If at least one carrier is in the truck, the truck may move forward. Given two mail carriers per truck, the objective is to minimize the time from the start to the end of the route while ensuring that each service stop is fully serviced and obeys all feasibility constraints. We develop a mixed integer programming (MIP) formulation and two fast heuristics for the PMCP. The MIP formulation obtains optimal solutions for smaller instances within reasonable running times. Furthermore, we demonstrate that, in addition to being very efficient (running time is on the order of milliseconds, even for large instances), our heuristics are near-optimal (within 5% of optimality) on instances up to 80 stops. More importantly, we evaluate the impact of the paired mail carrier (PMC) setting on both a one-truck situation and a fleet (multiple trucks) situation, relative to the single mail carrier (SMC) setting. Overall, the PMC setting not only can accomplish over 50% extra work within the same shift hours but also can lead to 22% cost savings. Finally, we discuss an extension where we can have three or more mail carriers per truck.

Integrated energy system region model with renewable energy and optimal control method

In the context of global energy transition, integrated regional energy systems containing renewable energy sources play an important role. While improving the economic and carbon efficiency of energy utilization, renewable energy sources also bring research challenges to the safe and reliable operation of energy systems. Based on the region concept, a region model and optimal control method for integrated energy systems containing renewable energy are proposed. Firstly, the key pipeline is taken as the observation object, and the feasible region model of the integrated energy system is determined according to the capacity of key equipment and its pipeline capacity with the multi-energy balance equation as the feasible constraint. Then, considering the mutual backup relationship of different equipment and pipelines, the regional integrated energy system security region model is constructed based on the N-1 security criterion, and the optimal control method based on the region concept is proposed. Finally, the validity of the model is analyzed with arithmetic examples, and the influence of the access capacity and access location of renewable energy on the feasible and safe regions of the regional integrated energy system is discussed. And according to the actual situation of the working state point, the optimal adjustment strategy based on the efficiency function and security constraint is given.

A Validated Preharvest Sampling Simulation Shows that Sampling Plans with a Larger Number of Randomly Located Samples Perform Better than Typical Sampling Plans in Detecting Representative Point-Source and Widespread Hazards in Leafy Green Fields.

Commercial leafy greens customers often require a negative preharvest pathogen test, typically by compositing 60 produce sample grabs of 150 to 375 g total mass from lots of various acreages. This study developed a preharvest sampling Monte Carlo simulation, validated it against literature and experimental trials, and used it to suggest improvements to sampling plans. The simulation was validated by outputting six simulated ranges of positive samples that contained the experimental number of positive samples (range, 2 to 139 positives) recovered from six field trials with point source, systematic, and sporadic contamination. We then evaluated the relative performance between simple random, stratified random, or systematic sampling in a 1-acre field to detect point sources of contamination present at 0.3% to 1.7% prevalence. Randomized sampling was optimal because of lower variability in probability of acceptance. Optimized sampling was applied to detect an industry-relevant point source [3 log(CFU/g) over 0.3% of the field] and widespread contamination [-1 to -4 log(CFU/g) over the whole field] by taking 60 to 1,200 sample grabs of 3 g. More samples increased the power of detecting point source contamination, as the median probability of acceptance decreased from 85% with 60 samples to 5% with 1,200 samples. Sampling plans with larger total composite sample mass increased power to detect low-level, widespread contamination, as the median probability of acceptance with -3 log(CFU/g) contamination decreased from 85% with a 150-g total mass to 30% with a 1,200-g total mass. Therefore, preharvest sampling power increases by taking more, smaller samples with randomization, up to the constraints of total grabs and mass feasible or required for a food safety objective. IMPORTANCE This study addresses a need for improved preharvest sampling plans for pathogen detection in leafy green fields by developing and validating a preharvest sampling simulation model, avoiding the expensive task of physical sampling in many fields. Validated preharvest sampling simulations were used to develop guidance for preharvest sampling protocols. Sampling simulations predicted that sampling plans with randomization are less variable in their power to detect low-prevalence point source contamination in a 1-acre field. Collecting larger total sample masses improved the power of sampling plans in detecting widespread contamination in 1-acre fields. Hence, the power of typical sampling plans that collect 150 to 375 g per composite sample can be improved by taking more, randomized smaller samples for larger total sample mass. The improved sampling plans are subject to feasibility constraints or to meet a particular food safety objective.

On advance payments in tenders with budget constrained contractors

AbstractWe consider procurement auctions in settings where potential contractors have limited funds and face ex post risks, that is, cost overruns that can lead to the contractors' defaults. The bidding strategies and the default decisions are shaped by the incentive—willing to finish—constraints, and the resource—able to finish and feasibility—constraints. We examine payment schemes where the advance share of the award is paid immediately after the auction with the rest payable upon successful completion of the project. We identify the trade‐offs the procurer faces when choosing among such schemes, and explore the factors that influence the optimal advance share.