Original Constraints Research Articles

Reinforcement Learning for Fuselage Shape Control during Aircraft Assembly

Critical safety requirements necessitate ultra-high precision quality control during the assembly of large aerospace components to reduce the mismatch between parts to be joined. Traditional methods use heuristic shape adjustment or surrogate model-based control. These methods are limited by reliance on accurate model learning and inadequate robustness to varying initial assembly conditions. To address these limitations, this paper proposes a model-free reinforcement learning approach for adaptive fuselage shape control during aircraft assembly. The trained reinforcement learning agent directly adjusts the aircraft components in response to their part variations and enables an autonomous system (like AlphaGo) to learn the optimal shape control policy. Specifically, the reinforcement learning environment is built on the finite element simulator. A reward function is developed to capture the optimization objective and introduces a scheme to enforce the original constraints. The proximal policy optimization algorithm is modified to speed up the learning progress and achieve better final performance. In the case study, the root-mean-square gap between components is reduced by 98.4% on average compared with their initial shape mismatch. Our proposed method outperforms the benchmark methods with smaller final shape errors, smaller maximum forces, and lower variations across different test samples.

Optimal IOFL-based economic model predictive control technique for boiler-turbine system

The optimal control design of the boiler-turbine system is vital to ensure feasibility and high responsiveness over desired load variations. Using the traditional linear control techniques realization of this task is difficult, as the boiler-turbine mechanism has strong nonlinearities. Besides, environmental and economic concerns have replaced existing tracking control ones as the primary concerns of advanced power plants. Thus, this study proposes an optimal economic model predictive controller (EMPC) scheme for this unit on the basis of the input/output feedback linearization (IOFL) method. By employing the IOFL method, this unit is decoupled into a new linearized model that is utilized for developing the suggested optimal IOFL EMPC technique. The proposed control scheme is formulated in an economic quadratic programming form that considers the input-rate and input limits of the unit for optimal economic performance. In addition, an adaptive iterative algorithm is utilized for constraints mapping with guaranteeing a feasible solution in a finite number of steps without violation of original constraints over the entire predictive horizon. The outcomes of the simulation show that the suggested optimal IOFL EMPC scheme offers an improved dynamic and economic output performance over fuzzy hierarchical MPC, fuzzy EMPC, and nonlinear EMPC techniques during various load variations.

Adaptive Decentralized Control for Constrained Strong Interconnected Nonlinear Systems and Its Application to Inverted Pendulum.

This work is dedicated to adaptive decentralized tracking control for a class of strong interconnected nonlinear systems with asymmetric constraints. Currently, there are few related studies on unknown strongly interconnected nonlinear systems with asymmetric time-varying constraints. To deal with the assumptions of the interconnection terms in the design process, which include upper functions and structural restrictions, the properties of Gaussian function in radial basis function (RBF) neural networks are applied to overcome this difficulty. By constructing the nonlinear state-dependent function (NSDF) and using a new coordinate transformation, the conservative step that the original state constraint converts into a new boundary of the tracking error is removed. Meanwhile, the virtual controller's feasibility condition is removed. It is proven that all the signals are bounded, especially the original tracking error and the new tracking error, which are both bounded. In the end, simulation studies are carried out to verify the effectiveness and benefits of the proposed control scheme.

Nash-equilibrium strategies of orbital Target-Attacker-Defender game with a non-maneuvering target

This study investigates the orbital Target-Attacker-Defender (TAD) game problem in the context of space missions. In this game, the Attacker and the Defender compete for a Target that is unable to maneuver due to its original mission constraints. This paper establishes three TAD game models based on the thrust output capabilities: unconstrained thrust output, thrust constrained by an upper bound, and fixed thrust magnitude. These models are then solved using differential game theory to obtain Nash equilibrium solutions for the game problems, and the correctness and effectiveness of the solution methods are verified through simulations. Furthermore, an analysis of the winning mechanisms of the game is conducted, identifying key factors that influence the game’s outcomes, including weight coefficients in payoffs, the maximum thrust acceleration limit, and the initial game state. Considering the unique characteristics of space missions, a specific focus is given to the analysis of the Defender’s initial states in the hovering formation and in-plane circling formation, revealing overall success patterns for defense strategies from these two formations. In summary, this study provides valuable insights into the control strategies and winning mechanisms of orbital TAD games, deepening our understanding of these games and offering practical guidance to improve success rates in real-world scenarios.

Joint track initiation of resolvable group target

This paper studies the problem of resolvable group target track initiation (RGTI) and proposes a novel method to obtain the discrete association vectors and continuous trajectory parameters of individual targets within the group, which benefits from the fitting representations of target tracks and the utilization of group target motion constraint. Specifically, every target track within the group is modeled as a weighted sum of a same set of time basis functions with different weights, and the aim is to solve multiple pairs of association vectors and trajectory parameters, i.e., unknown weights, according to the measurement equation and group target motion constraint. Next, a joint RGTI framework, which includes track extraction, track purification, trajectory parameter and association vector correction, is proposed to transform the original complex constraint set solving problem into multiple solvable sub-problems. And the convergence of RGTI is ensured through iterative optimization of track purification, trajectory parameter correction and association vector correction. Finally, simulation example demonstrates the superiority of the proposed method compared with existing multi-target track initiation methods.

A Reinforcement Learning-Based Incentive Mechanism for Task Allocation Under Spatiotemporal Crowdsensing

With the development of the Industrial Internet of Things (IoT), the work of large-scale data collection makes spatiotemporal crowdsensing (SC) play an important role. Mobile devices equipped with sensors could act as workers to collect and process data for uploading. In the task allocation process, a fully static allocation fails to meet the needs of realistic conditions, while a completely dynamic allocation fails to achieve the desired results. Therefore, we assume a task-scheduled execution scenario that combines the above two conditions. In the pre-allocation process, an original time location constraints (ORTA) allocation algorithm is first proposed. Then it is optimized (OPTA) to fully utilize the remaining time of the workers and increase the matched number. In addition, the design of the incentive mechanism is an effective means to improve the task completion rate of the platform. To efficiently utilize the limited platform budget in the long run, a Q-learning-based algorithm is proposed to identify target inspire tasks and subsequently increase their reward to attract workers’ participation. Finally, comparison experiments are conducted on real datasets to verify the effectiveness of our algorithm. Furthermore, the experiments on a Raspberry Pi local terminal are conducted under a satellite-based environment.

Immersed Boundary Double Layer method: An introduction of methodology on the Helmholtz equation

The Immersed Boundary (IB) method of Peskin (1977) [1] is useful for problems that involve fluid-structure interactions or complex geometries. By making use of a regular Cartesian grid that is independent of the geometry, the IB framework yields a robust numerical scheme that can efficiently handle immersed deformable structures. Additionally, the IB method has been adapted to problems with prescribed motion and other PDEs with given boundary data. IB methods for these problems traditionally involve penalty forces which only approximately satisfy boundary conditions, or they are formulated as constraint problems. In the latter approach, one must find the unknown forces by solving an equation that corresponds to a poorly conditioned first-kind integral equation. This operation can therefore require a large number of iterations of a Krylov method, and since a time-dependent problem requires this solve at each step in time, this method can be prohibitively inefficient without preconditioning. This work introduces a new, well-conditioned IB formulation for boundary value problems, called the Immersed Boundary Double Layer (IBDL) method. In order to lay the groundwork for similar formulations of Stokes and Navier-Stokes equations, this paper focuses on the Poisson and Helmholtz equations to introduce the methodology and to demonstrate its efficiency over the original constraint method. In this double layer formulation, the equation for the unknown boundary distribution corresponds to a well-conditioned second-kind integral equation that can be solved efficiently with a small number of iterations of a Krylov method without preconditioning. Furthermore, the iteration count is independent of both the mesh size and spacing of the immersed boundary points. The method converges away from the boundary, and when combined with a local interpolation, it converges in the entire PDE domain. Additionally, while the original constraint method applies only to Dirichlet problems, the IBDL formulation can also be used for Neumann boundary conditions.

Stability constraints in a 3D knapsack problem with non parallelepipedic items

This paper concerns stability issues that we encountered while solving an industrial pallet loading problem. The practical problem can be modeled as a three-dimensional knapsack with original constraints related to the stability of the pallet: when the placement of the boxes on the pallet is computed, the weight of the boxes and the placement sequence are not known.Despite this lack of information, the placement must remain stable throughout the construction of the pallet. Even more important, the major difference with classical placement problems is that the boxes are parallelepipedic rectangle with edge reduction (the upper surface may be smaller than the bottom face).In this paper, we review stability constraints used in the literature and the assumptions under which these constraints can be used and we detail their adequacy to the problem we consider. We then propose a new stability constraint which takes into account the practical features, which can be integrated into a placement algorithm and which is not too restrictive.Numerical experiments on benchmarks from the literature show that this constraint, added to a classical placement algorithm, obtains results which are similar to algorithms from the literature dedicated to a specific stability constraint for parallelepipedic boxes. By adjusting the benchmark to take into account the practical problem specificities, we show that this new stability constraint is perfectly suited to the industrial problem and obtains very good results compared to classical constraints. Therefore, it has been integrated in the placement software developed by the company.

Estimator-Based Reinforcement Learning Consensus Control for Multiagent Systems With Discontinuous Constraints.

This article focuses on the optimal consensus control problem for multiagent systems (MASs) with discontinuous constraints. The case of discontinuous constraints is a particular instance of state constraints, which has been studied less but occurs in many practical situations. Due to the discontinuous constraint boundaries, the traditional barrier function-based backstepping methods cannot be used directly. In response to this thorny problem, a novel constraint boundary reconstruction technique is proposed by designing a class of switch-like functions. The technique can convert discontinuous constraint boundaries into continuous ones, and it strictly proves that when the states satisfy the transformed constraint boundaries, the original constraints are also absolutely fulfilled. Meanwhile, with the aid of the barrier function and distributed event-triggered estimator, an improved coordinate transformation is constructed, which can remove the "feasibility condition" and simplify the controller design. In addition, by introducing prediction error and revised term into the learning process of neural networks (NNs), the optimal consensus problem is resolved by constructing a modified reinforcement learning strategy. Finally, the stability of the MASs is testified through the Lyapunov stability theory, and a simulation example verifies the effectiveness of the proposed method.

NN-Based Reinforcement Learning Optimal Control for Inequality-Constrained Nonlinear Discrete-Time Systems With Disturbances.

Based on actor-critic neural networks (NNs), an optimal controller is proposed for solving the constrained control problem of an affine nonlinear discrete-time system with disturbances. The actor NNs provide the control signals and the critic NNs work as the performance indicators of the controller. By converting the original state constraints into new input constraints and state constraints, the penalty functions are introduced into the cost function, and then the constrained optimal control problem is transformed into an unconstrained one. Further, the relationship between the optimal control input and worst-case disturbance is obtained using the Game theory. With Lyapunov stability theory, the control signals are ensured to be uniformly ultimately bounded (UUB). Finally, the effectiveness of the control algorithms is tested through a numeral simulation using a third-order dynamic system.

Adaptive robust control for unmanned combat platform: Obstacles avoiding and dynamic trajectory tracking

AbstractThis paper proposes an adaptive robust control scheme to deal with the uncertainty problem of unmanned combat platform. Under the constraint of the controller, the rescue vehicle aims to follow the trajectory of the reconnaissance vehicle and avoid obstacles (e.g., craters and destroyed tanks), while they eventually reach the defined target location (an accident area). First, for the control objective, the original constraints are innovatively separated into two parts: arrival constraint and tracking‐avoidance constraint. An approximate constraint‐following control substitutes for the triple problem, and the constraint‐following error is subsequently established. Second, for the control strategy, a ‐measure is introduced to measure the constraint‐following error. To ensure the tracking‐avoidance constraint and the arrival constraint can be fully satisfied by the system, an adaptive robust control is designed. Finally, for the fast time‐varying uncertainty with unknown boundary, an adaptive law is introduced to evaluate the triple tracking‐avoidance‐arrival performance. In conclusion, the main contribution of this paper is to achieve triple tracking‐avoidance arrival for unmanned combat platform, and the problem of military detection and rescue on complex battlefields can be eliminated.

On inequality constraints in well-known optimisation problems: properties and applications

This work studies transportation, assignment, transshipment, shortest path, and dynamic lot sizing problems. Particularly, it shows how to modify their formulations to handle excess supply and node elimination. The paper proceeds by using the conservation of flow to derive the original constraints of these problems. Thereafter, a general form of the conservation of flow is used to reformulate these problems. The results are problems with inequality constraints. This paper shows that solving each of these new formulations returns the same optimal solution as its original form. It also shows how problems with inequality constraints can handle excess supply and node elimination. Along the way, some additional properties of these alternative formulations are explored.

Efficient Scenario Generation for Heavy-Tailed Chance Constrained Optimization

We consider a generic class of chance-constrained optimization problems with heavy-tailed (i.e., power-law type) risk factors. As the most popular generic method for solving chance constrained optimization, the scenario approach generates sampled optimization problem as a precise approximation with provable reliability, but the computational complexity becomes intractable when the risk tolerance parameter is small. To reduce the complexity, we sample the risk factors from a conditional distribution given that the risk factors are in an analytically tractable event that encompasses all the plausible events of constraints violation. Our approximation is proven to have optimal value within a constant factor to the optimal value of the original chance constraint problem with high probability, uniformly in the risk tolerance parameter. To the best of our knowledge, our result is the first uniform performance guarantee of this type. We additionally demonstrate the efficiency of our algorithm in the context of solvency in portfolio optimization and insurance networks. Funding: The research of B. Zwart is supported by the NWO (Dutch Research Council) [Grant 639.033.413]. The research of J. Blanchet is supported by the Air Force Office of Scientific Research [Award FA9550-20-1-0397], the National Science Foundation [Grants 1820942, 1838576, 1915967, and 2118199], Defense Advanced Research Projects Agency [Award N660011824028], and China Merchants Bank.

Incorporating Normalized L1 Penalty and Eigenvalue Constraint for Causal Structure Learning

Inferring causal relationships is key to data science. Learning causal structures in the form of directed acyclic graphs (DAGs) has been widely adopted for uncovering causal relationships, nonetheless, it is a challenging task owing to its exponential search space. A recent approach formulates the structure learning problem as a continuous constrained optimization task that aims to learn causal relation matrix. Following it are nonlinear variants that can uncover nonlinear causal relationships. However, the nonlinear variant which considers the ℓ1 penalty as part of its optimization objective may not effectively eliminate false predictions. In this paper, we investigate the defect of the model that the ℓ1 penalty cannot effectively make the relation matrix sparse, thus introduces false predictions. Besides, the acyclicity constraint is unable to identify large circles within the margin of identification error, thus is unable to guarantee acyclicity of inferred causal relationships. Based on the theoretical and empirical analysis of the defects, we propose the normalized ℓ1 penalty which replaces the original ℓ1 penalty with a normalized first-order matrix norm, and propose a constraint based on eigenvalue to substitute the original acyclicity constraint. We then compare our proposed model NEC with three models to show considerable performance improvement. We further conduct experiments to show the effectiveness of the normalized ℓ1 penalty and the eigenvalue constraint.

Primal–dual interior-point algorithm for symmetric model predictive control

This paper presents a primal–dual interior-point (pdip) optimization algorithm for solving extreme-scale model predictive control (mpc) problems with linear dynamics, polytopic constraints, and quadratic/linear costs which are all invariant under the symmetric-group. We show that exploiting symmetry can reduce the computational and memory burden of extreme-scale or fast-paced applications of mpc. Our algorithm transforms the original inputs, states, and constraints of the mpc problem into a symmetric domain. The premise of our algorithm is that the numerical linear algebra used to solve the optimization problem has lower computational and memory complexity in the transformed domain. We demonstrate our algorithm for a heating, ventilation, and air-conditioning (hvac) numerical example. We show that, for our largest hvac control problem, our symmetry exploiting the pdip algorithm reduces the computation-time from minutes to seconds in comparison with the baseline pdip algorithm. Furthermore, we show that the presented symmetry exploiting pdip algorithm outperforms a state-of-the-art symmetry exploiting optimization algorithm.

Minimizing Age of Information in Downlink Wireless Networks With Time-Varying Channels and Peak Power Constraint

The rapid development of real-time applications such as the Internet of Things (IoT) puts forward high requirements for the data freshness of wireless networks. The metric Age of Information (AoI) is adopted to measure the data freshness from the user side [1]. In this paper, we investigate the AoI-minimization problem of wireless networks with time-varying channels and the peak power constrained base station (BS). Firstly we model the time-varying channels as a multi-state ergodic Markov chain and formulate the multi-user scheduling problem. Next, we relax the original strict power constraint and formulate the relaxed problem as a constrained Markov decision process (CMDP). To reduce the computational complexity, we exploit the threshold structure of the optimal policy for the CMDP and search for the optimal policy via Linear programming (LP). To satisfy the original strict power constraint, we propose an truncated multi-user scheduling policy, which is proven asymptotic optimal. Finally, we simulate our proposed scheduling policy and compare the AoI performance with other policies. Simulation results verify the theoretical analysis and indicate that our policy can significantly reduce the AoI of users with bad channel quality, thus outperforming other policies.

Coexistence of Thread and Sheet Chaotic Attractors for Three-Dimensional Lozi Map

Since its original publication in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications have analyzed its particular structure or applied its properties in many fields (electronic devices such as memristors, A.I. with swarm intelligence, etc.). Several generalizations have been proposed, transforming the initial two-dimensional map into a multidimensional one. However, they do not respect the original constraint that allows this map to be one of the few strictly hyperbolic: a constant Jacobian. In this paper, we introduce a three-dimensional piece-wise linear extension respecting this constraint and we explore a special property never highlighted for chaotic mappings: the coexistence of thread chaotic attractors (i.e., attractors that are formed by a collection of lines) and sheet chaotic attractors (i.e., attractors that are formed by a collection of planes). This new three-dimensional mapping can generate a large variety of chaotic and hyperchaotic attractors. We give five examples of such behavior in this article. In the first three examples, there is the coexistence of thread and sheet chaotic attractors. However, their shapes are different and they are constituted by a different number of pieces. In the last two examples, the blow up of the attractors with respect to parameter a and b is highlighted.

Abnormal Status Detection of Catenary Based on TSNE Dimensionality Reduction Method and IGWO-LSSVM Model

Background: Catenary is a crucial component of an electrified railroad's traction power supply system. There is a considerable incidence of abnormal status and failures due to prolonged outside exposure. Driving safety will be directly impacted if an abnormal status or failure occurs. Currently, catenary detection vehicles are the most often utilized technique for gathering data and identifying faults based on manual experience. However, this technology cannot meet the demands of prompt detection and correction of faults in railways engineering due to its extremely low work efficiency. Objective: Based on the above, an abnormal status detection method of catenary based on the improved gray wolf (IGWO) algorithm optimized the least squares support vector machine (LSSVM) with the t-distributed stochastic neighbor embedding (TSNE) is proposed in this paper. In order to improve the accuracy of catenary abnormal status detection and shorten the detection time. Methods: Firstly, the TSNE dimensionality reduction technology is used to reduce the original catenary data to three-dimensional space. Then, in order to address the issue that the parameters of the LSSVM detection model are hard to determine, the improved GWO algorithm is used to optimize the penalty factor and kernel parameter in the LSSVM and establish the TSNE-IGWO-LSSVM catenary abnormal status detection model. Finally, contrasting experimental results of different detection models. The T-distributed Stochastic Domain Embedding (TSNE) is an improved nonlinear dimensionality reduction method based on the Stochastic Neighbor Embedding (SNE). TSNE no longer adopts the distance invariance in linear dimensionality reduction methods such as ISOMAP. TSNE is much better than the linear dimensionality reduction method in the reduction degree of the original dimension. The GWO algorithm, which is frequently used in engineering research, has the advantages of a simple model, great generalization capability, and good optimization performance. The premature convergence is one of the remaining flaws. By applying a good point set to initialize the gray wolf population and the nonlinear control parameters, the gray wolf algorithm is improved in this research. The IGWO algorithm effectively makes up for the problem of balancing the local exploitation and global search capabilities of GWO. Additionally, this IGWO algorithm performs the Cauchy variation operation on the current generation optimal solution to improve population diversity, enlarge the search space, and increase the likelihood of the algorithm escaping the local optimal solution in order to prevent the algorithm from failing the local optimum. The Least Squares Support Vector Machine (LSSVM) is an improved version of the Support Vector Machine (SVM), which replaces the original inequality constraint with a linear least squares criterion for the loss function. The kernel parameters of the RBF function and the penalty factor, these two parameters directly determine the detection effect of LSSVM. In this paper, the IGWO is utilized to adjust and determine the LSSVM parameters in order to enhance the detection capacity of the LSSVM model. Results:: In this paper, in order to minimize the experiment's bias, the training data and the test data are allocated in a ratio of 4:1, the training data are set to 400 groups, and the test data are set to 100 groups. After training the five models, the test data is used to validate and compare the detection capacity of the models. After each of the five detection models was tested ten times, the TSNE-IGWO-LSSVM model is compared with the IGWO-LSSVM model, the TSNE-FA-LSSVM model, the GWO-LSSVM model, and the GWO-ELM model, the results show that the TSNE-IGWO-LSSVM model has the highest average detection accuracy of 97.1% and the shortest running time of 26.9s. For the root mean squared error (RMSE) and the root mean squared error (RMSE), the TSNE-IGWO-LSSVM model is 0.17320 and 2.51% respectively, which is the best among the five models, indicating that it not only has higher detection accuracy but also better convergence of detection accuracy than the other models. Conclusions: With the thousands of miles of catenary and the complexity of the data, it is crucial to shorten the running time in order to improve the efficiency and ease the burden of the processors. The experiments demonstrate that the TSNE-IGWO-LSSVM detection model can detect the abnormal status of catenary more accurately and quickly, providing a new method for the abnormal status detection of catenary, which has certain application value and engineering significance in the era of fully electrified railways.

An efficient null-broadening adaptive beamformer based on magnitude response constraints

To reduce computational complexity of the minimum power distortionless response (MPDR) beamformer, a novel efficient null-broadening method based on magnitude response constraints is proposed in this paper. We convert the original quadratic power constraint to multiple first-order magnitude response constraints using Gauss-Legendre quadrature (GLQ) rather than eigenvalue decomposition (EVD). In addition, the number of first-order constraints only depends on the order of Legendre polynomials. Furthermore, based on the conjugate symmetry of the beamforming weight vector on centro-symmetric array, the nonlinear modular operation in magnitude response constraints is transformed into equivalent linear real operation. Finally, we relax the inequality constraints in the model into equality constraints, which can be solved by Lagrange multiplier method. Simulation shows that the proposed magnitude response constrained MPDR (MRC-MPDR) beamformer can achieve the same dynamic interference suppression capability as other beamformers with shorter calculation time.

A General Framework for Learning-Based Distributionally Robust MPC of Markov Jump Systems

We present a learning model predictive control (MPC) scheme for chance-constrained Markov jump systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show that under sufficient decrease of the confidence levels, the resulting MPC scheme renders the closed-loop system mean-square stable with respect to the true-but-unknown distributions, while remaining less conservative than a fully robust approach. Finally, we show that the value function of the learning MPC converges from above to its nominal counterpart as the sample size grows to infinity. We illustrate our approach on a numerical example.