Unconstrained Counterpart Research Articles

Adaptive optimized backstepping tracking control for full‐state constrained nonlinear strict‐feedback systems without using barrier Lyapunov function method

AbstractIn this article, the problem of adaptive optimal tracking control is studied for nonlinear strict‐feedback systems. While not directly measurable, the states of these systems are subject to both time‐varying and asymmetric constraints. Bypassing the conventional barrier Lyapunov function method, the constrained system is transformed into its unconstrained counterpart, thereby obviating the need for feasibility conditions. A specially designed reinforcement learning (RL) algorithm, featuring an observer‐critic‐actor architecture, is deployed in an adaptive optimal control scheme to ensure the stabilization of the converted unconstrained system. Within this architecture, the observer estimates the unmeasurable system states, the critic evaluates the control performance, and the actor executes the control actions. Furthermore, enhancements to the RL algorithm lead to relaxed conditions of persistent excitation, and the design methodology for the observer overcomes the restrictions imposed by the Hurwitz equation. The Lyapunov stability theorem is applied for two primary purposes: to ascertain the boundedness of all signals within the closed‐loop system, and to ensure the accuracy of the output signal in tracking the desired reference trajectory. Finally, numerical and practical simulations are provided to corroborate the effectiveness of the proposed control strategy.

Comparison of supervised-learning approaches for designing a channelized observer for image quality assessment in CT.

The current paradigm for evaluating computed tomography (CT) system performance relies on a task-based approach. As the Hotelling observer (HO) provides an upper bound of observer performances in specific signal detection tasks, the literature advocates HO use for optimization purposes. However, computing the HO requires calculating the inverse of the image covariance matrix, which is often intractable in medical applications. As an alternative, dimensionality reduction has been extensively investigated to extract the task-relevant features from the raw images. This can be achieved by using channels, which yields the channelized-HO (CHO). The channels are only considered efficient when the channelized observer (CO) can approximate its unconstrained counterpart. Previous work has demonstrated that supervised learning-based methods can usually benefit CO design, either for generating efficient channels using partial least squares (PLS) or for replacing the Hotelling detector with machine-learning (ML) methods. Here we investigated the efficiency of a supervised ML-algorithm used to design a CO for predicting the performance of unconstrained HO. The ML-algorithm was applied either (1) in the estimator for dimensionality reduction, or (2) in the detector function. A channelized support vector machine (CSVM) was employed and compared against the CHO in terms of ability to predict HO performances. Both the CSVM and the CHO were estimated with channels derived from the singular value decomposition (SVD) of the system operator, principal component analysis (PCA), and PLS. The huge variety of regularization strategies proposed by CT system vendors for statistical image reconstruction (SIR) make the generalization capability of an observer a key point to consider upfront of implementation in clinical practice. To evaluate the generalization properties of the observers, we adopted a 2-step testing process: (1) achieved with the same regularization strategy (as in the training phase) and (2) performed using different reconstruction properties. We generated simulated- signal-known-exactly/background-known-exactly (SKE/BKE) tasks in which different noise structures were generated using Markov random field (MRF) regularizations using either a Green or a quadratic, function. The CSVM outperformed the CHO for all types of channels and regularization strategies. Furthermore, even though both COs generalized well to images reconstructed with the same regularization strategy as the images considered in the training phase, the CHO failed to generalize to images reconstructed differently whereas the CSVM managed to successfully generalize. Lastly, the proposed CSVM observer used with PCA channels outperformed the CHO with PLS channels while using a smaller training data set. These results argue for introducing the supervised-learning paradigm in the detector function rather than in the operator of the channels when designing a CO to provide an accurate estimate of HO performance. The CSVM with PCA channels proposed here could be used as a surrogate for HO in image quality assessment.

Balancing Constraints and Objectives by Considering Problem Types in Constrained Multiobjective Optimization.

Constrained multiobjective optimization problems widely exist in real-world applications. To handle them, the balance between constraints and objectives is crucial, but remains challenging due to non-negligible impacts of problem types. In our context, the problem types refer particularly to those determined by the relationship between the constrained Pareto-optimal front (PF) and the unconstrained PF. Unfortunately, there has been little awareness on how to achieve this balance when faced with different types of problems. In this article, we propose a new constraint handling technique (CHT) by taking into account potential problem types. Specifically, inspired by the prior work, problems are classified into three primary types: 1) I; 2) II; and 3) III, with the constrained PF being made up of the entire, part and none of the unconstrained counterpart, respectively. Clearly, any problem must be one of the three types. For each possible type, there exists a tailored mechanism being used to handle the relationships between constraints and objectives (i.e., constraint priority, objective priority, or the switch between them). It is worth mentioning that exact problem types are not required because we just consider their possibilities in the new CHT. Conceptually, we show that the new CHT can make a tradeoff among different types of problems. This argument is confirmed by experimental studies performed on 38 benchmark problems, whose types are known, and a real-world problem (with unknown types) in search-based software engineering. Results demonstrate that within both decomposition-based and nondecomposition-based frameworks, the new CHT can indeed achieve a good tradeoff among different problem types, being better than several state-of-the-art CHTs.

TESTING THE IMPACT OF INPUT AND OUTPUT SUBSTITUTABILITY IN NONPARAMETRIC PRODUCTION ANALYSIS: EVIDENCE FROM LIFE INSURANCE INDUSTRY IN INDIA

In this paper, two different variants (constrained and unconstrained) of a data envelopment analysis (DEA) model are used to compare inferences about production correspondence of the life insurance industry in India. While the unconstrained model implicitly assumes input substitutions and output transformations without their empirical verification, the constrained model explicitly incorporates weight restrictions on those inputs and outputs that are not substitutable and transformable, respectively. Our key findings are as follows. First, although the constrained model seems closely related to the notion of industry (structural) efficiency model, this link remains unexplored: we suggest a link between both models. Second, though the constrained model generates efficiency scores that are no more than those of its unconstrained counterpart, both models are in broad agreement in revealing that the life insurance industry experiences a sustained surge in its efficiency due to competition arising from insurance reforms adopted by the government over years, thus supporting the competition and X-efficiency hypothesis. Third, when the economic requirement of input substitutions is absent, both the models are found to give statistically significant results on efficiency ratings, returns to scale possibilities, and total factor productivity growth. In such a case, the unconstrained model generates benchmarking results based on an incorrect production frontier, which are potentially misleading and can hardly be used in managerial contexts. This finding, therefore, cautions the researchers not to blindly use any unconstrained model to evaluate the efficiency, productivity growth and returns to scale characterizations of firms without empirically verifying the presence/absence of input substitutions and output transformations.

Order-Constrained ROC Regression With Application to Facial Recognition

The receiver operating characteristic (ROC) curve is widely used to assess discriminative accuracy of two groups based on a continuous score. In a variety of applications, the distributions of such scores across the two groups exhibit a stochastic ordering. Specific examples include calibrated biomarkers in medical diagnostics or the output of matching algorithms in biometric recognition. Incorporating stochastic ordering as an additional constraint into estimation can improve statistical efficiency. In this article, we consider modeling of ROC curves using both the order constraint and covariates associated with each score given that the latter (e.g., demographic characteristics of the underlying subjects) often have a substantial impact on discriminative accuracy. The proposed method is based on the indirect ROC regression approach using a location-scale model, and quadratic optimization is used to implement the order constraint. The statistical properties of the proposed order-constrained least squares estimator are studied. Based on the theoretical results developed herein, we deduce that the proposed estimator can achieve substantial reductions in mean squared error relative to its unconstrained counterpart. Simulation studies corroborate the superior performance of the proposed approach. Its practical usefulness is demonstrated in an application to face recognition data from the “Good, Bad, and Ugly” face challenge, a domain in which accounting for covariates has hardly been studied.

Permutation flowshop scheduling with periodic maintenance and makespan objective

This paper addresses the permutation flowshop scheduling problem with availability constraints where the machines are not available cyclically and the starting and finishing times of the periodic unavailability intervals are known in advance. In our case, this constraint is due to the shift calendar in a company in the aerospace industry, where all machines must stop at the same time (shift changes, nights, weekends, etc.). In this company, shifts are formed by different teams of workers, and having one worker to complete the tasks of another worker is not desirable in terms of efficiency and quality of the operation. In the literature, this cyclical constraint is also reported due to preventive deterministic and fixed maintenance activities. For this reason, this constraint is known as periodic maintenance, and –to the best of our knowledge– it has been addressed for the single machine and parallel machines layouts, but not for the flowshop. For this layout, it can be observed that different scheduling problems may arise depending on the assumptions about the preemption of the operations. In our case, the preemption of operations is not allowed, and therefore, if an operation cannot be finished within the current availability period, then it should be scheduled in the next one. For this problem, the objective considered is the makespan minimisation. The structure and hardness of the problem depending on the size of the availability periods is studied using Mixed Integer Linear Programming and complete enumeration, in order to determine the range of values for the availability period that makes the problem under consideration to be substantially different than its classical (unconstrained) counterpart. For these cases, specific heuristics with different computational complexity are developed, and an extensive computational experience is carried out to establish the efficiency of the proposed heuristics. Additionally, an iterated greedy metaheuristic is employed, showing excellent results.

Energy storage in steady states under cyclic local energy input.

We study periodic steady states of a lattice system under external cyclic energy supply using simulation. We consider different protocols for cyclic energy supply and examine the energy storage. Under the same energy flux, we found that the stored energy depends on the details of the supply, period, and amplitude of the supply. Further, we introduce an adiabatic wall as an internal constraint into the lattice and examine the stored energy with respect to different positions of the internal constrain. We found that the stored energy for constrained systems is larger than its unconstrained counterpart. We also observe that the system stores more energy through large and rare energy delivery, comparing to small and frequent delivery.

Bayesian WIV Estimators for 3-D Bearings-Only TMA With Speed Constraints

This paper develops Bayesian weighted instrumental variable (WIV) estimators under equality and inequality speed constraints for the three-dimensional (3-D) bearings-only target motion analysis (TMA) problem, which show improved estimation accuracies compared to their unconstrained counterpart. Incorporating the speed constraint information into our previously proposed Bayesian WIV estimator imposes a quadratic constraint on this problem. Finding an optimal solution for the resulting non-convex problem is by no means straightforward. The main problem with iterative optimization methods such as the maximum a posteriori is that they require initialization and may converge to a local minimum if poorly initialized. Using advanced linear and nonlinear algebra techniques, non-iterative accurate estimators under equality and inequality constraints are developed for this problem. Furthermore, it is proven that the proposed equality constrained estimator is approximately asymptotically unbiased and that the inequality constrained estimator is the optimal solution. An approximate covariance matrix has also been developed for the constrained WIV under equality constraint. Simulation results indicate that the equality and inequality constrained estimators outperform their unconstrained counterpart in the simulated scenarios.

Multiple Kernel Clustering With Neighbor-Kernel Subspace Segmentation.

Multiple kernel clustering (MKC) has been intensively studied during the last few decades. Even though they demonstrate promising clustering performance in various applications, existing MKC algorithms do not sufficiently consider the intrinsic neighborhood structure among base kernels, which could adversely affect the clustering performance. In this paper, we propose a simple yet effective neighbor-kernel-based MKC algorithm to address this issue. Specifically, we first define a neighbor kernel, which can be utilized to preserve the block diagonal structure and strengthen the robustness against noise and outliers among base kernels. After that, we linearly combine these base neighbor kernels to extract a consensus affinity matrix through an exact-rank-constrained subspace segmentation. The naturally possessed block diagonal structure of neighbor kernels better serves the subsequent subspace segmentation, and in turn, the extracted shared structure is further refined through subspace segmentation based on the combined neighbor kernels. In this manner, the above two learning processes can be seamlessly coupled and negotiate with each other to achieve better clustering. Furthermore, we carefully design an efficient iterative optimization algorithm with proven convergence to address the resultant optimization problem. As a by-product, we reveal an interesting insight into the exact-rank constraint in ridge regression by careful theoretical analysis: it back-projects the solution of the unconstrained counterpart to its principal components. Comprehensive experiments have been conducted on several benchmark data sets, and the results demonstrate the effectiveness of the proposed algorithm.

Economic constraints and stock return predictability: A new approach

In this paper, we propose a new approach to impose economic constraints on the time-series forecasts of stock return. It is unlikely or risky for a rational investor to rely on forecast outliers to trade stocks. Given this, our new constraint approach truncates the stock return forecasts at the extremely positive and negative values. The empirical results suggest that the new economic constraint approach generate more accurate and reliable return forecasts than the unconstrained method for both univariate regression models and multivariate models. Furthermore, our new constraint approach also outperforms two prevailing constraint approaches of Campbell and Thompson (2008) and Pettenuzzo, Timmermann, and Valkanov (2014). In addition, a mean-variance investor can realize sizeable economic gains by using our new constraint approach to allocate asset relative to using unconstrained counterpart or other popular constrained models.

A paradox in time-consistency in the mean–variance problem?

We establish new conditions under which a constrained (no short-selling) time-consistent equilibrium strategy, starting at a certain time, will beat the unconstrained counterpart, as measured by the magnitude of their corresponding equilibrium mean–variance value functions. We further show that the pure strategy of solely investing in a risk-free bond can sometimes simultaneously dominate both constrained and unconstrained equilibrium strategies. With numerical experiments, we also illustrate that the constrained strategy can dominate the unconstrained one for most of the commencement dates (even more than 90%) of a prescribed planning horizon. Under a precommitment approach, the value function of an investor increases with the size of the admissible sets of strategies. However, this may fail to be true under the game-theoretic paradigm, as the constraint of time-consistency itself affects the value function differently when short-selling is and is not prohibited.

An efficient Peaceman–Rachford splitting method for constrained TGV-shearlet-based MRI reconstruction

ABSTRACTAs a fundamental application of compressive sensing, magnetic resonance imaging (MRI) can be efficiently achievable by exploiting fewer k-space measurements. In this paper, we propose a constrained total generalized variation and shearlet transform-based model for MRI reconstruction, which is usually more undemanding and practical to identify appropriate tradeoffs than its unconstrained counterpart. The proposed model can be facilely and efficiently solved by the strictly contractive Peaceman–Rachford splitting method, which generally outperforms some state-of-the-art algorithms when solving separable convex programming. Numerical simulations demonstrate that the sharp edges and grainy details in magnetic resonance images can be well reconstructed from the under-sampling data.

The compressive properties of sandwich structures based on an egg-box core design

Abstract Lightweight cores, based on an egg-box core design, have been manufactured using a simple compression-moulding technique. Two types of composite prepreg were used to manufacture the core materials, these being a woven carbon fibre reinforced epoxy and a woven glass fibre reinforced epoxy. The resulting cores were of a high quality, exhibiting little or no wrinkling following the manufacturing procedure. Subsequent compression tests at quasi-static rates of loading showed that the compression strength of the core depended strongly on the level of constraint applied during testing, with sandwich panels based on composite skins bonded to an egg-box core offering a load-bearing capability that was more than double that of its unconstrained counterpart. The quasi-static compression strength of the carbon-based cores has been shown to be slightly higher than the glass fibre systems, particularly at higher core densities. Local splitting damage at cell joining regions and crushing of the cell of the egg-box structure was identified as the primary failure mechanism in the sandwich panels. Impact tests, conducted using a drop-weight impact tower, have shown that the compression strength of the egg-box cores is higher at dynamic rates of loading than at quasi-static rates. Here again, the local splitting and crushing was the primary mode of failure in the sandwich structures. Finally, the finite element technique has been used to model the mechanical response of these core designs under both quasi-static and impact loading testing conditions. Here, agreement between the predicted and observed responses was found to be good for both extremes of loading-rate.

Optimal Lagrange multipliers for dependent rate allocation in video coding

In a typical video rate allocation problem, the objective is to optimally distribute a source rate budget among a set of (in)dependently coded data units to minimize the total distortion. Conventional Lagrangian approaches convert the lone rate constraint to a linear rate penalty scaled by a multiplier in the objective, resulting in a simpler unconstrained formulation. However, the search for the “optimal” multiplier – one that results in a distortion-minimizing solution among all Lagrangian solutions that satisfy the original rate constraint – remains an elusive open problem in the general setting. To address this problem, we are the first in the literature to construct a computation-efficient search strategy to identify this optimal multiplier numerically in the general dependent coding scenario. Specifically, we first formulate a general rate allocation problem where each data unit can be dependently coded at different quantization parameters (QP) using a previous unit as predictor, or left uncoded at the encoder and subsequently interpolated at the decoder using neighboring coded units. After converting the original rate-constrained problem to the unconstrained Lagrangian counterpart, we design an efficient dynamic programming (DP) algorithm that finds the optimal Lagrangian solution for a fixed multiplier. In extensive monoview and multiview video coding experiments, we show that for fixed target rate constraints, our algorithm is able to find the optimal multipliers in a distortion minimum sense among all Lagrangian solutions. Moreover, we show that our simple solution is able to compete with complex rate control (RC) solutions used in video compression standards such as HEVC and 3D-HEVC, which outlines the importance of the proper choice of the Lagrangian multipliers.

Unified Power Allocation for Receive Spatial Modulation Based on Approximate Optimization

In this paper, a novel unified power allocation (PA) framework is proposed for receive (pre-coding aided) spatial modulation (RSM). We find that the PA matrix design can be formulated as a non-convex quadratically constrained quadratic program (QCQP) problem, whose solution is generally intractable. To tackle this problem, we propose a pair of solvers having different trade-offs in terms of bit-error-rate and complexity. Specifically, we first propose a successive convex approximation (SCA) method, to convert the non-convex QCQP problem under consideration into a series of linear convex subproblems, where the latter can be easily solved by the classic polynomial-time-based optimization method, i.e., the interior point method. To further reduce the computational complexity, we propose an augmented Lagrangian multiplier (ALM) method, which transforms the challenging non-convex constrained PA optimization problem into its unconstrained counterpart, which can be efficiently solved by an iterative manner. Our simulation results show that both the proposed SCA and ALM methods are capable of substantially improving the system error performance compared with the conventional RSM system without PA as well as conventional PA-aided RSM schemes.

Solving Constrained TV2L1-L2 MRI Signal Reconstruction via an Efficient Alternating Direction Method of Multipliers

AbstractHigh order total variation (TV2) andℓ1based (TV2L1) model has its advantage over the TVL1 for its ability in avoiding the staircase; and a constrained model has the advantage over its unconstrained counterpart for simplicity in estimating the parameters. In this paper, we consider solving the TV2L1 based magnetic resonance imaging (MRI) signal reconstruction problem by an efficient alternating direction method of multipliers. By sufficiently utilizing the problem's special structure, we manage to make all subproblems either possess closed-form solutions or can be solved via Fast Fourier Transforms, which makes the cost per iteration very low. Experimental results for MRI reconstruction are presented to illustrate the effectiveness of the new model and algorithm. Comparisons with its recent unconstrained counterpart are also reported.

Constrained state estimation for stochastic jump systems: moving horizon approach

ABSTRACTWe discuss the state estimation advantages for a class of linear discrete-time stochastic jump systems, in which a Markov process governs the operation mode, and the state variables and disturbances are subject to inequality constraints. The horizon estimation approach addressed the constrained state estimation problem, and the Bayesian network technique solved the stochastic jump problem. The moving horizon state estimator designed in this paper can produce the constrained state estimates with a lower error covariance than under the unconstrained counterpart. This new estimation method is used in the design of the restricted state estimator for two practical applications.

Liquidity constraints and labor supply

In this paper we shed some light on how restrictions in financial markets, the so-called liquidity constraints, might act in affecting labour supply decisions of Italian workers. One way to neutralize the existence of binding liquidity constraints is simply by supplying additional labor, instead of reducing consumption. We estimate whether resorting to additional labor supply as a smoothing consumption device is at work by using the Italian Survey of Households Income and Wealth (SHIW). The longitudinal dimension of the SHIW dataset allows us to control for individual unobserved heterogeneity. We also use an IV strategy to address the endogeneity of our measure for credit constraints in labor supply equations due to time varying factors.Our results show that liquidity constraints increase the intensity in the supply of men׳s labor. Constrained men work, on average, 4hours more than their unconstrained counterpart. Self-employed workers turn out to be more sensitive to binding liquidity constraints, possibly because they are more flexible in adjusting the intensity of their labor supply.

The Constrained Misspecified Cramér–Rao Bound

The aim of this letter is to provide a constrained version of the misspecified Cramer–Rao bound (MCRB). Specifically, the MCRB is a lower bound on the error covariance matrix of any unbiased (in a proper sense) estimator of a deterministic parameter vector under misspecified models, i.e., when the true and the assumed data distributions are different. Here, we aim at finding an expression of the MCRB for estimation problems involving continuously differentiable equality constraints. Our proof generalizes the derivation of the classical constrained CRB (CCRB) by showing that the constrained MCRB (CMCRB) can be obtained by exploiting the building blocks of its unconstrained counterpart and a basis of the null space of the constraint’s Jacobian matrix. The conditions for the existence of the CMCRB are also discussed.

Reinforcement Learning of Potential Fields to achieve Limit-Cycle Walking

Reinforcement learning is a powerful tool to derive controllers for systems where no models are available. Particularly policy search algorithms are suitable for complex systems, to keep learning time manageable and account for continuous state and action spaces. However, these algorithms demand more insight into the system to choose a suitable controller parameterization. This paper investigates a type of policy parameterization for impedance control that allows energy input to be implicitly bounded: Potential fields. In this work, a methodology for generating a potential field-constrained impedance controller via approximation of example trajectories, and subsequently improving the control policy using Reinforcement Learning, is presented. The potential field-const rained approximation is used as a policy parameterization for policy search reinforcement learning and is compared to its unconstrained counterpart. Simulations on a simple biped walking model show the learned controllers are able to surpass the potential field of gravity by generating a stable limit-cycle gait on flat ground for both parameterizations. The potential field-constrained controller provides safety with a known energy bound while performing equally well as the unconstrained policy.