This article considers the two-stage approach to solving a partially observable Markov decision process (POMDP): the identification stage and the (optimal) control stage. We present an inexact sequential quadratic pro...
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This article considers the two-stage approach to solving a partially observable Markov decision process (POMDP): the identification stage and the (optimal) control stage. We present an inexact sequential quadratic programming framework for recurrent neural network learning (iSQPRL) for solving the identification stage of the POMDP, in which the true system is approximated by a recurrent neural network (RNN) with dynamically consistent overshooting (DCRNN). We formulate the learning problem as a constrained optimization problem and study the quadratic programming (QP) subproblem with a convergence analysis under a restarted Krylov-subspace iterative scheme that implicitly exploits the structure of the associated Karush-Kuhn-Tucker (KKT) subsystem. In the control stage, where a feedforward neural network (FNN) controller is designed on top of the RNN model, we adapt a generalized Gauss-Newton (GGN) algorithm that exploits useful approximations to the curvature terms of the training data and selects its mini-batch step size using a known property of some regularization function. Simulation results are provided to demonstrate the effectiveness of our approach.
We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non-convex cont...
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We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non-convex continuous variable products. In this paper, we consider MIP relaxations based on separable reformulation. The main focus is the introduction of the enhanced separable MIP relaxation for non-convex quadratic products of the form z=xy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z=xy$$\end{document}, called hybrid separable (HybS). Additionally, we introduce a logarithmic MIP relaxation for univariate quadratic terms, called sawtooth relaxation, based on Beach (Beach in J Glob Optim 84:869-912, 2022). We combine the latter with HybS and existing separable reformulations to derive MIP relaxations of MIQCQPs. We provide a comprehensive theoretical analysis of these techniques, underlining the theoretical advantages of HybS compared to its predecessors. We perform a broad computational study to demonstrate the effectiveness of the enhanced MIP relaxation in terms of producing tight dual bounds for MIQCQPs. In Part II, we study MIP relaxations that extend the MIP relaxation normalized multiparametric disaggregation technique (NMDT) (Castro in J Glob Optim 64:765-784, 2015) and present a computational study which also includes the MIP relaxations from this work and compares them with a state-of-the-art of MIQCQP solvers.
This paper introduces a novel approach to solving time-varying quadratic programming (TVQP) problems with time-dependent constraints, using gradient-based differential neural networks (GDNN). We establish the theoreti...
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This paper introduces a novel approach to solving time-varying quadratic programming (TVQP) problems with time-dependent constraints, using gradient-based differential neural networks (GDNN). We establish the theoretical framework for both conventional gradient neural networks (CGNN) and GDNN models, highlighting their effectiveness in addressing dynamic optimization challenges. Comparative theoretical analyses show that the proposed GDNN model achieves higher accuracy than the CGNN model, significantly reducing solution errors with exponential convergence. Moreover, the use of a sign-bi-power activation function (SBPAF) ensures reasonable convergence times for the GDNN model. Our approach is validated through simulations of TVQP problems under specific constraints. The results demonstrate that while both models are capable of solving these problems, the GDNN model outperforms the CGNN model in minimizing optimization errors (residual errors), especially when varying the scaling factor gamma, the GDNN model also shows superior performance and more efficient convergence.
This article proposes a variable-gain fixed-time convergent and noise-tolerant error-dynamics based neurodynamic network (VGFxTNT-EDNN) to solve time-varying quadratic programming problems, while being robust to unkno...
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This article proposes a variable-gain fixed-time convergent and noise-tolerant error-dynamics based neurodynamic network (VGFxTNT-EDNN) to solve time-varying quadratic programming problems, while being robust to unknown noises. Unlike existing finite-time convergent EDNNs, the newly designed VGFxTNT-EDNN guarantees fixed-time convergence by dynamically adjusting its variable parameters. Moreover, the VGFxTNTEDNN effectively handles unknown noise, addressing a limitation of existing fixed-time or predefined-time convergent models, which typically assume that the noise is known. Theoretical analysis utilizing Lyapunov theory proves that the VGFxTNT-EDNN possesses fixed-time convergence and robustness properties. Numerical validations demonstrate superior noise tolerance and fixed-time convergence of the VGFxTNT-EDNN, as compared with the existing models. Finally, a path-tracking experiment is conducted by utilizing a Franka Emika Panda robot to verify the practicality of the VGFxTNT-EDNN.
Microgrids are fundamental elements in modern energy systems. Among the various microgrid components, the Energy Storage System (ESS) plays a pivotal role in ensuring system reliability, but its high cost and inevitab...
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Microgrids are fundamental elements in modern energy systems. Among the various microgrid components, the Energy Storage System (ESS) plays a pivotal role in ensuring system reliability, but its high cost and inevitable degradation over time pose significant challenges. Many current studies overlook the impact of ESS degradation on operational optimization, potentially leading to cost-ineffective systems. To address this gap, we introduce a quadratic ESS degradation model that captures intricate battery dynamics, such as State of Charge (SoC) and Depth of Discharge (DoD), using Markovian properties. Based on this model, we propose an optimal energy management framework for DC microgrids using quadratic programming (QP). The objective is to minimize the combined costs of degradation and electricity, considering the Time-of-Use (ToU) tariff while adhering to ESS constraints. This financially focused approach provides a pragmatic and economically aligned optimization strategy. Testing across various State of Health (SoH) scenarios demonstrates that our proposed model reduces total operational costs by 3-18%. This research advances microgrid optimization techniques and offers practical insights to enhance efficiency and economic resilience in real-world scenarios.
A sequential quadratic programming numerical method is proposed for American option pricing based on the variational inequality formulation. The variational inequality is discretized using the theta-method in time and...
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A sequential quadratic programming numerical method is proposed for American option pricing based on the variational inequality formulation. The variational inequality is discretized using the theta-method in time and the finite element method in space. The resulting system of algebraic inequalities at each time step is solved through a sequence of box-constrained quadratic programming problems, with the latter being solved by a globally and quadratically convergent, large-scale suitable reflective Newton method. It is proved that the sequence of quadratic programming problems converges with a constant rate under a mild condition on the time step size. The method is general in solving the variational inequalities for the option pricing with many styles of optimal stopping and complex underlying asset models. In particular, swing options and stochastic volatility and jump diffusion models are studied. Numerical examples are presented to confirm the effectiveness of the method.
Autonomous Underwater Vehicles (AUVs) play a significant role in ocean-related research fields as tools for human exploration and the development of marine resources. However, the uncertainty of the underwater environ...
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Autonomous Underwater Vehicles (AUVs) play a significant role in ocean-related research fields as tools for human exploration and the development of marine resources. However, the uncertainty of the underwater environment and the complexity of underwater motion pose significant challenges to the fault-tolerant control of AUV actuators. This paper presents a fault-tolerant control strategy for AUV actuators based onTakagi and Sugeno (T-S) fuzzy logic and pseudo-inverse quadratic programming under control constraints, aimed at addressing potential actuator faults. Firstly, considering the steady-state performance and dynamic performance of the control system, a T-S fuzzy controller is designed. Next, based on the redundant configuration of the actuators, the propulsion system is normalized, and the fault-tolerant control of AUV actuators is achieved using the pseudo-inverse method under thrust allocation. When control is constrained, a quadratic programming approach is used to compensate for the input control quantity. Finally, the effectiveness of the fuzzy control and fault-tolerant control allocation methods studied in this paper is validated through mathematical simulation. The experimental results indicate that in various fault scenarios, the pseudo-inverse combined with a nonlinear quadratic programming algorithm can compensate for the missing control inputs due to control constraints, ensuring the normal thrust of AUV actuators and achieving the expected fault-tolerant effect.
Time-variant quadratic programming (QP) with multi-type constraints including equality, inequality, and bound constraints is ubiquitous in practice. In the literature, there exist a few zeroing neural networks (ZNNs) ...
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Time-variant quadratic programming (QP) with multi-type constraints including equality, inequality, and bound constraints is ubiquitous in practice. In the literature, there exist a few zeroing neural networks (ZNNs) that are applicable to time-variant QPs with multi-type constraints. These ZNN solvers involve continuous and differentiable elements for handling inequality and/or bound constraints, and they possess their own drawbacks such as the failure in solving problems, the approximated optimal solutions, and the boring and sometimes difficult process of tuning parameters. Differing from the existing ZNN solvers, this article aims to propose a novel ZNN solver for time-variant QPs with multi-type constraints based on a continuous but not differentiable projection operator that is deemed unsuitable for designing ZNN solvers in the community, due to the lack of the required time derivative information. To achieve the aforementioned aim, the upper right-hand Dini derivative of the projection operator with respect to its input is introduced to serve as a mode switcher, leading to a novel ZNN solver, termed Dini-derivative-aided ZNN (Dini-ZNN). In theory, the convergent optimal solution of the Dini-ZNN solver is rigorously analyzed and proved. Comparative validations are performed, verifying the effectiveness of the Dini-ZNN solver that has merits such as guaranteed capability to solve problems, high solution accuracy, and no extra hyperparameter to be tuned. To illustrate potential applications, the Dini-ZNN solver is successfully applied to kinematic control of a joint-constrained robot with simulation and experimentation conducted.
Reactive kinematic control in velocity space is closely related to the Jacobian presented in the system. However, if the Jacobian is rank-deficient, certain task-space velocities become unachievable, leading to contro...
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This paper introduces a framework for implementing log-domain interior-point methods (LDIPMs) using inexact Newton steps. A generalized inexact iteration scheme is established that is globally convergent and locally q...
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This paper introduces a framework for implementing log-domain interior-point methods (LDIPMs) using inexact Newton steps. A generalized inexact iteration scheme is established that is globally convergent and locally quadratically convergent towards centered points if the residual of the inexact Newton step satisfies a set of termination criteria. Three inexact LDIPM implementations based on the conjugate gradient (CG) method are developed using this framework. In a set of computational experiments, the inexact LDIPMs demonstrate a 24-72% reduction in the total number of CG iterations required for termination relative to implementations with a fixed termination tolerance. This translates into an important computation time reduction in applications such as real-time optimization and model predictive control.
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