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Recently, numerous investors have shifted from active strategies to passive strategies because the passive strategy approach affords stable returns over the long term. Index tracking is a popular passive strategy. Over the preceding year, most researchers handled this problem via a two-step procedure. However, such a method is a suboptimal global-local optimization technique that frequently results in uncertainty and poor performance. This paper introduces a framework to address the comprehensive index tracking problem (IPT) with a joint approach based on metaheuristics. The purpose of this approach is to globally optimize this problem, where optimization is measured by the tracking error and excess return. Sparsity, weights, assets under management, transaction fees, the full share restriction, and investment risk diversification are considered in this problem. However, these restrictions increase the complexity of the problem and make it a nondeterministic polynomial-time-hard problem. Metaheuristics compose the principal process of the proposed framework, as they balance a desirable tradeoff between the computational resource utilization and the quality of the obtained solution. This framework enables the constructed model to fit future data and facilitates the application of various metaheuristics. Competitive results are achieved by the proposed metaheuristic-based framework in the presented simulation.

In tilt-rotor UAVs, both the fuselage and tilting rotors contribute to the vehicle’s rotational motion. Consequently, the system’s dynamics rise to a highly-nonlinear system, making it challenging to find feasible and desired control solutions. The common control practices devise a logic-based controller to switch between different flight modes or map the control inputs to the conventional helicopter-type control inputs. However, they fail to provide energy-efficient fast trajectory tracking, especially in the presence of external disturbances. This paper proposes a general-model dynamic formulation and a two-layered constrained model predictive control (MPC) strategy to tackle the trajectory tracking problem for tilt-rotor UAVs. After splitting the vehicle’s dynamics into translational and rotational parts, a constrained linear MPC (LMPC) is designed for the translational dynamics to follow a reference trajectory. We formulate the LMPC as a quadratically-constrained quadratic problem that leads to a feasible set-point solution for the rotational control layer without violating the physical constraints. Also, an optimizer is designed to generate a thrust vector, which leverages the vehicle’s full potential via a continuous transition between the rotation in the fuselage and that in tilting rotors. In the second layer, the nonlinear rotational dynamics are approximated via piecewise affine subsystems. A constrained robust switching MPC with mode-dependent dwell time (MDT) is then designed to follow the first layer’s generated trajectories (Euler angles and thrust vectors). By providing admissible MDTs, the rotational dynamics feasibility, stability, and robustness are preserved in the presence of disturbances. Also, by employing an augmented dynamic model, this control design would allow for directly incorporating actuator constraints into the problem formulation. We demonstrate the controller’s performance and effectiveness via simulations.

In recent years, distributionally robust optimization (DRO) has received a lot of interest due to its ability to reduce the worst-case risk when there is a perturbation to the data-generating distribution. A good statistical model is expected to perform well on both the normal and the perturbed data. On the other hand, variable selection and regularization is a research area that aims to identify the important features and remove the redundant ones. It helps to improve the prediction accuracy as well as the interpretability of the model. In this paper, we propose an optimization model that is a regularized version of the canonical distributionally robust optimization (DRO) problem where the ambiguity set is described by a general class of divergence measures that admit a suitable conic structure. The divergence measures we examined include several popular divergence measures used in the literature such as the Kullback–Leibler divergence, total variation, and the Chi-divergence. By exploiting the conic representability of the divergence measure, we show that the regularized DRO problem can be equivalently reformulated as a nonlinear conic programming problem. In the case where the regularization is convex and semi-definite programming representable, the reformulation can be further simplified as a tractable linear conic program and hence can be efficiently solved via existing software. More generally, if the regularization can be written as a difference of convex functions, we demonstrate that a solution for the regularized DRO problem can be found by solving a sequence of conic linear programming problems. Finally, we apply the proposed regularized DRO model to both simulated and real financial data and demonstrate its superior performance in comparison with some non-robust models.

In this manuscript, we study a benchmark tracking problem when prices evolve through a Binomial model with a random environment. The agent invests a given fund’s capital into different assets in a predetermined market to replicate at each stage of time a financial index or benchmark. To measure the actual deviation between the agent’s wealth and the current benchmark, we apply a deviation error expressed as a total sum of quadratic functions. We also assume the agent is obligated to change her/his investment between two markets when it is mandatory. This obligation happens when the fund’s wealth falls down a predetermined bankruptcy barrier. The dynamic programming method is then used to get optimal investment strategies that minimize the deviation error as well as to characterize the minimum deviation. We also apply the so-called potential function to analyze the influence of the environment on the prices. Numerical simulations are provided to illustrate our results.

This study addresses the robust consensus tracking problem of multi-agent systems with uncertain Lur’e-type non-linear dynamics under a fixed topology. To achieve consensus tracking, a class of discontinuous control protocols are first proposed, which rely on the relative information among the neighbouring agents. Theoretical analysis indicates that the robust consensus tracking of uncertain Lur’e network can be achieved if the coupling strength and the control gain are both larger than the thresholds depending on some global information of the network. Then, an adaptive consensus tracking protocol is further designed to solve the robust consensus tracking problem as a modification of a fully distributed version without the need of any global information of the multi-agent systems. Furthermore, as an expansion of the discontinuous protocols, a new class of continuous control laws are developed based on the boundary layer concept. Finally, a couple of examples are given to illustrate the effectiveness of the theoretical results.

In this paper, we solve a stochastic linear quadratic tracking problem. The controlled dynamical system is modeled by a system of linear Itô differential equations subject to jump Markov perturbations. We consider the case when there are two decision-makers and each of them wants to minimize the deviation of a preferential output of the controlled dynamical system from a given reference signal. We assume that the two decision-makers do not cooperate. Under these conditions, we state the considered tracking problem as a problem of finding a Nash equilibrium strategy for a stochastic differential game. Explicit formulae of a Nash equilibrium strategy are provided. To this end, we use the solutions of two given terminal value problems (TVPs). The first TVP is associated with a hybrid system formed by two backward nonlinear differential equations coupled by two algebraic nonlinear equations. The second TVP is associated with a hybrid system formed by two backward linear differential equations coupled by two algebraic linear equations.

Investing vast amounts of money with the goal of fostering medium to long-term growth in returns is a challenging task in financial optimization. A method might be mirroring the market index as closely as possible by choosing from the stocks that make up the index. This approach is known as index tracking and the objective of this paper is to address this problem in order to solve it by means of mathematical programming techniques. In particular, we are interested in investigating the index tracking problem (ITP) as a mixed integer linear program in presence of some real-world constraints known as cardinality constraints as well as transaction costs. These ITP models are NP-hard, and consequently, difficult to solve by classical exact methods even for medium-sized instances. In order to overcome this issue, we propose a method based on nonconvex programming techniques. More precisely, we reformulate the problem as a difference of convex functions (DC) program and solve it by means of an approach known as DC algorithm. In order to evaluate the performance of the proposed algorithm, we conducted numerical experiments using benchmark instances. The results of the algorithm are compared with those provided by the state-of-the-art MILP solver Gurobi. The numerical results confirm the efficiency of the method in solving the ITP.

We introduce a novel variant of GNN for particle tracking—called Hierarchical Graph Neural Network (HGNN). The architecture creates a set of higher-level representations which correspond to tracks and assigns spacepoints to these tracks, allowing disconnected spacepoints to be assigned to the same track, as well as multiple tracks to share the same spacepoint. We propose a novel learnable pooling algorithm called GMPool to generate these higher-level representations called “super-nodes”, as well as a new loss function designed for tracking problems and HGNN specifically. On a standard tracking problem, we show that, compared with previous ML-based tracking algorithms, the HGNN has better tracking efficiency performance, better robustness against inefficient input graphs, and better convergence compared with traditional GNNs.

This paper investigates the trajectory tracking problem of the quadrotor unmanned aerial vehicles (UAV) with consideration of both attitude and position dynamics. First of all, the trajectory tracking problem is divided into the commands tracking in position and attitude loops by introducing the virtual attitude angle commands. Secondly, the high-order sliding mode observers (HSMOs) are introduced to estimate the lumped disturbances in position loop and the derivatives of the attitude angle tracking errors, the lumped disturbances in the attitude loop. And then the composite nonlinear dynamical inversion controller in position loop and the composite nonsingular terminal sliding mode controller in attitude loop are constructed by introducing the estimation information of HSMOs into controller design process. Finally, the simulations based on the data of a practical UAV are carried out to verify the effectiveness of the proposed method.

In this paper, an extended state observer based fractional‐order sliding mode control strategy is studied for vehicle steer‐by‐wire systems (SBWSs). The parameter perturbation and external interference are considered in the dynamic model of SBWSs. A fractional‐order sliding mode control scheme is designed to solve the tracking problem and improve the control performance. An extended state observer is further used to estimate the lumped disturbance, and then the estimated value is considered as a feedforward compensation to reduce the chattering phenomenon. Finally, comparison simulation results show that the excellent steering tracking and strong robustness performance have been achieved by the proposed control strategy for SBWSs. A fractional‐order sliding mode control with extended state observer strategy is studied to control a vehicle steer‐by‐wire system. It investigates the dynamic equation of motion of steer‐by‐wire system with lumped disturbance. An extended state observer is used to estimate the lumped disturbance and provide with a compensation.