Time-optimal Problem Research Articles

Public Policy Timing in a Sustainable Approach to Shaping Public Policy

This study addresses the problem of optimal public policy timing and the relation to public health policy. Ways of recognizing this problem are presented, as well as the role of public policy timing, which is perceived or can be performed from various economic theories and concepts, mainly: regulation theory; the concept of adaptive public policy; and the theory of policy timing based on the concepts of option value and the transaction costs of the political process. The approach of methodological pluralism adopted by the authors made it possible to reach for various cognitive inspirations borrowed from numerous theoretical approaches, in order to create a comprehensive and coherent theoretical foundation for the purposes of analyzing the role of timing in applied public policies. Next, an attempt was made to define the role of public policy timing in the applied approach, i.e., the case of Polish policy towards the public hospital care sector. The final conclusion is that the role of timing is marginalized in Polish public health policy. The time dimension of its creation was ignored or treated as an exogenous event in relation to the rest of the policy formulation process. There is no political approach that adaptively links the right combination of resources and regulatory activity to timing for specific stages of development or growth in public hospital care.

ПМП, (ко)присоединённое представление и нормальные геодезические левоинвариантных (суб)финслеровых метрик на группах Ли

С помощью основ теории групп и алгебр Ли, их (ко)присоединенных представлений и принципа максимума Понтрягина для задачи оптимального быстродействия даны независимое обоснование методов геодезического векторного поля поиска геодезических левоинвариантных (суб)финслеровых метрик на группах Ли и поиска соответствующих локально оптимальных управлений в (суб)римановом случае, а также несколько их применений.

Time Optimal Trajectories for a Mobile Robot Under Nonsliding and Radius-of-Turn Constraints

Abstract The time-optimal path problem for a point mass mobile robot is considered. Given initial and target states, we seek the time optimal path subject to the following constraints: (1) A limitation on its maximal linear acceleration; (2) a speed-dependent nonsliding condition; and (3) a minimal radius of turn. The paper formulates and analyzes the time optimal path problem using standard optimal control formulation with extensive use of the classical Hodograph method. Based on the analysis, the time optimal path consists of five path primitives. Numerical solutions are obtained to support and illustrate the analysis.

Performance of four meta-heuristics to solve a forestry production planning problem

The use of artificial intelligence as a tool to aid in the planning of forest production has gained more and more space. Highlighting the metaheuristics, due to the ability to generate optimal solutions for a given optimization problem in a short time, without great computational effort. The present study aims to evaluate the performance of the metaheuristics Genetic Algorithm, Simulated Annealing, Variable Neighborhood Search and Clonal Selection Algorithm applied in a model of regulation of forest production. It was considered a planning horizon of 16 years, in which the model aims to maximize the Net Present Value (NPV), having as restrictions age of cut between 5 and 7 years and minimum and maximum logging demand of 140,000 and 160,000 m3, respectively. Different combinations of configurations were considered for each of the metaheuristics, 30-second processing time and 30 replicates for each configuration, all processing being performed in MeP - Metaheuristics for forest Planning software. The Simulated Annealing metaheuristic obtained the best results when compared to the others, reaching the minimum and maximum demand demanded in all tested configurations, in contrast, the Genetic Algorithm was the one with the worst performance. Thus, the capacity to use metaheuristics as a tool for forest planning is observed.

Time optimal control based on classification of quantum gates

We study the minimum time to implement an arbitrary two-qubit gate in two heteronuclear spins systems. We give a systematic characterization of two-qubit gates based on the invariants of local equivalence. The quantum gates are classified into four classes, and for each class the analytical formula of the minimum time to implement the quantum gates is explicitly presented. For given quantum gates, by calculating the corresponding invariants one easily obtains the classes to which the quantum gates belong. In particular, we analyze the effect of global phases on the minimum time to implement the gate. Our results present complete solutions to the optimal time problem in implementing an arbitrary two-qubit gate in two heteronuclear spins systems. Detailed examples are given to typical two-qubit gates with or without global phases.

Segmentation of Certificate With Connected Component Labeling Method

Certificate is one of the documents that can be used as evidence of ownership or an event. For example, when certificate used as requirement to participate in an event. If a document is made as a requirement, of course the file verification process will be done. Seeing the time optimization problem when verifying the file, the authors carry out research by segmenting important data contained in a certificate as an initial step in the development of an automatic document verification system. The segmentation process carried out in this study uses the Connected Component Labeling method in determining the area to be segmented and Automatic Cropping to cut the results of the segmentation process. By using these two methods obtained an accuracy of 60% with a total of 15 pieces of test data

Energy efficiency resource allocation for D2D communication network based on relay selection

In order to solve the problem of spectrum resource shortage and energy consumption, we put forward a new model that combines with D2D communication and energy harvesting technology: energy harvesting-aided D2D communication network under the cognitive radio (EHA-CRD), where the D2D users harvest energy from the base station and the D2D source communicate with D2D destination by D2D relays. Our goals are to investigate the maximization energy efficiency (EE) of the network by joint time allocation and relay selection while taking into the constraints of the signal-to-noise ratio of D2D and the rates of the Cellular users. During this process, the energy collection time and communication time are randomly allocated. The maximization problem of EE can be divided into two sub-problems: (1) relay selection problem; (2) time optimization problem. For the first sub-problem, we propose a weighted sum maximum algorithm to select the best relay. For the last sub-problem, the EE maximization problem is non-convex problem with time. Thus, by using fractional programming theory, we transform it into a standard convex optimization problem, and we propose the optimization iterative algorithm to solve the convex optimization problem for obtaining the optimal solution. And, the simulation results show that the proposed relay selection algorithm and time optimization algorithm are significantly improved compared with the existing algorithms.

Local Controllability and a Family of Maximum Principles for a Free Time Optimal Control Problem

We introduce the concept of local controllability for a control system of ordinary differential equations with free time and provide sufficient conditions for its controllability. As a direct consequence, for time-optimal problems, we obtain necessary conditions for a local infimum---this notion generalizes that of an optimal trajectory. These conditions constitute a family of relations, each of which has the form of a maximum principle. Examples are given to demonstrate the meaningfulness of the necessary conditions obtained in the present paper, which generalize and strengthen the Pontryagin maximum principle.

A routing algorithm based on simulated annealing algorithm for maximising wireless sensor networks lifetime with a sink node

Energy saving becomes a central issue in the design of wireless sensor network routing algorithms. In the wireless sensor networks (WSNs), when intra-network communication is ensured, the lifetime of node can be extended by reducing data transmission or data volume as much as possible. However, the problem is that energy of the nodes around the sink node becomes exhausted quickly due to excessive communication overhead. To handle this problem, in this study, we propose a routing algorithm based on the sink node path optimisation. The study uses the energy consumption model as a constraint, transforms the time optimisation problem into an optimisation model, optimises the sink node path with the aid of simulated annealing (SA) algorithm, and uses data fusion to reduce the intra-network redundant data in the time domain. The proposed algorithm innovatively self-adjusts the path of sink node that is optimised by SA using new fitness function. Comprehensive simulation results show that the proposed algorithm can reduce the node energy consumption of waiting of sink node at the address of sink node, balance the network load and improve survival time of WSNs by 30% in comparison with results produced with the state-of-the art algorithms REAC-IN and DALMDT.

Wide band time optimal spectrum sensing

Conventional methods for spectrum sensing do not consider historical traffic data. Equal amount of time is allocated to each channel of interest for sensing. In this research paper, we formulate the time optimization problem for spectrum sensing keeping historical traffic data into account. We have solved the problem for interesting constraints. For the solution of these constraints stochastic programming formulation has been done. The problem is also formulated as a quadratic/hybrid programming problem where the variance of discrete random variable constitutes a quadratic form associated with a laplacian like matrix. Using this result, time optimal spectrum sensing is formulated as a multi-linear objective function optimization problem.

The minimal time function associated with a collection of sets

We define the minimal time function associated with a collection of sets which is motivated by the optimal time problem for nonconvex constant dynamics. We first provide various basic properties of this new function: lower semicontinuity, principle of optimality, convexity, Lipschitz continuity, among others. We also compute and estimate proximal, Fréchet and limiting subdifferentials of the new function at points inside the target set as well as at points outside the target. An application to location problems is also given.

Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems

We consider control-linear left-invariant time-optimal problems on step 2 Carnot groups with a strictly convex set of control parameters (in particular, sub-Finsler problems). We describe all Casimirs linear in momenta on the dual of the Lie algebra. In the case of rank 3 Lie groups we describe the symplectic foliation on the dual of the Lie algebra. On this basis we show that extremal controls are either constant or periodic. Some related results for other Carnot groups are presented.

Time-optimal trajectories for a trolley-like system with state constraint

We consider a time-optimal problem for trolley-like system (matherial point with inertia) passage from start to zero position (i.e. origin) under bounded control (acceleration) and linear state constraint. We solve it with Pontryagin maximum principle for state-constrained problems usage. We construct optimal trajectories synthesis and show that it is not simple “cut” of classical trolleyplike problem synthesis. State constraint generates “forbidden zone” bounded by state constraint boundary and half of parabola. We also shows that optimal trajectory (for selected range of state constraint line coefficient) has no more than three switching points (for the classical case, there is no more than one switching point). We analyse synthesis for different cases of parameters and demonstrates its evolution.

Joint Channel Assignment and Occupancy Time Optimization in Frame-Based Listen-Before-Talk

We study the performance optimization problem of the long term evolution (LTE) network operating in the unlicensed band and sharing it with an existing WiFi network. We consider the LTE network to be based on the frame-based listen-before-talk protocol. We formulate the joint channel assignment and channel occupancy time optimization problem using a stochastic integer programming (IP) model. By applying the Lyapunov drift-plus-penalty theorem, we develop an asymptotically optimal solution with polynomial time-complexity for the stochastic IP problem. Numerical results are presented and the performance of the proposed solution is compared to the performance of two alternative approaches in which the channel assignment and channel occupancy time are determined sequentially.

Autonomous racing using Linear Parameter Varying-Model Predictive Control (LPV-MPC)

This article presents an innovative control approach for autonomous racing vehicles. Linear Parameter Varying (LPV) theory is used to model the dynamics of the vehicle and implement an LPV-Model Predictive Controller (LPV-MPC) that can be computed online with reduced computational cost. The optimal time problem is solved by an optimal off-line trajectory planner that calculates the best trajectory under the constraints of the circuit. An identification of the system model based on optimization is also carried out. The planning and control scheme is validated in simulation and experimentally in a real platform where the effectiveness of the proposed LPV-MPC is demonstrated.

Logistic map and wavelet transform based differential evolution

Differential evolution (DE) is a popular evolutionary technique which can be applied in various constrained and unconstrained optimization problems along with the real time problems by modifying its operators like mutation, crossover and selection. In this paper initialization process of population along with the mutation rate is modified using the concept of logistic map and wavelet transformation in DE respectively. This modification increases the convergence rate. The modified proposal is tested on various benchmark problems. Also the evaluated results are compared for performance with state of the art algorithms, along with three real time non linear engineering problems, which dictates that the modified DE is easily applicable to the real time optimization problems.

Time Optimality for Systems with Multidimensional Control and Vector Moment Min-Problem

The linear time-optimal problem for some classes of linear systems with a multidimensional control is considered. The general position condition, which guarantees the uniqueness of the optimal control, is not assumed to be satisfied. We introduce a vector moment min-problem, which is a further development of the moment min-problem proposed by V.I. Korobov and G.M. Sklyar in 1987 for solving linear time-optimal problems with a one-dimensional control. In the paper the case of the time-optimal problem for linear systems with two-dimensional control is thoroughly studied by use of the vector moment min-problem.

Path-Following Control of Autonomous Underwater Vehicles Subject to Velocity and Input Constraints via Neurodynamic Optimization

In this paper, a design method is presented for path-following control of underactuated autonomous underwater vehicles subject to velocity and input constraints, as well as internal and external disturbances. In the guidance loop, a kinematic control law of the desired surge speed and pitch rate is derived based on a backstepping technique and a line-of-sight guidance principle. In the control loop, an extended state observer is developed to estimate the extended state composed of unknown internal dynamics and external disturbances. Then, a disturbance rejection control law is constructed using the extended state observer. To bridge the guidance loop and the control loop, a reference governor is proposed for computing optimal guidance signals within the velocity and input constraints. The reference governor is formulated as a quadratically constrained optimization problem. A projection neural network is employed for solving the optimization problem in real time. Simulation results illustrate the effectiveness of the proposed method for path-following control of autonomous underwater vehicles subject to constraints and disturbances simultaneously in the vertical plane.

Almost mixed semi-continuous perturbation of Moreau's sweeping process

In this work, we introduce a new concept of semi-continuous set-valued mappings, called almost mixed semi-continuity, by taking maps that are upper semi-continuous with almost convex values in some points and lower semi-continuous in remaining points. We generalize earlier results obtained for both mixed semi-continuous maps and almost convex sets. We discuss the existence of solution for evolution problems driven by the so-called sweeping process subject to external forces, known as perturbation to the system, by this type of set-valued mappings. Finally, we give some topological properties of the attainable and solution sets in order to solve an optimal time problem.

Asymptotic Optimality of a Time Optimal Path Parametrization Algorithm

Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed. However, its optimality was proved for only a strict subclass of problems solved optimally by more computationally intensive approaches based on convex programming. In this paper, we prove that the same linear-time algorithm is asymptotically optimal for all problems solved optimally by convex optimization approaches. We also characterize the optimum of the Time Optimal Path Parametrization Problem, which may be of independent interest.