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An approach for optimal control of the interface between water and ferrofluid in a 2-D two-phase flow is proposed in the presence of a magnetic field generated by a matrix of driving electromagnets. First, a model combining Navier-Stokes equations and level set methods is developed. Since it is very computationally demanding, an approximate black-box model based on neural networks replacing the original model is constructed for the purpose of control design. In particular, one-hidden-layer feedforward neural networks with a different number of neurons are trained to predict the water-ferrofluid behavior with accuracy. Then, optimal control based on such black-box models is addressed by selecting the currents flowing in the electromagnets that minimize a cost function given by the symmetric difference between the desired shape and the actual interface separating water and ferrofluid. Numerical results based on both simulation and experimental data collected on the field showcase the effectiveness of the proposed approach.

The spatial and time behaviors of fluid flows at different Reynolds numbers and free-stream turbulence intensity levels are studied by combining dynamic mode decomposition (DMD) and moving horizon estimation to detect flow-regime transitions. In more detail, the norm of residuals provided by DMD when processing successive snapshots of the flow velocity field shows a trend that is identified by means of a moving horizon estimator based on a switching model. This allows detecting the change from stable to unstable flow regimes, which in turn enables to extract modes, frequencies, and growth rates of com- plex structures such as vortices, characterizing the fluid flow in the spatial and temporal domains. Different cases of experimental measurements given by a particle image velocimetry are analyzed to recognize the complexity of the underlying flow physics, while showing the effectiveness of the proposed approach.

This paper investigates the policy optimization paradigm, where a learning model is trained to find the solution of complex Markov decision problems, as a tool to address the berth allocation problem in multimodal terminals. To this purpose, we drop the typical formulation of the latter as a mixed-integer static scheduling one, and we model it instead as an evolving scenario in which berths are assigned to ships according to a parameterized policy function that drives the temporal evolution of the environment. We adopt a cross-entropy optimization scheme to optimize the policy parameters, which is a simple and highly parallelizable gradient-free technique. As compared to the static mixed-integer formulation, the proposed approach relies on a much lighter optimization problem in the continuous space of the policy parameters, thus making it feasible to replan in real time when needed. Furthermore, the generality of the policy optimization approach allows to take into account any performance metric and specific feature of the scenario straightforwardly, without the need to devise ad hoc heuristics. Simulation tests showcase the good performance of the policy approach under various conditions.

Modern datacenters rely on virtualization to deliver complex and scalable cloud services. To avoid inflating costs or reducing the perceived service level, suitable resource optimization techniques are needed. Placement can be used to prevent inefficient maps between virtual and physical machines. In this perspective, we propose a holistic placement framework considering conflicting performance metrics, such as the service level delivered by the cloud, the energetic footprint, hardware or software outages, and security policies. Unfortunately, computing the best placement strategies is nontrivial, as it requires the ability to trade among several goals, possibly in a real-time manner. Therefore, we approach the problem via model predictive control to devise optimal maps between virtual and physical machines. Results show the effectiveness of our technique in comparison with classical heuristics. Note to Practitioners —This paper is motivated by the success of cloud-based services. Specifically, we consider the case where the resources of datacenters are accessed through the infrastructure-as-a-service paradigm. To efficiently handle the load of requests and to tame operational costs, a proper optimization is needed. To this end, we focus on the selection of the best maps between virtual and physical machines. We propose a holistic placement framework for the deployment of user-requested virtual machines by pursuing different performance goals, such as counteract to hardware outages or reboots due to software aging issues, ensure proper security policies, maintain a suitable service level perceived by users, and reduce power requirements. The optimal strategies are computed with model predictive control, which allows to consider complex constraints and take advantage of future information. The proposed framework is tested in different scenarios characterized by a variety of workloads and traces gathered in a real cloud datacenter. Results indicate that our approach outperforms bin-packing techniques.

Summary This paper investigates the use of lattice point sets as an efficient method to sample uniformly the state space of discrete-time dynamic systems for the solution of finite-horizon optimal control problems using approximate dynamic programming. Lattice point sets are a kind of discretization method, commonly employed for efficient numerical integration, providing a regular and balanced sampling of the state space based on the repetition of elementary unit cells. A convergence analysis of the approximate solution of the control problem to the optimal one is provided, pointing out that such sampling schemes allow one to efficiently exploit possible regularities of the cost-to-go functions. Furthermore, it is shown that a higher accuracy may be obtained through suitable transformations of the state vector of the dynamic system. Another advantage of lattice point sets over other sampling schemes is the possibility of evaluating a priori the goodness of a given set over another through the explicit computation of a specific parameter. Simulation results concerning the optimal control of a water reservoirs system are presented to show the effectiveness of the proposed approach.

The Internet is a core tool for developing commercial and social relationships. As a consequence, cyber security must be properly assessed, for instance, to face new and sophisticated threats. To deliver large-scale services, proper countermeasures characterized by a non-negligible energetic impact have to be pursued. From this perspective, this article proposes to investigate the energy required by the most popular cryptographic algorithms. The collected measures are used to model relationships between power drains and size of the key or offered load via a black box approach. Results can also be used to prevent classical traffic analysis campaigns.

Page 2: Column 2, lines 2-4, previously read: “Specifically, we consider a decision maker that, after a proper training, is able to select the most suitable heuristic for compute the placement for each VM requested by end users”.

An approach to address the berth allocation problem is presented that is based on the receding horizon paradigm. In more detail, berthing decisions are computed by solving an optimization problem at each time step aimed at minimizing the waiting times of vessels, exploiting predictions on the ship arrivals and berth occupancy over a moving window starting from the current time instant. A discrete time dynamic model is devised to forecast the state of the terminal in the forward window, and a computationally-efficient approximate solution method based on random search is proposed. The considered framework can be used either for real time planning or scheduling in advance. Simulation results are reported to show the effectiveness of the method in different terminal configurations, forward horizons, and traffic intensities, in comparison with state-of-the-art approaches.

We address the optimal control of level sets associated with the solution of normal flow equations. The problem consists in finding the normal velocity to the front described by a certain level set in such a way to minimize a given cost functional. First, the considered problem is shown to admit a solution on a suitable space of functions. Then, since in general it is difficult to solve it analytically, an approximation scheme that relies on the extended Ritz method is proposed to find suboptimal solutions. Specifically, the control law is forced to take on a neural structure depending nonlinearly on a finite number of parameters to be tuned, i.e., the neural weights. The selection of the optimal weights is performed with two different approaches. The first one employs classical line-search descent methods, while the second one is based on a quasi-Newton optimization that can be regarded as a neural learning based on the extended Kalman filter. If compared to line-search methods, such an approach reveals to be successful with a reduced computational effort and an increased robustness with respect to the trapping into local minima, as confirmed by simulations in both two and three dimensions.

The goal of this work is the optimal control of level sets generated by the normal flow equation. The problem consists in finding the normal velocity that minimizes a given performance index expressed by means of a cost functional. In this perspective, a sufficient condition of optimality requiring the solution of a system of partial differential equations is derived. As in general it is difficult to solve such a system, an approximation scheme based on the extended Ritz method is proposed to find suboptimal solutions. The control law is forced to take on a fixed structure depending nonlinearly on a finite number of parameters to be suitably chosen. The selection of the parameters is accomplished by using a gradient-based technique. To this end, the adjoint equation is derived to compute the gradient of the cost functional with respect to the parameters of the control law. The effectiveness of the proposed approach is shown by means of simulations.

Fast moving horizon state estimation for constrained discrete-time systems is investigated through an approach based on an incomplete optimization at each time step. In particular, only few iterations of the gradient, conjugate gradient, and Newton descent methods are executed. Constraints on the state variables are explicitly considered by exploiting the "dead time" between two consecutive time steps, where a projection requiring the minimization of a distance function is performed. Instead, a simpler line search is computed on line that consists in searching for a state estimate satisfying the constraints by solving a one-dimensional optimization. Stability conditions for the estimation error are derived. The proposed approach is well-suited to being applied for state estimation of rapidly-evolving constrained systems, as confirmed by simulations in comparison with the application of the online "full" projection at each time step.

We address the problem of estimating the constant parameters involved in the normal flow equation, which is a Hamilton-Jacobi PDE widely used in many different research areas. The identification of such parameters allows one to estimate the flow function, which is the velocity vector field that governs the dynamics of the level sets associated with the solution of the equation. The estimates are obtained by using a Luenberger observer and a parameter estimator based on the adaptation law proposed by Pomet and Praly in 1992. Such a law makes it possible to explicitly take into account bounds on the parameters. Conditions for the stability of the parameter estimation error are established. Simulation results are presented that confirm the theoretical achievements.

Robotic networks are increasingly used to under- take complex missions and are often composed of heterogeneous agents executing well-defined tasks. To react against external disturbances and hardware failures, a typical technique is to change at runtime how tasks are assigned to robots. In this perspective, the paper presents an approach based on predictive control for the on-line selection of the optimal time instants when perform reassignments. To evaluate the effectiveness of the proposed approach, simulation results are showcased in comparison with reactive and proactive strategies.

This paper investigates techniques for reducing the computational burden of local learning methods relying on kernel functions in the framework of approximate minimization, i.e., when they are employed to find the minimum of a given cost functional. The considered approach is based on an optimal choice of the kernel width parameters through the minimization of an empirical cost and can provide a solution to important problems, such as function approximation and multistage optimization. However, when the stored data are too many, the kernel model output evaluation can take a long time, making local learning unsuited to contexts where a fast function evaluation is required. At the same time, the training procedure to obtain the kernel widths can become too demanding as well. Here it is shown that a large saving in the computational effort can be achieved by considering subsets of the available data suitably chosen according to different criteria. An analysis of the performance of the new approach is provided. Then, simulation results show in practice the effectiveness of the proposed techniques when applied to learning and approximate minimization problems.

Optimal control for systems described by partial differential equations is investigated by proposing a methodology to design feedback controllers in approximate form. The approximation stems from constraining the control law to take on a fixed structure, where a finite number of free parameters can be suitably chosen. The original infinite-dimensional optimization problem is then reduced to a mathematical programming one of finite dimension that consists in optimizing the parameters. The solution of such a problem is performed by using sequential quadratic programming. Linear combinations of fixed and parameterized basis functions are used as the structure for the control law, thus giving rise to two different finite-dimensional approximation schemes. The proposed paradigm is general since it allows one to treat problems with distributed and boundary controls within the same approximation framework. It can be applied to systems described by either linear or nonlinear elliptic, parabolic, and hyperbolic equations in arbitrary multidimensional domains. Simulation results obtained in two case studies show the potentials of the proposed approach as compared with dynamic programming.

This paper is concerned with a multiresolution approach to the piecewise-linear approximation of multivariate nonlinear continuous functions. The proposed technique has no restrictions on the number of variables the functions depend on, and is based on the use of piecewise-linear ''hat'' functions. The approximation levels are related to nested function spaces. The multiresolution approach allows one to define a simple model reduction strategy that is based on a proper error definition. The interest in the piecewise-linear approximations and in the hat functions is motivated by the simplicity of their circuit implementations. The efficiency of the method is tested via two benchmark examples, one of which concerns the approximation of the vector field of a nonlinear dynamical system.

A dynamic discrete-time model of container flows in maritime terminals is proposed as a system of queues. Such queues are controlled via input variables that account for the use of the available resources given by the capacities of the handling machines used to move containers inside a terminal. Two feedback control strategies for the allocation of such resources are described. The first consists of a resource assignment that is proportional to the corresponding queue lengths; in the second, the assignment is obtained by the one-step-ahead optimization of a performance cost function according to a myopic approach. Simulation results are reported to compare such methodologies for the purpose of sensitivity and scenario analyses in the management of a maritime terminal.

This work addresses the problem of learning an unknown function from data when local models are employed. In particular, kernel smoothing models are considered, which use kernels in a straightforward fashion by modeling the output as a weighted average of values observed in a neighborhood of the input. Such models are a popular alternative to other kernel paradigms, such as support vector machines (SVM), due to their very light computational burden. The purpose of this work is to prove that a smart deterministic selection of the observation points can be advantageous with respect to input data coming from a pure random sampling. Apart from the theoretical interest, this has a practical implication in all the cases in which one can control the generation of the input samples (e.g., in applications from robotics, dynamic programming, optimization, mechanics, etc.) To this purpose, lattice point sets (LPSs), a special kind of sampling schemes commonly employed for efficient numerical integration, are investigated. It is proved that building local kernel smoothers using LPSs guarantees universal approximation property with better rates with respect to i.i.d. sampling. Then, a rule for automatic kernel width selection, making the computational burden of building the model negligible, is introduced to show how the regular structure of the lattice can lead to practical advantages. Simulation results are also provided to test in practice the performance of the proposed methods.

The widespread diffusion of Infrastructure-as-a- Service and cloud computing paradigms requires large-scale data centers with thousands of running nodes and high energy demands, thus causing relevant economical and environmental costs. In this perspective, the paper presents an energy-aware consolidation strategy based on predictive control, in which virtual machines are migrated among nodes to reduce the number of active units. To describe a general cloud infras- tructure, a discrete-time dynamic model is presented together with constraints. The migration strategies of virtual machines are obtained by solving finite-horizon optimal control problems involving integer variables. To reduce the computational effort, approximate solutions are searched for via Monte Carlo opti- mization. Besides power savings, the proposed method allows one to reduce violations of the service level agreement and aggressive on/off cycles of nodes. To showcase the effectiveness of the proposed approach, preliminary simulation results are provided.

When the problem of learning from data is solved through a regression tree estimator, the quality of the available observations is an important issue, since it influences directly the accuracy of the resulting model. It becomes particuarly relevant when there is freedom to sample the input space arbitrarily to build the tree model or, alternatively, when we need to select a subsample to train the tree estimator on a computationally feasible input set, or to evaluate the goodness of the estimation on a test set. Here the accuracy of estimation based on regression trees is analyzed from the point of view of geometric properties of the available input data. In particular, the concept of F-discrepancy, a quantity that measures how well a set of points represents the distribution underlying the input generation process, is applied to derive conditions for convergence to the optimal piecewise-constant estimator for the unknown function we want to learn. The analysis has a constructive nature, allowing to select in practice good input sets for the problem at hand, as shown in a simulation example involving a real data set.

The problem of optimal tracking of level sets is investigated. More specifically, we propose a novel method to design a controller that is able to track a reference curve generated by a level set equation. Such a functional optimal control problem is nonstandard as it involves a moving domain over time, thus requiring the development of both an ad-hoc approximation scheme and an efficient numerical solver. We address the approximate solution of the resulting optimization problem by using the extended Ritz method, which has been recently applied to the solution of a number of optimal control problems in high dimensional setting. Such a method relies on the use a control law of fixed structure that depends on a number of parameters to be suitably chosen. Toward this end, we derive the adjoint equation for the optimal tracking problem. Such an equation allows one to compute the gradient of the cost function with respect to the vector of parameters of the control law. Numerical results are reported to show the effectiveness and computational effort of the proposed approach for the purpose of tracking curves generated by the normal and mean curvature flow equations.

This paper analyzes quasi-random sampling techniques for approximate dynamic programming. Specifically, low-discrepancy sequences and lattice point sets are investigated and compared as efficient schemes for uniform sampling of the state space in high-dimensional settings. The convergence analysis of the approximate solution is provided basing on geometric properties of the two discretization methods. It is also shown that such schemes are able to take advantage of regularities of the value functions, possibly through suitable transformations of the state vector. Simulation results concerning optimal management of a water reservoirs system and inventory control are presented to show the effectiveness of the considered techniques with respect to pure-random sampling.

The design of closed-loop finite-dimensional con- trollers for systems described by partial differential equations is tackled by combining tools borrowed by research areas such as approximation and operator theory. The proposed paradigm is based on the idea of using operators to account for the dynamics, regulator, and measurement mappings. Specifically, we rely on a well-established setting of Banach spaces, which is well-suited to supporting the generality of the approach. First, we define a class of Lipschitz operators with finite seminorm and formulate a tracking problem in the Banach spaces of real- valued functions. Second, we search for controllers that ensure stability and minimize a given performance index. The design of such regulators is achieved by resorting to an approximation scheme based on the extended Ritz method. Such a scheme consists in constraining the regulation operator to take on a fixed structure, where a finite number of free parameters can be suitably chosen. The problem is then reduced to a mathematical programming one of nonlinear type in general, in which the values of the parameters are optimized to guarantee stability. A family of nonlinear approximators to which the most common classes of feedforward neural networks belong are employed to accomplish the design via a convenient choice of their parameters (i.e., the weights), as shown by means of simulations with the optimal control of an unstable heat equation.

The use of integer tree-based search and mixed- integer programming is investigated for the purpose of control of multi-item multi-echelon distribution chains. A discrete-time model is considered to describe the dynamics of a generic distribution chain. The decisions on the amounts of goods to transfer are made by referring to a performance index that accounts for transportation, storage, and backlog costs at two levels, i.e., strategic and tactical. As to the strategic level, a worst-case stock replenishment policy is adopted to exploit the uncertain information available on long-term predictions of the customers' demand. The solution of such a problem is obtained by using a top-down tree-based algorithm to select policy parameters such as the delivery cycle times of goods. At the tactical level, the on-line decisions on the transportation of goods are taken basing on model predictive control, which allows one to take into account recent, reliable, short-term predictions of the demand. The tactical optimal decisions are obtained by solving mixed-integer programming problems with fewer variables as compared with the strategic setting. Simulation results are presented to show the effectiveness of the proposed approach.

The goal of this paper is that of reporting the results obtained in the identification of a macroscopic dynamic model that can describe the freeway traffic using the informa- tion available from a wireless cellular network. To this end, we need to assume that the distribution of mobile terminals aboard cars be uniform along the freeway and to deal with the cells of the cellular network as the sections in which a freeway stretch is divided. The information on the mobile terminals concerns their positions and speed. Two different approaches are investigated. The former is an extension to quite a standard freeway macroscopic model, while the latter is a black-box approach that consists in using a neural network to represent the traffic dynamics. The parameters of the former and the neural weights of the latter are identified off line by a least-squares approach. Numerical results obtained after identification and validation are reported using the data generated by a microscopic simulator.