The linear-quadratic regulator (LQR) problem of optimal control of an uncertain discrete-time linear system (DTLS) is revisited in this paper from the perspective of Tikhonov regularization. We show that an optimally chosen regularization parameter reduces, compared to the classical LQR, the values of a scalar error function, as well as the cost function. The scalar regularization parameter can be calculated using a standard parameter choice method. Simulations confirm performance improvement when this regularized control signal is applied to a DTLS subject to a varying sampling rate.

The Sterile Insect Technique (SIT) is a promising control method against insect pests and insect vectors. It consists in releasing males previously sterilized in laboratory, in order to reduce or eliminate a specific wild population. We study the implementation of SIT-based elimination campaign of Aedes mosquitoes using feedback control. We provide state-feedback and output-feedback control laws and establish their convergence, as well as their robustness properties. In this design procedure, a pivotal role is played by the use of properties of monotone systems. Simple illustrative simulations are provided.

This paper generalizes two recently proposed opinion dynamics models with control. The generalized model is made up of a standard model of agents interacting with each other, to which affine controls are added. The controls, influencing opinions of agents, are exercised by entities called players, who specify targets, possibly conflicting, for agents. Three play procedures, sequential, parallel and asynchronous are defined. Each player has knowledge of the current state of all agents, but \textit{no other information about the other players}. We design the player controls using one step ahead optimization leading to the following novel results: easily computable controls for each player only dependent on its own information; conditions for convergence to the Nash equilibrium, and formulas for the latter.

Model predictive control (MPC) is a powerful tool to control discrete-time dynamical systems in a wide range of application areas. However, its application in real-time control is challenging because the computational complexity to solve the associated nonlinear programming (NLP) problem increases with the dimension of the problem and the prediction horizon. Reducing this prediction horizon to only one sampling interval yields the so called one step ahead optimal control (OSAOC). In general, OSAOC is suboptimal with respect to the optimal control calculated over the entire control horizon. This paper shows in an illustrative example that the suboptimality of the OSAOC decreases with the problem dimension while presenting a computational cost that is low and increases sublinearly making OSAOC suitable for application to large scale real-time control problems.

Rio de Janeiro is a well-known, international tourist destination, and its charms also attract visitors to its many reputed institutions, among them the Federal University of Rio de Janeiro (UFRJ). Within the university, the Graduate School of Engineering (COPPE), which is composed of 13 graduate engineering programs, is a center of excellence in engineering. The Control, Automation, and Robotics (CAR) group in the Electrical Engineering Department is one of Brazil’s top research groups, and it is making its presence felt internationally, being slated to host the 2025 IEEE Conference on Decision and Control, with group faculty member João Carlos Basilio as general cochair. In this issue of IEEE Control Systems , we speak with Amit Bhaya (currently the group head of CAR, COPPE, UFRJ) and a few others in their group.

This paper uses a compartmental model that accounts for some of the main features of the COVID-19 pandemic. Assuming a control that represents the aggregated intensity of non pharmaceutical interventions, such as lockdown in varying degrees and the use of masks and social distancing, this text proposes an N-step-ahead optimal control (NSAOC) method that is easy to calculate and provides a guideline for implementation. The compartmental model is extended to account for vaccination, and the N-step-ahead optimal control is calculated for this case as well. The proposed control is robust to parameter variation in all model parameters, when they are assumed to be normally distributed about nominal values. In addition, the proposed NSAOC is shown to compare favorably with a recently proposed PID-like controller.

This paper proposes a discrete-time model for dynamic trading, interconnecting cash and asset stocks. The trading action or control is based on the evolution of the asset prices, and any suitable asset price predictor can be used. Based on the model introduced, a one step ahead optimal control strategy, based on linear programming, is proposed. This leads to a trading algorithm which specfies a rule to buy or sell assets in a given portfolio. The addition of trade trigger logic to the basic scheme is also proposed, in order to allow return and risk to be traded off in the dynamic one step ahead trading scheme. The proposed one step ahead optimal policy is independent of the predictor of prices and their variances, chosen in this paper as the moving average, but replaceable by any desired estimator. Numerical examples are given to show that the proposed strategy performs reasonably well, with and without risk reduction, over datasets relating to different portfolios (banks, computers, ETFs and stocks).

In discrete-time Vidale–Wolfe–Deal duopoly models and variants, two firms compete for market share, in a dynamic game setting, described by a pair of difference equations. This paper studies these dynamic games, using the natural concept of one-step-ahead optimal control, in which each firm optimizes its own performance index at the next step, and only has access to some information about its competitor. Two cases are studied: with and without stipulating target market shares for each firm, under sequential and parallel game playing procedures. It is shown that when target market shares are not specified, for the VWD model, limit cycles of large period can occur when each firm uses linear performance indices, while multiple equilibria may arise when quadratic performance indices are used. Three other proposed models result in games that lead to equilibria and do not have limit cycle behavior. When target market shares are specified, convergence to an equilibrium occurs for all the models proposed in this paper.

A one step ahead optimal strategy is proposed for the inventory control and management problem, and rewritten as a linear programming problem, permitting practical implementation. Important novel aspects of the proposed solution are that it uses economic value added (EVA), a comprehensive performance index commonly used in business management, instead of regulation to a set point or to a interval of stock values; it does not require knowledge or prediction of the demand distribution; it achieves good efficiency with respect to a globally optimal value, defined in this paper, and no significant bullwhip effect, while being robust to demand and lead time variations. The proposed one step ahead optimal controller is compared with the classical ( s , S ) controller, as well as with a representative of the inventory and order-based production controller family. In order to make a fair comparison, this paper also proposes a tuning method for the latter two controllers. Numerical experiments based on average performance of the three controllers for a set of normally distributed demands show the superiority of the proposed one step ahead optimal controller, in terms of EVA as well as in terms of other measures proposed in the paper.

This paper generalizes the Sethi-Thompson model of cash balance dynamics to the case of multiple current and investment accounts, with the cash flows or demands incident on the current accounts. Cash transfers can occur between any pair of current-current or current-investment accounts, with transaction costs proportional to the amount transferred, always deducted from current accounts. Performance indices are defined and maximization of an index for the next instant (day), by suitable choice of cash transfers that satisfy desired constraints on account balances, defines the basic optimal control problem referred to as one step ahead optimal control. It is shown that this one step ahead optimal control can be written as a mixed integer linear program of small size, leading to an implementable real time strategy for the generalized cash balance problem. In addition, for the simple case of a single cash and investment account, the proposed strategy is derived analytically and compared with a strategy of Miller-Orr type, called a three-level strategy. Omniscient optimal control over a horizon is defined as the globally optimal control strategy, assuming the demands over the entire horizon to be known: although computable a posteriori, it is not implementable a priori, and only serves as a benchmark for comparison. The proposed one step ahead optimal or myopic approach makes no assumptions about the distribution of cash demands, and examples show that it attains performance indices which are superior to those attained by three-level control strategies, and compare favorably with the omniscient benchmark performance indices.

This paper proposes definitions of implementation and adoption delays, arising from firm and client behaviors, in the context of market share dynamics. Information delay refers to the existence of lags in the information used for the advertising policy, while adoption delay refers to the existence of a lag in the effect of the advertising policy. These are natural lags in the flow of information and have not been considered in several models proposed in the literature. In this paper, these delays are introduced into recently proposed extensions of the Vidale-Wolfe-Deal and Lanchester models of market share dynamics subjected to affine advertising control policies. Conditions for stability of the equilibrium market share are derived. In addition, it is shown that Hopf bifurcations leading to oscillatory behavior exist for certain parameter values, and corresponding conditions for these are given. The main results are: the equilibrium market shares of the extended Vidale-Wolfe-Deal and Lanchester models are both robust to implementation delays, but, in the case of adoption delays, for both models, numerical results show that there is a critical value such that if the sum of the adoption delays exceeds this value, there is an onset of oscillations of market shares, through a Hopf bifurcation.

The recently proposed Minimal Complexity Machine (MCM) finds a hyperplane classifier by minimizing an upper bound on the Vapnik–Chervonenkis (VC) dimension. The VC dimension measures the capacity or model complexity of a learning machine. Vapnik’s risk formula indicates that models with smaller VC dimension are expected to show improved generalization. On many benchmark datasets, the MCM generalizes better than SVMs and uses far fewer support vectors than the number used by SVMs. In this paper, we describe a neural network that converges to the MCM solution. We employ the MCM neurodynamical system as the final layer of a neural network architecture. Our approach also optimizes the weights of all layers in order to minimize the objective, which is a combination of a bound on the VC dimension and the classification error. We illustrate the use of this model for robust binary and multi-class classification. Numerical experiments on benchmark datasets from the UCI repository show that the proposed approach is scalable and accurate, and learns models with improved accuracies and fewer support vectors.

Public transportation in urban centers is of fundamental importance, being a widely investigated topic. Smart autonomous vehicles (SAVs) present a great potential in revolutionizing transportation systems in urban areas, providing more flexible and efficient solutions. This work proposes a new transportation model based on SAVs that provides a station-based, point-to-point service, with distributed coordination. The model offers two different modes of operation, one with exclusive rides, and the other with ride sharing between clients. A simulator has been developed, through which the system’s characteristics are analyzed, and the two modes of operation compared. It was observed that with the increase in the system client demand over time the ride sharing mode gets more efficient than the mode with exclusive rides, both in terms to the average time required to deliver clients and the total distance traveled.

Methods to stabilize discrete-time linear control systems subject to variable sampling rates, i.e., using state feedback controllers, are well known in the literature. Several recent works address the use of the Tikhonov regularization method, originally designed to attenuate the noise effects on ill-posed problems, with the aim of improving performance and stabilizing approximately controllable dynamical systems. Inspired by these works, we propose the use of a feedback controller designed using the Tikhonov method to regularize discrete-time linear systems subject to varying sampling rates. The goal is to minimize an error function, thus improving the performance of the closed loop system and reducing the possibility of instability. Illustrative examples show the effectiveness of the proposed method.

Using a compute infrastructure efficiently to execute jobs while respecting Service Level Agreements (SLAs) and thereby guaranteeing Quality of Service (QoS) poses a number of challenges. One such challenge lies in the fact that SLAs are set prior to the execution of a job, but the execution environment is subject to a number of possible disturbances, such as poor knowledge about actual resource necessity, demand peaks and hardware malfunctions, amongst others. Thus by using a fixed resource allocation, the manager of a shared computing environment risks violating user SLAs. Furthermore, the complexity of managing several workload executions increases with the number of workloads, implying the need for an automatic method to manage and control the execution of workloads. The execution time SLA is specially important in streaming scenarios such as web applications and continuous video processing, and is the focus of this paper. A method based on adaptive model predictive control (aMPC) is proposed here to adapt the amount of allocated resources to iterative workloads. The methodology is tested applied to Deep Learning Workloads, in standalone and multi-workload versions. The results show that using adaptive optimal control with a linearized model improves performance with respect to simpler control laws as well as reinforcement learning approaches.

This paper extends the Deal-Vidal-Wolfe and Lanchester models of duopoly dynamics, which involve two populations, by explicitly introducing a third population of undecided users. An analysis of these extended models establishes conditions for the existence of equilibria, as well as their stability properties under different classes of advertising policies. This analysis also leads to the surprising result that the extended Vidale–Wolfe and Lanchester models, despite having different dynamics, under the general class of decentralized affine feedback advertising policies have equilibria in identical locations, with the same stability properties.

A single echelon supply chain model problem, consisting of a store with known inventory and shipping capacities, a known delivery delay or lead time and a random demand for a product at the store is formulated as an optimal control problem. In the practical case when only current and past demands are known, using the concept of one step ahead optimal control, the problem is reformulated as the mathematical programming problem of maximizing economic value added (EVA), subject to the dynamics and constraints, such as inventory size. Illustrative examples are given and performance indices are proposed to evaluate the performance of the proposed controller, which exhibits good efficiency and no bullwhip effect.

The restarted generalized minimal residual (denoted as GMRES(m)) normally used for solving a linear system of equations of the formAx=bhas the drawback of eventually presenting a stagnation or a slowdown in its rate of convergence at certain restarting cycles. In this article, a switching controller is introduced to modify the structure of the GMRES(m) when a stagnation is detected, enlarging and enriching the subspace. In addition, an adaptive control law is introduced to update the restarting parameter to modify the dimension of the Krylov subspace. This combination of strategies is competitive from the point of view of helping to avoid the stagnation and accelerating the convergence with respect to the number of iterations and the computational time. Computational experiments corroborate the theoretical results.

Iterative methods to solve linear large-scale discrete problems are well known in the literature. When the linear system is ill-posed and contaminated by noise, some kind of regularization must be applied in order to achieve a feasible solution. In the first part of this paper, we revisit briefly some known methods to solve large-scale ill-posed discrete linear problems which are easy to implement and have low computational cost, formulating them in a unified manner and also proposing simple modifications in order to improve their performances. Matrix forms of iterative algorithms can be formulated depending on certain conditions on the blurring process, and have the advantage of avoiding the formation and storage in memory of the matrix that represents the blurring process, which is generally of very large dimension. As an original contribution, in the final part of this paper we present the matrix forms of the iterative algorithms revisited and test them in the problem of restoration of an image degraded by blurring and noise.