Nash Optimality Research Articles

Distributed robust [formula omitted]asso-[formula omitted] based on [formula omitted]ash optimization for smart grid: Guaranteed robustness and stability

The integration of variable renewable energy supplies into smart grid energy management poses several obstacles to system operation. An efficient solution for resource management is essential to ensuring reliable operation. This research presents distributed robust Lasso-model predictive control (D − RLMPC) as a way to handle energy problems in a multi-layer and multi-time frame optimization method. The D − RLMPC is a hierarchical system that integrates a centralized supervisory management (SM) layer for long-term optimization with a distributed coordination management (CM) layer for short-term adaptation to high power fluctuations. The higher layer, known as the SM, is responsible for providing the grid operator with specific operating plans and offering guidance to the bottom layer, known as the CM. The CM is responsible for coordinating the interaction between the centralized optimization goals and the physical power system layer. Furthermore, a distributed extended Kalman filter (DEKF) is used to ascertain the inter-dependencies among subsystems. Next, an iterative approach based on Nash optimization is proposed to get the globally optimum solution of the whole system in a partly distributed manner. The simulation results demonstrate the effectiveness of the proposed control approach, which combines the advantages of centralized and distributed control to provide a comprehensive solution for the grid operating issue. To verify and assess the effectiveness of the suggested approach, the acquired outcomes are compared to those of the centralized robust, distributed robust, and distributedMPC approaches. The simulation findings confirm the practicality of using the suggested system to manage future smart grid assets.

Data-driven distributed control of input-coupled interconnected systems based on Nash optimality

Data-driven distributed control of input-coupled interconnected systems based on Nash optimality

Cooperation and market socialism: Kant versus Nash

Abstract The idea that socialism depends upon cooperation, as capitalism depends on competition, has always been inherent in the conception of socialism. Yet precise models of market socialism – ones, that is, that are sufficiently articulated so as to be able to discuss and compute an equilibrium in the economy – do not model cooperation in production, or more generally, in economic behavior. We introduce a Kantian optimization protocol, which, in contrast to Nash optimization, models how individuals can cooperate in labor and/or investment decisions. We prove that the ‘cooperative equilibrium’, thus modeled, is Pareto efficient whenever, in addition to receiving wages and rents, profits are distributed not to shareholders, but to workers and investors in proportion to their contributions to the firm. Pareto efficiency is achieved when the firms entire output is distributed to factor owners and shareholders do not exist.

Synchronization tracking control of networked multi-axis motion systems: A cooperative distributed model predictive control approach

Synchronization tracking control is an essential technique in networked multi-axis motion systems (NMAMSs). However, the uncertainties induced by network, such as delay and packet disordering, have great influence on control performance of the motion systems. To improve the influence of the uncertainties induced by network on synchronization tracking control performance in NMAMSs, a cooperative distributed model predictive control (CDMPC) strategy for NMAMSs is proposed. Firstly, the synchronization tracking control of the NMAMS is designed in a networked control framework. By introducing the synchronization error into performance index as a coupling term, a local controller adopting a CDMPC strategy is designed for each subsystem. Then, a Nash optimization iteration strategy is presented to deal with the CDMPC optimization problem, and the convergence and stability of the system are also analyzed. Finally, experiments are carried out to demonstrate the practicability and effectiveness of the proposed control strategy.

Distributed Multi-Agent Target Tracking: A Nash-Combined Adaptive Differential Evolution Method for UAV Systems

Multi-agent cooperative target tracking plays a significant role in distributed artificial intelligence for unmanned aerial vehicle (UAV) systems. Most existing tracking solutions using online path planning focus on general target trajectories. Such trajectories have strong regularity and are smooth with minimal fluctuations. However, in real UAV applications a target will change its trajectory frequently to prevent from being tracked, and thus its trajectory will fluctuate greatly and randomly. To this end, in this paper we consider a realistic scenario where the UAV target trajectory is changeable and random. For real-time target tracking, we formulate the tracking task as a distributed model predictive control (DMPC) problem, the objective of which is to optimize tracking performance under various constraints. To do so, we innovatively combine the adaptive differential evolution (ADE) algorithm with Nash optimization, and then propose a Nash-combined ADE method. Specifically, we use ADE to adaptively adjust the predicted trajectory of each UAV agent and Nash optimization to efficiently solve DMPC formulation for global optimization, which can improve the tracking accuracy and simultaneously reduce the computational complexity. The simulation results show that the proposed method performs well in terms of tracking accuracy, UAV collision avoidance and tracking stability for realistic target trajectories.

Nash optimality based distributed model predictive control for vehicle platoon

In this paper, a distributed model predictive control algorithm (DMPC) based on Nash optimality is proposed for automated vehicle platoon control. The optimization decision of vehicle platoon is decomposed into the decentralized optimization of single vehicles, in which the Nash optimality algorithm is adopted to solve the decentralized optimization problem. Thus, each vehicle can reach the local optimal target and the whole team can reach its Nash equilibrium. The methodology employs neighborhood information of the entire platoon through on-board sensors and V2V communication to achieve coordination of the entire platoon. The ability of the methods in terms of robustness to disturbances and cyber-physical interaction is demonstrated with simulation case studies.

Persistent Tracking of Maneuvering Target Using IMM Filter and DMPC by Initialization-Guided Game Approach

In this paper, we focus on planning the paths of multiple unmanned aerial vehicles (UAVs) attached with camera sensors for persistently tracking a maneuvering ground target in urban environment. Considering the case of changing among various models, the interacting multiple model filter along with the state-vector fusion is utilized to estimate and predict the target motion, observed by multisensor networks. Then, based on the estimation results, the distributed model predictive control (DMPC) is taken as the framework of optimizing multi-UAVs paths with applications to persistent target tracking. When it comes to the DMPC solver, the game approach based on Nash optimization is adopted iteratively, and the guided initialization is introduced especially to improve the quality of initial solutions. Finally, we give numerical simulations to verify the high efficiency and feasibility of our proposed method.

A theory of cooperation in games with an application to market socialism

Economic theory has focused almost exclusively on how humans compete with each other in their economic activity, culminating in general equilibrium (Walras–Arrow–Debreu) and game theory (Cournot–Nash). Cooperation in economic activity is, however, important, and is virtually ignored. Because our models influence our view of the world, this theoretical lacuna biases economists’ interpretation of economic behavior. Here, I propose models that provide micro-foundations for how cooperation is decentralized by economic agents. It is incorrect, in particular, to view competition as decentralized and cooperation as organized only by central diktat. My approach is not to alter preferences, which is the strategy behavioral economists have adopted to model cooperation, but rather to alter the way that agents optimize. Whereas Nash optimizers view other players in the game as part of the environment (parameters), Kantian optimizers view them as part of action. When formalized, this approach resolves the two major failures of Nash optimization from a welfare viewpoint – the Pareto inefficiency of equilibria in common-pool resource problems (the tragedy of the commons) and the inefficiency of equilibria in public-good games (the free rider problem). An application to market socialism shows that the problems of efficiency and distribution can be completely separated: the dead-weight loss of taxation disappears.

A new Nash optimization method based on alternate elitist information exchange for multi-objective aerodynamic shape design

Traditionally, it is considered that Nash equilibrium is based on the symmetric elitist information exchange. This paper presents a new Nash optimization method based on alternate elitist information exchange, it makes the information exchange and decision-making more convenient. Moreover, the subsequent decision-making can get the reward from the decision of the previous one, so the new method is more flexible in numerical implementation than that of the traditional symmetric elitist information exchanged algorithm. The equivalence of the solution of the new algorithm with the Nash optimization problem is proved in the paper. Then it is combined with evolutionary algorithms and/or adjoint methods to solve not only unconstrained but also constrained multi-objective optimization problems in aerodynamics. Numerical results show the potential efficiency and flexibility of new algorithms in solving complex multi-objective/disciplinary optimization problems in aeronautics.

A Theory of Cooperation in Games with an Application to Market Socialism

Economic theory has focused almost exclusively on how humans compete with each other in their economic activity, culminating in general equilibrium (Walras) and game theory (Nash). Cooperation in economic activity is, however, important, and is virtually ignored. Because our models influence our view of the world, this theoretical lacuna biases economists’ interpretation of economic behavior. Here, I propose models that provide micro-foundations for how cooperation is decentralized by economic agents. It is wrong, in particular, to view competition as decentralized and cooperation as organized only by central diktat. My approach is not to alter preferences, which is the strategy behavioral economists have adopted to produce cooperation, but rather to alter the way that agents optimize. Whereas Nash optimizers view other players in the game as part of the environment (parameters), Kantian optimizers view them as part of action. When formalized, this approach resolves the two major failures of Nash optimization from a welfare viewpoint -- the Pareto inefficiency of equilibria in common-pool resource problems (the tragedy of the commons) and the inefficiency of equilibria in public-good games (the free rider problem). An application to market socialism shows that the problems of efficiency and distribution can be completely separated: the dead-weight loss of taxation disappears.

An Axiomatic Control for Rational Behavior of Political Leaders in Democratic States

The main purpose of the present paper is to develop a new axiomatic system for the control or self-control of rational behavior of political leaders in contemporary democratic states. The axiomatic system is based on stringent criteria for rational behavior (proposed by A. N. Kolmogorov and R. Wilson) and contains 14 axioms. Axioms with ordinal numbers 4, 10, and 14 have a particular important role. In the present study we use Nash optimization principle, as well as a generalization of this principle developed by N. N. Vorobiev. The proposed axiomatic system is clear, meaningful and enjoys the lack of contradiction property.The obtained theoretical results are applied in Republic of Albania.

Distributed Model Predictive Control Based on Nash Optimality for Large Scale Irrigation Systems

Irrigation system is a large scale system, consisting of many interacting channels, and spanning vast geographical areas. In practice, the water level is expected to the desired reference values for safety and efficiency. In this paper, the model of irrigation system is modeled by the principle on conservation of mass. Because of the strong coupling between neighboring pools in irrigation system and large disturbance from the environment, a non-cooperative distributed model predictive control (NDMPC) algorithm based on Nash optimality is proposed for the large scale irrigation system to design the controller for setting points regulation. Finally, a simulation example is given to demonstrate the effectiveness of the proposed algorithm.

Distributed model predictive control of steel slab reheating furnace

Nowadays, distributed model predictive control (DMPC) is known as an attractive strategy to control a class of large-scale systems. In this paper, a DMPC algorithm based on Nash optimality is developed for online optimization and control of a class of large-scale systems with output coupling. This DMPC algorithm is further applied to the control of a reheating furnace in steel industry, illustrating the effectiveness of the proposed approach in terms of energy consumption and tracking performance in comparison to control strategies currently implemented in the steel group ArcelorMittal.

Based on Nash Optimization Decoupling Control System for Special Shape Pipe Automatic Welding Machine

A new decoupling control structure is presented for complex special shape pipe welding process, which consists of model construction by reorganization method. Using this structure, an decoupling control system is established which realizes an adaptive decoupling control strategy for the welding processes with integrated complexities by using structure of decoupling control system and based on multivariable predictive function and nash optimization to making sure the right coefficient. Such system can be easily implemented on the welding peocess and simulation show this approach is effective.

Bidding strategy of generation companies using PSO combined with SA method in the pay as bid markets

This paper proposes a new method that uses the combination of particle swarm optimization (PSO) and simulated annealing (SA) to predict the bidding strategy of Generating Companies (Gencos) in an electricity market where they have incomplete information about their opponents and market mechanism of payment is pay as bid. In the proposed methodology, Gencos prepare their strategic bids according to Supply Function Equilibrium (SFE) model and they change their bidding strategies until Nash equilibrium points are obtained. Nash equilibrium points constitute a central solution concept in game theory and they are computed with solving a global optimization problem. In this paper a new computational intelligence technique is introduced that can be used to solve the Nash optimization problem. This new procedure, is based on the PSO algorithm, which uses SA method to avoid becoming trapped in local minima or maxima and improve the velocity’s function of particles. The performance of this procedure is compared with results of other computational intelligence techniques such as PSO, Genetic Algorithm (GA), and a mathematical method (GAMS/DICOPT). The IEEE 39-bus test system is employed to illustrate and verify the results of the proposed method.

The stability analysis of distributed model predictive control with limited communication

For large scale system, distributed model predictive control(MPC) based on Nash optimality can reduce the online computational burden. However, the convergence condition implies that a lot of communication may be needed during one sampling interval, which is unacceptable for practical applications. Under limited communication, the stability conditions for distributed MPC based on Nash optimality is discussed. The conditions can be used to determine the least number of communication times during one sampling interval to guarantee the closed-loop stability. Meanwhile, several special cases, which appear in previous works, are discussed. Furthermore, based on the conditions, a method to design a distributed MPC under limited communication with closed-loop stability guarantee is presented with LMI formulation.

Distributed control of underwater vehicles

Despite the closed-loop performance of centralized multi-variable controllers, the vast majority of control applications are still based on decentralized controllers. Because of their single-loop structure, decentralized controllers cannot suppress interactions of the system, which are only taken into account in the controller tuning phase. Therefore, it would be useful in many cases to tackle the undesirable effects of the interactions on the closed-loop system. A novel model predictive control scheme based on Nash optimality is presented to achieve this goal. In this algorithm the centralized optimization is decomposed into that of several small coupled optimization problems. The relevant computational convergence, the closed-loop performance, and the effect of communication failures on the closed-loop behaviour are analysed. The control problem is illustrated to verify the effectiveness and practicality of the proposed control algorithm.

Distributed Control Design for Underwater Vehicles

The vast majority of control applications are based on non-interacting decentralized control designs. Because of their single-loop structure, these controllers cannot suppress interactions of the system. It would be useful to tackle the undesirable effects of the interactions at the design stage. A novel model predictive control scheme based on Nash optimality is presented to achieve this goal. In this algorithm, the control problem is decomposed into that of several small-coupled mixed integer optimisation problems. The relevant computational convergence, closed-loop performance and the effect of communication failures on the closed-loop behaviour are analysed. Simulation results are presented to illustrate the effectiveness and practicality of the proposed control algorithm.

Investigating equilibria stability on the basis of individual optimum principle

The so-called individual optimum principle is considered that is a generalization of the Nash and Pareto optimality principles. Based on it, the stability of various types of equilibria in game problems is characterized and investigated.

A Special Dynamic Programming Technique for Multiobjective Discrete Control and for Dynamic Games on Graph-Based Networks

Abstract In this paper we extend the dynamic programming technique for the multiobjective version of a special class of problems representing a graph-theoretic structure on a certain network. We assume that the dynamics of the system is controlled by p actors (players) and each of them intend to minimize his own integral-time cost which is described by a certain trajectory. Applying Nash and Pareto optimality principles we study the multiobjective control problems on dynamic networks where the dynamics is described by a directed graph. Polynomial-time algorithms for determining the optimal strategies of the players in the considered multiobjective control problems are proposed exploiting the special structure of the underlying graph.