Distributed Extremum Seeking Control for a Variable Refrigerant Flow System

The variable refrigerant flow (VRF) technology has facilitated the development of multi-split ductless air conditioning systems, in which multiple indoor units (IDU) are used to regulate the refrigerant flow to achieve individualized zoning control. Model based control for VRF system demands for more modeling efforts in part due to diverse configuration, as well as changes in load and ambient conditions. As a model-free control strategy, Extremum Seeking Control (ESC) has been investigated for VRF systems. Dong et al. (2015) applied the standard centralized ESC scheme to a VRF system that consists of one outdoor unit (ODU) and four IDU’s. Simulation results have indicated the effectiveness of such strategy. As the number of IDU’s increases, the complexity of centralized controllers will increase accordingly. Therefore distributed ESC becomes a natural consideration for VRF systems with large number of IDU’s. In this paper, the Shashahani gradient based distributed ESC scheme proposed by Poveda and Quijano (2013, 2015), is applied to the four-zone VRF system simulated by Dong et al. (2015). In particular, this scheme is enhanced by appending a band-pass filter array at the output to achieve a better “isolation†among individual input channels. A single-input ESC is applied to the ODU, while the distributed ESC is applied to the four IDU’s with each acting as an agent. For each agent, the respective power consumption is used as feedback. The objective is to minimize the total power consumption of all agents. For the ODU ESC, the compressor suction pressure (PCS) set-point is employed as the manipulative input. For the IDU DESC, the evaporator superheat (SH) set-point is used as the manipulative input for each IDU agent. The distributed ESC scheme assumes full information communication among all IDU’s. Simulation study is performed to evaluate the proposed strategy with the Modelica based dynamic simulation model developed by Dong et al. (2015). The ESC is designed under the ambient condition of 35oC and 40 %RH, respectively. The initial temperature of all four IDUs zone is 29oC, and the zone temperature set-point is 26oC. The heat loads for IDU1 through IDU4 are 3000W, 2600W, 2400W and 2000W, respectively. It takes the average total power about 10000 seconds to converge to about 3200W in steady state, with PCS around 13bar, and the SH values of IDU1 through IDU4 at 4.5oC, 4.5oC, 6oC, and 5.5oC, respectively. The total power consumption was decreased from 4500 W to 3200 W, i.e. by 29%. In comparison with the centralized ESC Dong et al. (2015), the steady state error of total power is less than 50w. Work is under way to improve transient and steady-state performance, as well as simulation of other operation modes.  Â

A Tutorial on Distributed Optimization for Cooperative Robotics: from Setups and Algorithms to Toolboxes and Research Directions

Several interesting problems in multi-robot systems can be cast in the framework of distributed optimization. Examples include multi-robot task allocation, vehicle routing, target protection and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this paper, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss their implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots

Distributed population dynamics : optimization and control applications

© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Population dynamics have been widely used in the design of learning and control systems for networked engineering applications, where the information dependency among elements of the network has become a relevant issue. Classic population dynamics (e.g., replicator, logit choice, Smith, and projection) require full information to evolve to the solution (Nash equilibrium). The main reason is that classic population dynamics are deduced by assuming well-mixed populations, which limits the applications where this theory can be implemented. In this paper, we extend the concept of population dynamics for nonwell-mixed populations in order to deal with distributed information structures that are characterized by noncomplete graphs. Although the distributed population dynamics proposed in this paper use partial information, they preserve similar characteristics and properties of their classic counterpart. Specifically, we prove mass conservation and convergence to Nash equilibrium. To illustrate the performance of the proposed dynamics, we show some applications in the solution of optimization problems, classic games, and the design of distributed controllers.Peer ReviewedPostprint (author's final draft

Distributed population dynamics: Optimization and control applications

Population dynamics have been widely used in the design of learning and control systems for networked engineering applications, where the information dependency among elements of the network has become a relevant issue. Classic population dynamics (e.g., replicator, logit choice, Smith, and projection) require full information to evolve to the solution (Nash equilibrium). The main reason is that classic population dynamics are deduced by assuming well-mixed populations, which limits the applications where this theory can be implemented. In this paper, we extend the concept of population dynamics for nonwell-mixed populations in order to deal with distributed information structures that are characterized by noncomplete graphs. Although the distributed population dynamics proposed in this paper use partial information, they preserve similar characteristics and properties of their classic counterpart. Specifically, we prove mass conservation and convergence to Nash equilibrium. To illustrate the performance of the proposed dynamics, we show some applications in the solution of optimization problems, classic games, and the design of distributed controllers.This work has been supported by COLCIENCIAS–COLFUTURO, grants No: 528 and 6172; and by Project ALTERNAR, Acuerdo 005, 07/19/13 CTeI–SGR–Narino, Colombia.Peer reviewe

Nondisturbing extremum seeking control for multi-agent industrial systems

Industrial applications of extremum seeking control (ESC) can be a hit and miss affair. Although a gain in performance can be achieved, the dither applied to excite the system causes unwanted fluctuations in the performance of the system. The fluctuations in systems with a single extremum seeking loop are generally small. However, for systems with many extremum seeking loops, the fluctuations in each loop may add up to an intolerable amount of fluctuation in the total performance. In this article, we propose a method to cancel the dither-induced fluctuations in the overall system performance to a large extent by smartly constructing the dither signals in each extremum seeking loop using a centralized coordinator. The novelty of our method lies in the direct calculation of the dither signals that avoids the heavy computations required by other methods. Moreover, we provide a solvability analysis for the problem of cancelling dither-induced fluctuations in the total performance of the system. Furthermore, a complete stability analysis of the overall ESC scheme with dither coordination is given.publishedVersio

Gradient-Free Nash Equilibrium Seeking in N-Cluster Games with Uncoordinated Constant Step-Sizes

In this paper, we consider a problem of simultaneous global cost minimization and Nash equilibrium seeking, which commonly exists in $N$-cluster non-cooperative games. Specifically, the agents in the same cluster collaborate to minimize a global cost function, being a summation of their individual cost functions, and jointly play a non-cooperative game with other clusters as players. For the problem settings, we suppose that the explicit analytical expressions of the agents' local cost functions are unknown, but the function values can be measured. We propose a gradient-free Nash equilibrium seeking algorithm by a synthesis of Gaussian smoothing techniques and gradient tracking. Furthermore, instead of using the uniform coordinated step-size, we allow the agents across different clusters to choose different constant step-sizes. When the largest step-size is sufficiently small, we prove a linear convergence of the agents' actions to a neighborhood of the unique Nash equilibrium under a strongly monotone game mapping condition, with the error gap being propotional to the largest step-size and the smoothing parameter. The performance of the proposed algorithm is validated by numerical simulations

Robust Hybrid Systems for Control, Learning, and Optimization in Networked Dynamical Systems

The deployment of advanced real-time control and optimization strategies in socially-integratedengineering systems could significantly improve our quality of life whilecreating jobs and economic opportunity. However, in cyber-physical systems such assmart grids, transportation networks, healthcare, and robotic systems, there still existseveral challenges that prevent the implementation of intelligent control strategies.These challenges include the existence of limited communication networks, dynamicand stochastic environments, multiple decision makers interacting with the system,and complex hybrid dynamics emerging from the feedback interconnection of physicalprocesses and computational devices.In this dissertation, we study the problem of designing robust control and optimizationalgorithms for cyber-physical systems using the framework of hybrid dynamicalsystems. We propose different theoretical frameworks for the design and analysis offeedback mechanisms that optimize the performance of dynamical systems without requiringan explicit characterization of their mathematical model, i.e., in a model-freeway. The closed-loop system that emerges of the interconnection of the plant with thefeedback mechanism describes, in general, a set-valued hybrid dynamical system. Thesetypes of systems combine continuous-time and discrete-time dynamics, and they usuallylack the uniqueness of solutions property. The framework of set-valued hybriddynamical systems allows us to study many complex dynamical systems that emerge indifferent engineering applications, such as networked multi-agent systems with switching graphs, non-smooth mechanical systems, dynamic pricing mechanisms in transportationsystems, autonomous robots with logic-based controllers, etc. We proposea step-by-step approach to the design of different types of discrete-time, continuous-time,hybrid, and stochastic controllers for different types of applications, extendingand generalizing different results in the literature in the area of extremum seeking control,sampled-data extremization, robust synchronization, and stochastic learning innetworked systems. Our theoretical results are illustrated via different simulations andnumerical examples