We present D-Phi iteration: an algorithm for distributed, localized, and scalable robust control of systems with structured uncertainties. This algorithm combines the System Level Synthesis (SLS) parametrization for distributed control with stability criteria from L1, LInf, and nu robust control. We show in simulation that this algorithm achieves good nominal performance while greatly increasing the robust stability margin compared to the LQR controller. To the best of our knowledge, this is the first distributed and localized algorithm for structured robust control; furthermore, algorithm complexity depends only on the size of local neighborhoods and is independent of global system size. We additionally characterize the suitability of different robustness criteria for distributed and localized computation.
Chance-constrained programming (CCP) is a promising approach to handle uncertainties in optimal power flow (OPF). However, conventional CCP usually assumes that uncertainties follow Gaussian distributions, which may not match reality. A few papers employed the Gaussian mixture model (GMM) to extend CCP to cases with non-Gaussian uncertainties, but they are only appropriate for cases with uncertainties on the right-hand side but not applicable to DC OPF that containing left-hand side uncertainties. To address this, we develop a tractable GMM-based chance-constrained DC OPF model. In this model,…
We present a new, scalable alternative to the structured singular value, which we call $ν$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the relationship between robust control of dynamical systems and non-negative constant matrices.
In this paper, we propose state- and static output-feedback generalized guaranteed cost control (GCC) approaches for discrete-time linear systems subject to norm-bounded structured parametric uncertainties. This method enables the convex synthesis for a more general class of systems, where uncertainties are uncorrelated block diagonal, and no feed-through uncertainty is multiplicative with control input ones. It also provides necessary and sufficient conditions for state-feedback and sufficient conditions for static output-feedback. We also present a comparative study among the proposed contro…
This paper proposes a reliable energy scheduling framework for distributed energy resources (DER) of a residential area to achieve an appropriate daily electricity consumption with the maximum affordable demand response. Renewable and non-renewable energy resources are available to respond to customers' demands using different classes of methods to manage energy during the time. The optimal operation problem is a mixed-integer-linear-programming (MILP) investigated using model-based predictive control (MPC) to determine which dispatchable unit should be operated at what time and at what power …
This paper considers the distributed consensus problem of linear multi-agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input. Due to the existence of nonidentical uncertainties, the multi-agent systems discussed in this paper are essentially heterogeneous. For the case where the communication graph is undirected and connected, a distributed continuous static consensus protocol based on the relative state information is first designed, under which the consensus error is uniformly ultimately bounded and exponential…
We propose a tube-based guaranteed cost model predictive controller considering a homothetic formulation for constrained linear systems subject to multiplicative structured norm-bounded uncertainties. It provides an upper bound to the general min-max model predictive control. The invariance property of the proposed tube holds for any arbitrary scaling. It yields a second-order cone programming problem which is less computationally expensive than standard semi-definite programming problems. We also present a numerical example with a comparative study among the proposed approach, an open-loop gu…
This paper addresses the leader-follower flocking problem with a moving leader for networked Lagrange systems with parametric uncertainties under a proximity graph. Here a group of followers move cohesively with the moving leader to maintain connectivity and avoid collisions for all time and also eventually achieve velocity matching. In the proximity graph, the neighbor relationship is defined according to the relative distance between each pair of agents. Each follower is able to obtain information from only the neighbors in its proximity, involving only local interaction. We consider two cas…
This paper considers the distributed robust suboptimal consensus control problem of linear multi-agent systems, with both H2 and H_infty performance requirements. A novel two-step complementary design approach is proposed. In the first step, a distributed control law is designed for the nominal multi-agent system to achieve consensus with a prescribed H2 performance. In the second step, an extra control input, depending on some carefully chosen residual signals indicating the modeling mismatch, is designed to complement the H2 performance by providing robustness guarantee in terms of H_infty r…
Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs Jacobi-type proximal updates of the augmented Lagrangian function, requiring only local solutions of separable block nonlinear programming (NLP) problems. We provide a cheap and explicitly computable Lyapunov function that allows us to establish global and local sublinear convergence of our algorithm, its iteration complexity, as well as simple, practical and theoreti…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or communications among computational agents. Furthermore, some of these distributed algorithms put a considerable computational demand on the agents. In this paper, we show that for tree-structured scattered sensor networks, which are networks that their inter-sensor range measurement graphs have few edges (few range measurements among sensors) and can be represented…
We present a framework which incorporates three aspects of the estimation problem, namely, sparse sensor configuration, optimal precision, and robustness in the presence of model uncertainty. The problem is formulated in the $\mathcal{H}_{\infty}$ optimal observer design framework. We consider two types of uncertainties in the system, i.e. structured affine and unstructured uncertainties. The objective is to design an observer with a given $\mathcal{H}_{\infty}$ performance index with minimal number of sensors and minimal precision values, while guaranteeing the performance for all admissible …
Incorporating Renewable Energy Sources (RES) incurs a high level of uncertainties to electric power systems. This level of uncertainties makes the conventional energy management methods inefficient and jeopardizes the security of distribution systems. In this connection, a scenario-based stochastic programming is introduced to harness uncertainties in the load, electricity price, and photovoltaic generation. Further, a hybrid evolutionary algorithm based on Grey Wolf Optimizer and Particle Swarm Optimisation algorithm is proposed to find the best operation cost, and Energy Not Supplied (ENS) a…
This paper deals with the problem of distributed control synthesis. We seek to find structured controllers that are stably realizable over the underlying network. We address the problem using an operator form of discrete-time linear systems. This allows for uniform treatment of various classes of linear systems, e.g., Linear Time Invariant (LTI), Linear Time Varying (LTV), or linear switched systems. We combine this operator representation for linear systems with the classical Youla parameterization to characterize the set of stably realizable controllers for a given network structure. Using t…
The penetration of distributed renewable energy (DRE) greatly raises the risk of distribution network operation such as peak shaving and voltage stability. Battery energy storage (BES) has been widely accepted as the most potential application to cope with the challenge of high penetration of DRE. To cope with the uncertainties and variability of DRE, a stochastic day-ahead dynamic optimal power flow (DOPF) and its algorithm are proposed. The overall economy is achieved by fully considering the DRE, BES, electricity purchasing and active power losses. The rainflow algorithm-based cycle countin…
In this paper, a stochastic approximation (SA) based distributed algorithm is proposed to solve the resource allocation (RA) with uncertainties. In this problem, a group of agents cooperatively optimize a separable optimization problem with a linear network resource constraint and allocation feasibility constraints, where the global objective function is the sum of agents' local objective functions. Each agent can only get noisy observations of its local function's gradient and its local resource, which cannot be shared by other agents or transmitted to a center. Moreover, there are communicat…
Load frequency control (LFC) is a key factor to maintain the stable frequency in multi-area power systems. As the modern power systems evolve from centralized to distributed paradigm, LFC needs to consider the peer-to-peer (P2P) based scheme that considers limited information from the information-exchange graph for the generator control of each interconnected area. This paper aims to solve a data-driven constrained LQR problem with mean-variance risk constraints and output structured feedback, and applies this framework to solve the LFC problem in multi-area power systems. By reformulating the…
This paper studies the behavior of a strategic aggregator offering regulation capacity on behalf of a group of distributed energy resources (DERs, e.g. plug-in electric vehicles) in a power market. Our objective is to maximize the aggregator's revenue while controlling the risk of penalties due to poor service delivery. To achieve this goal, we propose data-driven risk-averse strategies to effectively handle uncertainties in: 1) The DER parameters (e.g., load demands and flexibilities) and 2) sub-hourly regulation signals (to the accuracy of every few seconds). We design both the day-ahead and…
This paper presents a Distributed Stochastic Model Predictive Control algorithm for networks of linear systems with multiplicative uncertainties and local chance constraints on the states and control inputs. The chance constraints are approximated via Cantelli's inequality by means of expected value and covariance. The cooperative control algorithm is based on the distributed Alternating Direction Method of Multipliers, which renders the controller fully distributedly implementable, recursively feasible and ensures point-wise convergence of the states. The aforementioned properties are guarant…
Variable Stepsize Distributed Forward-Backward Splitting Methods as Relocated Fixed-Point Iterations
Centro de Modelamiento Matemático (CNRS IRL2807), Universidad de Chile（智利大学数学建模中心）；School of Science, RMIT University（皇家墨尔本理工大学理学院）；School of Mathematics & Statistics, The University of Melbourne（墨尔本大学数学与统计学院）
This paper presents a new distributed control framework to coordinate inverter-interfaced distributed energy resources (DERs) in island microgrids. We show that under bounded load uncertainties, the proposed control method can steer the microgrid to a desired steady state with synchronized inverter frequency across the network and proportional sharing of both active and reactive powers among the inverters. We also show that such convergence can be achieved while respecting constraints on voltage magnitude and branch angle differences. The controller is robust under various contingency scenario…
We present a robust Distributed and Localized Model Predictive Control (rDLMPC) framework for large-scale structured linear systems. The proposed algorithm uses the System Level Synthesis to provide a distributed closed-loop model predictive control scheme that is robust to exogenous disturbances. The resulting controllers require only local information exchange for both synthesis and implementation. We exploit the fact that for polytopic disturbance constraints, SLS- based distributed control problems have been shown to have structure amenable for distributed optimization techniques. We show …
In this paper we propose a new operator splitting algorithm for distributed Nash equilibrium seeking under stochastic uncertainty, featuring relaxation and inertial effects. Our work is inspired by recent deterministic operator splitting methods, designed for solving structured monotone inclusion problems. The algorithm is derived from a forward-backward-forward scheme for solving structured monotone inclusion problems featuring a Lipschitz continuous and monotone game operator. To the best of our knowledge, this is the first distributed (generalized) Nash equilibrium seeking algorithm featuri…
Virginia Tech（弗吉尼亚理工大学）；California Institute of Technology（加州理工学院）
The aim of this work is to define a planner that enables robust legged locomotion for complex multi-agent systems consisting of several holonomically constrained quadrupeds. To this end, we employ a methodology based on behavioral systems theory to model the sophisticated and high-dimensional structure induced by the holonomic constraints. The resulting model is then used in tandem with distributed control techniques such that the computational burden is shared across agents while the coupling between agents is preserved. Finally, this distributed model is framed in the context of a predictive…
