We consider the optimal distributed controller design problem subject to two structural requirements: locality, i.e. available measurements and sub-controllers' interactions are governed by a graph structure, and relative feedback, i.e. only differences of measurements are available to the controller. We formalize controller locality in terms of the controller's transfer function, state-space realization, or resulting closed-loop mapping. We demonstrate that the relative feedback requirement can be written as a convex constraint on the controller and (in special cases) on the resulting closed-loop, and we characterize the allowable structures of relative feedback controllers. We prove that sparse closed-loop design is a convex relaxation of structured controller state-space design, even in the continuous time IIR setting. This formalizes and extends results of the recently developed System Level Synthesis framework. We take a first step toward quantifying the performance gap associated with this convex relaxation by constructing a class of examples (based on relative feedback requirements) for which the difference in performance, measured by an H2 norm, is infinite. The results presented are used to contrast several issues of structural constraints in distributed control design that remain as open problems.
Reliable and secure operation of power systems becomes increasingly challenging as the share of volatile generation rises, leading to largely changing dynamics. Typically, the architecture and structure of controllers in power systems, such as voltage controllers of power generators, are fixed during the design and buildup of the network. As replacing existing controllers is often undesired and challenging, setpoint adjustments, as well as tuning of the controller parameters, are possibilities to counteract large disturbances and changing dynamics. We present an approach for fast and computati…
This paper addresses the problem of designing an optimal output feedback controller with a specified controller structure for linear time-invariant (LTI) systems to maximize the passivity level for the closed-loop system, in both continuous-time (CT) and discrete-time (DT). Specifically, the set of controllers under consideration is linearly parameterized with constrained parameters. Both input feedforward passivity (IFP) and output feedback passivity (OFP) indices are used to capture the level of passivity. Given a set of stabilizing controllers, a necessary and sufficient condition is propos…
Osaka University（大阪大学）；National Institute of Informatics（国立信息学研究所）
In this paper, we propose a control synthesis method for signal temporal logic (STL) specifications with neural networks (NNs). Most of the previous works consider training a controller for only a given STL specification. These approaches, however, require retraining the NN controller if a new specification arises and needs to be satisfied, which results in large consumption of memory and inefficient training. To tackle this problem, we propose to construct NN controllers by introducing encoder-decoder structured NNs with an attention mechanism. The encoder takes an STL formula as input and en…
This paper proposes a distributed design method of controllers having a glocal (global/local) information structure for large-scale network systems. Distributed design, independent design of all subcontrollers that constitute a structured controller, facilitates scalable controller synthesis. While existing distributed design methods confine attention to the decentralized or distributed information structures, this study addresses distributed design of glocal-structured controllers. Glocal control exploits the nature that network system's behavior can typically be represented as a superpositio…
This study investigates a parameterization of all output-rectifying retrofit controllers for distributed design of a structured controller. It has been discovered that all retrofit controllers can be characterized as a constrained Youla parameterization, which is difficult to solve analytically. For synthesis, a tractable and insightful class of retrofit controllers, referred to as output-rectifying retrofit controllers, has been introduced. An unconstrained parameterization of all output-rectifying retrofit controllers can be derived under a technical assumption on measurability of particular…
In this paper, the problem of synthesizing a distributed controller from data is considered, with the objective to optimize a model-reference control criterion. We establish an explicit ideal distributed controller that solves the model-reference control problem for a structured reference model. On the basis of input-output data collected from the interconnected system, a virtual experiment setup is constructed which leads to a network identification problem. We formulate a prediction-error identification criterion that has the same global optimum as the model-reference criterion, when the con…
Designing a static state-feedback controller subject to structural constraint achieving asymptotic stability is a relevant problem with many applications, including network decentralized control, coordinated control, and sparse feedback design. Leveraging on the Projection Lemma, this work presents a new solution to a class of state-feedback control problems, in which the controller is constrained to belong to a given linear space. We show through extensive discussion and numerical examples that our approach leads to several advantages with respect to existing methods: first, it is computation…
Stability enforcement remains a challenge in data-driven control paradigms, where no parametrised model of the system is available. For instance, the system's instabilities can be estimated in order to enforce a closed-loop stability constraint on the controller reduction step. In order to avoid this preliminary estimation of instabilities, this paper proposes to embed a closed-loop stability constraint in the design. To that extent, an optimization problem is formulated in order to improve matching between the reference model and the closed-loop while maintaining internal stability. The propo…
Optimal Structured Static State-Feedback Control Design with Limited Model Information for Fully-Actuated Systems
ACCESS Linnaeus Center, School of Electrical Engineering, KTH-Royal Institute of Technology（ACCESS林奈斯中心，电气工程学院，KTH皇家理工学院）；Department of Aerospace Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校航空航天工程系与协同科学实验室）
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…
This paper presents a novel approach to synthesize dual controllers for unknown linear time-invariant systems with the tasks of optimizing a quadratic cost while reducing the uncertainty. To this end, a synthesis problem is defined where the feedback law has to simultaneously gain knowledge of the system and robustly optimize the cost. By framing the problem in a finite horizon setting, the trade-offs arising when the tasks include both identification and control are formally captured in the optimization problem. Results show that efficient exploration strategies are achieved when the structur…
We address the problem of designing optimal linear time-invariant (LTI) sparse controllers for LTI systems, which corresponds to minimizing a norm of the closed-loop system subject to sparsity constraints on the controller structure. This problem is NP-hard in general and motivates the development of tractable approximations. We characterize a class of convex restrictions based on a new notion of Sparsity Invariance (SI). The underlying idea of SI is to design sparsity patterns for transfer matrices Y(s) and X(s) such that any corresponding controller K(s)=Y(s)X(s)^-1 exhibits the desired spar…
Decentralized Disturbance Accommodation with Limited Plant Model Information
ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology（ACCESS林奈中心，电气工程学院，皇家理工学院）；Department of Aerospace Engineering, University of Illinois at Urbana-Champaign（航空航天工程系，伊利诺伊大学厄巴纳-香槟分校）
The University of Texas at Dallas（德克萨斯大学达拉斯分校）；The Australian National University（澳大利亚国立大学）
We propose a robust data-driven output feedback control algorithm that explicitly incorporates inherent finite-sample model estimate uncertainties into the control design. The algorithm has three components: (1) a subspace identification nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method comprising a coupled optimal dynamic output feedback filter and controller with multiplicative noise. A key advantage of the proposed approach is that the system identification…
We present a novel approach to control design for nonlinear systems which leverages model-free policy optimization techniques to learn a linearizing controller for a physical plant with unknown dynamics. Feedback linearization is a technique from nonlinear control which renders the input-output dynamics of a nonlinear plant \emph{linear} under application of an appropriate feedback controller. Once a linearizing controller has been constructed, desired output trajectories for the nonlinear plant can be tracked using a variety of linear control techniques. However, the calculation of a lineariz…
