In this article, we study the linear time-invariant state-feedback controller design problem for distributed systems. We follow the recently developed system level synthesis (SLS) approach and impose locality structure on the resulting closed-loop mappings; the corresponding controller implementation inherits this prescribed structure. In contrast to existing SLS results, we derive an explicit (rather than implicit) parameterization of all achievable stabilized closed-loops. This admits more efficient IIR representations of the temporal part of the closed-loop dynamics, and it allows for the H2 design problem with closed-loop spatial sparsity constraints to be converted to a standard model matching problem, with the number of transfer function parameters scaling linearly with the closed-loop spatial extent constraint. We illustrate our results with two applications: consensus of first-order subsystems and the vehicular platoons problem. In the case of first-order consensus, we provide analytic solutions and further analyze the architecture of the resulting controller implementation. Results for infinite extent spatially invariant systems are presented to provide insight to the case of a large but finite number of subsystems.
Control algorithms such as model predictive control (MPC) and state estimators rely on a number of different parameters. The performance of the closed loop usually depends on the correct setting of these parameters. Tuning is often done manually by experts based on a simulation model of the system. Two problems arise with this procedure. Firstly, experts need to be skilled and still may not be able to find the optimal parametrization. Secondly, the performance of the simulation model might not be able to be carried over to the real world application due to model inaccuracies within the simulat…
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…
We address the problem of sparsity-promoting optimal control of cyber-physical systems with feedback delays. The delays are categorized into two classes - namely, intra-layer delay, and inter-layer delay between the cyber and the physical layers. Our objective is to minimize the H2-norm of the closed-loop system by designing an optimal combination of these two delays along with a sparse state-feedback controller, while respecting a given bandwidth constraint. We propose a two-loop optimization algorithm for this. The inner loop, based on alternating directions method of multipliers (ADMM), han…
The linear-quadratic controller is one of the fundamental problems in control theory. The optimal solution is a linear controller that requires access to the state of the entire system at any given time. When considering a network system, this renders the optimal controller a centralized one. The interconnected nature of a network system often demands a distributed controller, where different components of the system are controlled based only on local information. Unlike the classical centralized case, obtaining the optimal distributed controller is usually an intractable problem. Thus, we ado…
Given one open-loop measured trajectory of a single-input single-output discrete-time linear time-invariant system, we present a framework for data-driven controller design for closed-loop finite-horizon dissipativity. First, we parametrize all closed-loop trajectories using the given data of the plant and a model of the controller. We then provide an approach to validate the controller by verifying closed-loop dissipativity in the standard feedback loop based on this parametrization. We use these conditions to design controllers leading to closed-loop dissipativity based on a quadratic matrix…
In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial dynamics, our approach allows to design controllers for unknown systems with rational or general non-polynomial dynamics. We first derive a data-driven parametrization of unknown nonlinear systems with rational dynamics. By applying robust control techniques to this parametrization, we obtain sum-of-squares based criteria for designing controllers with closed-loo…
We study the distributed Linear Quadratic Gaussian (LQG) control problem in discrete-time and finite-horizon, where the controller depends linearly on the history of the outputs and it is required to lie in a given subspace, e.g. to possess a certain sparsity pattern. It is well-known that this problem can be solved with convex programming within the Youla domain if and only if a condition known as Quadratic Invariance (QI) holds. In this paper, we first show that given QI sparsity constraints, one can directly descend the gradient of the cost function within the domain of output-feedback cont…
The goal of this paper is to address finite-horizon minimum variance and covariance steering problems for discrete-time stochastic (Gaussian) linear systems. On the one hand, the minimum variance problem seeks for a control policy that will steer the state mean of an uncertain system to a prescribed quantity while minimizing the trace of its terminal state covariance (or variance). On the other hand, the covariance steering problem seeks for a control policy that will steer the covariance of the terminal state to a prescribed positive definite matrix. We propose a solution approach that relies…
Multi-agent networked control systems (NCSs) are often subject to model uncertainty and are limited by large communication cost, associated with feedback of data between the system nodes. To provide robustness against model uncertainty and to reduce the communication cost, this paper investigates the mixed $H_2/H_{\infty}$ control problem for NCS under the sparsity constraint. First, proximal alternating linearized minimization (PALM) is employed to solve the centralized social optimization where the agents have the same optimization objective. Next, we investigate a sparsity-constrained nonco…
Model-based feedforward control improves tracking performance of motion systems, provided that the model describing the inverse dynamics is of sufficient accuracy. Model sets, such as neural networks (NNs) and physics-guided neural networks (PGNNs) are typically used as flexible parametrizations that enable accurate identification of the inverse system dynamics. Currently, these (PG)NNs are used to identify the inverse dynamics directly. However, direct identification of the inverse dynamics is sensitive to noise that is present in the training data, and thereby results in biased parameter est…
Various new implicit parameterizations for stabilizing controllers that allow one to impose structural constraints on the controller have been proposed lately. They are convex but infinite-dimensional, formulated in the frequency domain with no available efficient methods for computation. In this paper, we introduce a kernel version of the Youla parameterization to characterize the set of stabilizing controllers. It features a single affine constraint, which allows us to recast the controller parameterization as a novel robust filtering problem. This makes it possible to derive the first effic…
We investigate stability analysis and controller design of unknown continuous-time systems under state-feedback with aperiodic sampling, using only noisy data but no model knowledge. We first derive a novel data-dependent parametrization of all linear time-invariant continuous-time systems which are consistent with the measured data and the assumed noise bound. Based on this parametrization and by combining tools from robust control theory and the time-delay approach to sampled-data control, we compute lower bounds on the maximum sampling interval (MSI) for closed-loop stability under a given …
System Level Synthesis (SLS) parametrization facilitates controller synthesis for large, complex, and distributed systems by incorporating system level constraints (SLCs) into a convex SLS problem and mapping its solution to stable controller design. Solving the SLS problem at scale efficiently is challenging, and current attempts take advantage of special system or controller structures to speed up the computation in parallel. However, those methods do not generalize as they rely on the specific system/controller properties. We argue that it is possible to solve general SLS problems more effi…
Designing distributed optimal controllers subject to communication constraints is a difficult problem unless structural assumptions are imposed on the underlying dynamics and information exchange structure, e.g., sparsity, delay, or spatial invariance. In this paper, we borrow ideas from graph signal processing and define and analyze a class of Graph Symmetric Systems (GSSs), which are systems that are symmetric with respect to an underlying graph topology. We show that for linear quadratic problems subject to dynamics defined by a GSS, the optimal centralized controller is given by a novel cl…
Optimal distributed control for platooning via sparse coprime factorizations
Stevens Institute of Technology（史蒂文斯理工学院）；University “Politehnica” Bucharest（布加勒斯特理工大学）；Brigham Young University（杨百翰大学）；University of Pennsylvannia（宾夕法尼亚大学）
We address the problem of sparsity-promoting optimal control of cyber-physical systems (CPSs) in the presence of communication delays. The delays are categorized into two types - namely, an inter-layer delay for passing state and control information between the physical layer and the cyber layer, and an intra-layer delay that operates between the computing agents, referred to here as control nodes (CNs), within the cyber-layer. Our objective is to minimize the closed-loop H2-norm of the physical system by co-designing an optimal combination of these two delays and a sparse state-feedback contr…
MAD: A Magnitude And Direction Policy Parametrization for Stability Constrained Reinforcement Learning
Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL)（瑞士联邦理工学院机械工程学院）；Department of Engineering Science, University of Oxford（牛津大学工程科学系）；Institute for Data Science Foundations, Hamburg University of Technology (TUHH)（汉堡技术大学数据科学基础研究所）；School of Electrical Engineering and Computer Science and Digital Futures, KTH Royal Institute of Technology（皇家理工学院电气工程与计算机科学学院及数字未来学院）
Controller tuning based on black-box optimization allows to automatically tune performance-critical parameters w.r.t. mostly arbitrary high-level closed-loop control objectives. However, a comprehensive benchmark of different black-box optimizers for control engineering problems has not yet been conducted. Therefore, in this contribution, 11 different versions of Bayesian optimization (BO) are compared with seven metaheuristics and other baselines on a set of ten deterministic simulative single-objective tuning problems in control. Results indicate that deterministic noise, low multimodality, …
It is known that the set of internally stabilizing controller $\mathcal{C}_{\text{stab}}$ is non-convex, but it admits convex characterizations using certain closed-loop maps: a classical result is the Youla parameterization, and two recent notions are the system-level parameterization (SLP) and the input-output parameterization (IOP). In this paper, we address the existence of new convex parameterizations and discuss potential tradeoffs of each parametrization in different scenarios. Our main contributions are: 1) We reveal that only four groups of stable closed-loop transfer matrices are equ…
We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop data trajectory, which may be affected by noise. First, a data-driven characterization of the uncertain class of closed-loop matrices under state-feedback is derived. By considering this parametrization in the robust control framework, we design data-driven state-feedback gains with guarantees on stability and performance, containing, e.g., the $\mathcal{H}_…
Benchmarking Empirical and Learning-Based Approaches for Feedforward Steering Control in Autonomous Racing
Chair of Automatic Control, Department of Engineering Physics and Computation, Technical University of Munich（慕尼黑技术大学自动控制系）；Professorship of Autonomous Vehicle Systems (AVS), Department of Mobility Systems Engineering, Technical University of Munich（慕尼黑技术大学移动系统工程系自动驾驶车辆系统教授职位）
