An eigenvalue based framework is developed for the stability analysis and stabilization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations are analyzed and their stability properties are studied, taking into account the effect of small delay perturbations. Subsequently, numerical methods for stability assessment and for designing stabilizing controllers with a prescribed structure or order, based on a direct optimization approach, are briefly addressed. The effectiveness of the approach is illustrated with a software demo. The paper concludes by pointing out the similarities with the computation and optimization of H-infinity norms.
In this paper we consider a class of linear time invariant systems with infinitely many unstable modes. By using the parameterization of all stabilizing controllers, we show that H-infinity controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes. We illustrate connections between the problem solved here and an indirect method for strongly stabilizing H-infinity controller design for systems with time delays.
The increase in available data and complexity of dynamical systems has sparked the research on data-based system performance analysis and controller design. Recent approaches can guarantee performance and robust controller synthesis based on noisy input-state data of a single dynamical system. In this paper, we extend a recent data-based approach for guaranteed performance analysis to distributed analysis of interconnected linear systems. We present a new set of sufficient LMI conditions based on noisy input-state data that guarantees $\mathcal{H}_\infty$ performance and have a structure that …
Weighted sensitivity minimization is studied within the framework of strongly stabilizing (stable) H-infinity controller design for a class of infinite dimensional systems. This problem has been solved by Ganesh and Pearson, [11], for finite dimensional plants using Nevanlinna-Pick interpolation. We extend their technique to a class of unstable time delay systems. Moreover, we illustrate suboptimal solutions, and their robust implementation.
In this work, we propose a compositional scheme for the safety controller synthesis of interconnected discrete-time stochastic systems with Markovian switching signals. Our proposed approach is based on a notion of so-called control storage certificates computed for individual subsystems, by leveraging which, one can synthesize state-feedback controllers for interconnected systems to enforce safety specifications over finite time horizons. To do so, we employ a sum-of-squares (SOS) optimization approach to search for multiple storage certificates of each switching subsystem while synthesizing …
The current limitation in the synthesis of distributed $\mathscr{H}_2$ controllers for linear interconnected systems is scalability due to non-convex or unstructured synthesis conditions. In this paper we develop convex and structured conditions for the existence of a distributed $\mathscr{H}_2$ controller for discrete-time interconnected systems with an interconnection structure that corresponds to an arbitrary graph. Neutral interconnections and a storage function with a block-diagonal structure are utilized to attain coupling conditions that are of a considerably lower computational complex…
In this paper, we focus on mitigating the computational complexity in abstraction-based controller synthesis for interconnected control systems. To do so, we provide a compositional framework for the construction of abstractions for interconnected systems and a bottom-up controller synthesis scheme. In particular, we propose a notion of approximate composition which makes it possible to compute an abstraction of the global interconnected system from the abstractions (possibly of different types) of its components. Finally, by leveraging our notion of approximate composition, we propose a botto…
The design of an observer-based state feedback (OBSF) controller with guaranteed passivity properties for port-Hamiltonian systems (PHS) is addressed using linear matrix inequalities (LMIs). The observer gain is freely chosen and the LMIs conditions such that the state feedback is equivalent to control by interconnection with an input strictly passive (ISP) and/or an output strictly passive (OSP) and zero state detectable (ZSD) port-Hamiltonian controller are established. It is shown that the proposed controller exponentially stabilizes a class of infinite-dimensional PHS and asymptotically st…
Dissipativity-Based Data-Driven Decentralized Control of Interconnected Systems
ETH Zurich（苏黎世联邦理工学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of California Berkeley（加州大学伯克利分校）；University of Groningen（格罗宁根大学）
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 design fixed-order strong H-infinity controllers for general time-delay systems. The designer chooses the controller order and may introduce constant time-delays in the controller. We represent the closed-loop system of the plant and the controller as delay differential algebraic equations (DDAEs). This representation deals with any interconnection of systems with time-delays without any elimination techniques. We present a numerical algorithm to compute the strong H-infinity norm for DDAEs which is robust to arbitrarily small delay perturbations, unlike the standard H-infinity norm. We opt…
In this work, we present a compositional safety controller synthesis approach for the class of discrete-time linear control systems. Here, we leverage a state-of-the-art result on the computation of robust controlled invariant sets. To tackle the complexity of controller synthesis over complex interconnected systems, this paper introduces a decentralized controller synthesis scheme. Rather than treating the interconnected system as a whole, we first design local safety controllers for each subsystem separately to enforce local safety properties, with polytopic state and input constraints as we…
An eigenvalue based framework is developed for the H-infinity norm analysis and its norm minimization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations (DDAEs). For these equations H-infinity norms are analyzed and their sensitivity with respect to small delay perturbations is studied. Subsequently, numerical methods for the H-infinity norm computation and for designing controllers minimizing the H-infinity norm with a prescribed structure or order, based on a direct optimization approach, are briefly addressed. The effectiveness of th…
Declines in cost and concerns about the environmental impact of traditional generation have boosted the penetration of renewables and non-conventional distributed energy resources into the power grid. The intermittent availability of these resources causes the inertia of the power system to vary over time. As a result, there is a need to go beyond traditional controllers designed to regulate frequency under the assumption of invariant dynamics. This paper presents a learning-based framework for the design of stable controllers based on imitating datasets obtained from linear-quadratic regulato…
A state space based design method is given to find strongly stabilizing controllers for multiple-input-multiple-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H-infinity controller in terms of linear matrix inequalities (LMIs) and the controller order is twice that of the plant. A new parameterization of strongly stabilizing controllers is determined using linear fractional transformations (LFTs).
The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear controllers under quadratic costs model also known as linear quadratic regulators (LQR). We present two different semi-definite programs (SDP) which results in a controller that stabilizes all systems within an ellipsoid uncertainty set. We further show that the feasibility conditions of the proposed SDPs are \emph{equivalent}. Using the derived robust controller syn…
A controller synthesis method for state- and input-constrained nonlinear systems is presented that seeks continuous piecewise affine (CPA) Lyapunov-like functions and controllers simultaneously. Non-convex optimization problems are formulated on triangulated subsets of the admissible states that can be refined to meet primary control objectives, such as stability and safety, alongside secondary performance objectives. A multi-stage design is also given that enlarges the region of attraction (ROA) sequentially while allowing exclusive performance for each stage. A clear boundary for an invarian…
Self-triggered control is an improvement on event-triggered control methods. Unlike the latter, self-triggered control does not require monitoring the behavior of the system constantly. Instead, self-triggered algorithms predict the events at which the control law has to be updated before they happen, relying on system model and past information.\\ In this work, we present a self-triggered version of an event-triggered control method in which events are generated when a pseudo-Lyapunov function (PLF) associated with the system increases up to a certain limit. This approach has been shown to co…
We address the problem of model-free distributed stabilization of heterogeneous multi-agent systems using reinforcement learning (RL). Two algorithms are developed. The first algorithm solves a centralized linear quadratic regulator (LQR) problem without knowing any initial stabilizing gain in advance. The second algorithm builds upon the results of the first algorithm, and extends it to distributed stabilization of multi-agent systems with predefined interaction graphs. Rigorous proofs are provided to show that the proposed algorithms achieve guaranteed convergence if specific conditions hold…
This paper proposes a novel method for distributed controller synthesis of homogeneous interconnected systems consisting of identical subsystems. The objective of the designed controller is to minimize the L2-gain of the performance channel. The proposed method is an extended formulation of the Full Block S-Procedure (FBSP) where we introduce an additional set of variables. This allows relaxing the block-diagonal structural assumptions on the Lyapunov and multiplier matrices required for distributed control design, which reduces conservatism w.r.t most existing approaches. We show how to decom…
This paper introduces a framework for learning a minimum-norm stabilizing controller for a system with unknown dynamics using model-free policy optimization methods. The approach begins by first designing a Control Lyapunov Function (CLF) for a (possibly inaccurate) dynamics model for the system, along with a function which specifies a minimum acceptable rate of energy dissipation for the CLF at different points in the state-space. Treating the energy dissipation condition as a constraint on the desired closed-loop behavior of the real-world system, we use penalty methods to formulate an uncon…
Sydney Institute for Robotics and Intelligent Systems（悉尼机器人与智能系统研究所）；Australian Centre for Field Robotics（澳大利亚野外机器人中心）；School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney（悉尼大学航空航天、机械与机电工程学院）
This paper proposes a nonlinear policy architecture for control of partially-observed linear dynamical systems providing built-in closed-loop stability guarantees. The policy is based on a nonlinear version of the Youla parameterization, and augments a known stabilizing linear controller with a nonlinear operator from a recently developed class of dynamic neural network models called the recurrent equilibrium network (REN). We prove that RENs are universal approximators of contracting and Lipschitz nonlinear systems, and subsequently show that the the proposed Youla-REN architecture is a unive…
This paper proposes a novel load frequency control (LFC) approach formulated on an optimal structure of the coefficient diagram method (CDM) in a two-area thermal power system. As part of a realistic analysis, nonlinearities related to governor dead band (GDB) and generation rate constraint (GRC) have been considered. In this article, a hybrid CDM method is combined with the optimization of its mathematical equations to achieve an innovative controller. Furthermore, a new metaheuristic optimization technique called the water cycle algorithm (WCA) is used to determine the optimal coefficients o…
Stabilizing Controllers for Multi-Input, Singular Control Gain Systems
Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin（德克萨斯大学奥斯汀分校航空航天工程与应用力学）；Systems and Control Engineering, Indian Institute of Technology, Bombay（印度孟买理工学院系统与控制工程）
Switching control strategies that unite a potentially high-performance but uncertified controller and a stabilizing albeit conservative controller are shown to be able to balance safety with efficiency, but have been less studied under partial observation of state. To address this gap, we propose a switching control strategy for partially observed linear-Gaussian systems with provable performance guarantees. We show that the proposed switching strategy is both safe and efficient, in the sense that: (1) the linear-quadratic cost of the system is always bounded even if the original uncertified c…
Integral reinforcement learning (IRL) was proposed in literature to obviate the requirement of drift dynamics in adaptive dynamic programming framework. Most of the online IRL schemes in literature require two sets of neural network (NNs), known as actor-critic NN and an initial stabilizing controller. Recently, for RL-based robust tracking this requirement of initial stabilizing controller and dual-approximator structure could be obviated by using a modified gradient descent-based update law containing a stabilizing term with critic-only structure. To the best of the authors' knowledge, there…
Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems
Sharif University of Technology（谢里夫理工大学）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所（ISTA））；Massachusetts Institute of Technology（麻省理工学院）
Stability is one of the most fundamental requirements for systems synthesis. In this paper, we address the stabilization problem for unknown linear systems via policy gradient (PG) methods. We leverage a key feature of PG for Linear Quadratic Regulator (LQR), i.e., it drives the policy away from the boundary of the unstabilizing region along the descent direction, provided with an initial policy with finite cost. To this end, we discount the LQR cost with a factor, by adaptively increasing which gradient leads the policy to the stabilizing set while maintaining a finite cost. Based on the Lyap…
We analyze and design H-infinity controllers for general time-delay systems with time-delays in systems' state, inputs and outputs. We allow the designer to choose the order of the controller and to introduce constant time-delays in the controller. The closed-loop system of the plant and the controller is modeled by a system of delay differential algebraic equations (DDAEs). The advantage of the DDAE modeling framework is that any interconnection of systems and controllers prone to various types of delays can be dealt with in a systematic way, without using any elimination technique. We presen…
