Incremental Passivity Research Articles

Dissipative Dynamical Systems With Set-Valued Feedback Loops: Well-Posed Set-Valued Lur’e Dynamical Systems

Passivity and dissipativity, in Jan Willems’s sense, are known to be powerful tools for stability analysis and feedback control design. For instance, passive systems in negative feedback interconnection with slope-restricted, static, single-valued, smooth nonlinearities, known as Lur’e systems, have been thoroughly studied in automatic control, yielding the so-called absolute stability problem (with the famous Popov and circle criteria). On the other hand, large classes of nonsmooth systems (complementarity dynamical systems, relay systems, projected dynamical systems, evolution and differential variational inequalities, Moreau’s sweeping processes, and maximal monotone differential inclusions), with applications in circuits, mechanics, and economics, are interpreted as set-valued Lur’e systems, in which the feedback nonlinearity is a multivalued mapping. Therefore, the closed-loop system is a differential inclusion of a certain type, the well posedness of which must be analyzed as a prerequisite for stability and control. This introductory article focuses on the well posedness of such set-valued feedback systems. It is shown how the existence and uniqueness of solutions to these specific differential inclusions benefit a lot from the passivity of the system and the maximal monotonicity (which is a form of incremental passivity) of the feedback set-valued mapping. Available results are reviewed, many illustrative examples are given, and some open issues are highlighted.

Spiking Control Systems

Spikes and rhythms organize control and communication in the animal world, in contrast to the bits and clocks of digital technology. As continuous-time signals that can be counted, spikes have a mixed nature. This article reviews ongoing efforts to develop a control theory of spiking systems. The central thesis is that the mixed nature of spiking results from a mixed feedback principle, and a control theory of mixed feedback can be grounded in the operator theoretic concept of maximal monotonicity. As a nonlinear generalization of passivity, maximal monotonicity acknowledges at once the physics of electrical circuits, the algorithmic tractability of convex optimization, and the feedback control theory of incremental passivity. We discuss the relevance of a theory of spiking control systems in the emerging age of event-based technology.

A rolled-off passivity theorem

Given two nonlinear systems which only violate incremental passivity when their incremental gains are sufficiently small, we give a condition for their negative feedback interconnection to have finite incremental gain, which generalizes the incremental small gain and incremental passivity theorems. The property may be determined graphically by plotting the Scaled Relative Graphs (SRGs) of the systems, which provides engineering significance to the mathematical result.

Statement of Retraction: A new controller design method for optimal frequency regulation in smart grid based on incremental passivity

Statement of Retraction: A new controller design method for optimal frequency regulation in smart grid based on incremental passivity

RETRACTED ARTICLE: A new controller design method for optimal frequency regulation in smart grid based on incremental passivity

We, the Editor and Publisher of the International Journal of Control, have retracted the following article: Yiwei Feng & Zhijun Wu (2021): A new controller design method for optimal frequency regulation in smart grid based on incremental passivity, International Journal of Control, DOI: https://10.1080/00207179.2021.1886329 The content of this article contains a high level of similarity with the published article below: S. Trip, M. Cucuzzella, C. De Persis, A. van der Schaft and A. Ferrara (2019): Passivity-Based Design of Sliding Modes for Optimal Load Frequency Control, IEEE Transactions on Control Systems Technology, 27(5), pp. 1893-1906, DOI: 10.1109/TCST.2018.2841844 We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines on retractions. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as ‘Retracted’.

Current Sharing Based on Incremental Passivity and Unknown Load Finite-Time Estimation for Multilevel Connected DC–DC Converters

The multilevel connected dc–dc converters system is considered a practical technology to increase the capacity and reduce voltage and current stresses on the power devices. In practice, mismatched parameters are inevitable, which increase the challenge of output voltage regulation and current sharing control. In order to conquer these difficulties, this article investigates the current sharing based on incremental passivity control for multilevel connected dc–dc converters. Combined with passivity-based control, a finite-time estimator is given to improve the robustness against the load variations. The proposed method results in a linear control law despite the bilinear nature of this system. Moreover, analysis exhibits that stability and current sharing are independent of inductor parameters. Furthermore, stability of the closed-loop system has been proved that the proposed approach is valid both for a linear and nonlinear load. After introducing the proposed control scheme, simulation and experiments are offered to validate its fast transit response and antidisturbance performance.

Mixed Incremental H ∞ and Incremental Passivity Analysis for Markov Switched Stochastic Nonlinear Systems

The current study addresses the mixed incremental H∞ and incremental passivity analysis for Markov switched stochastic (MSS) nonlinear systems. The multiple Lyapunov functions approach and the structure of Markov framework are utilized to establish some sufficient conditions for the MSS nonlinear systems, which will be used for the incrementally globally asymptotically stable in the mean(IGASiM) and performance index analysis. Then, the mixed incremental H∞ and incremental passivity performance issues are solved for two instances: in the first case, all subsystems are not IGASiM, while in the second one, both of IGASiM and unstable subsystems exist. Hence, it is shown that when none of the subsystems is IGASiM, the MSS nonlinear systems are IGASiM and possess the mixed incremental H∞ and incremental passivity performance metric in the presence of specified conditions. The mathematical induction is selected to guarantee the robust incremental stability of MSS systems with IGASiM and non-IGASiM subsystems and the performance index can be exhibited a prescribed decay rate. The effectiveness of the proposed results is demonstrated by two simulation examples.

Incremental passivity and stabilization for switched nonlinear systems

This paper studies the problems of incremental passivity, incremental passification and incremental stabilization for a switched nonlinear system. First, an incremental passivity concept for switched nonlinear systems is proposed. Each subsystem is only required to be incrementally passive, when it is active. The energy change of each inactive subsystem is charaterized. Then, a sufficient condition for such a system to be incrementally passive is given. Second, a state-dependent switching law and state feedback controllers are designed to render a system with relative degree one incrementally passive. Third, we show that an incrementally passive switched nonlinear system can be incrementally stabilized under some constraints on the energy change of inactive subsystems. In particular, a recursive feedback incremental passification design technique is adopted to achieve the incremental stability for a switched nonlinear system with any same relative degree by designing a set of feedback controllers and a state-dependent switching law, constructively. Finally, two examples are provided to verify the effectiveness of the proposed theory.

Distributed algorithm design for optimal resource allocation problems via incremental passivity theory

The paper is concerned with distributed optimal resource allocation problems on multi-agent systems that each agent has single-integrator dynamics. For the single-integrator multi-agent system, a local feasible set constraint is introduced and a distributed algorithm with projection operator is proposed. Compared with the algorithms in the existing literature on the single-integrator multi-agent systems, the proposed algorithm has simpler structure that reduces computation burden but without sacrificing the optimality. Incremental passivity theory is utilized to analyze the convergence of the algorithms. The simulation results illustrate the effectiveness of the proposed algorithms.

A Passivity Interpretation of Energy-Based Forced Oscillation Source Location Methods

This paper develops a systematic framework for analyzing how low frequency forced oscillations propagate in electric power systems. Using this framework, the paper shows how to mathematically justify the so-called Dissipating Energy Flow (DEF) forced oscillation source location technique. The DEF's specific deficiencies are pinpointed, and its underlying energy function is analyzed via incremental passivity theory. This analysis is then used to prove that there exists no passivity transformation (i.e. quadratic energy function) which can simultaneously render all components of a lossy classical power system passive. The paper goes on to develop a simulation-free algorithm for predicting the performance of the DEF method in a generalized power system, and it analyzes the passivity of three non-classical load and generation components. The proposed propagation framework and performance algorithm are both tested and illustrated on the IEEE 39-bus New England system and the WECC 179-bus system.

Incremental Passivity Control in Multilevel Cascaded H-Bridge Converters

A low-capacitance static compensator (LC-StatCom) based on a cascaded H-bridge (CHB) multilevel converter can be an efficient and low-cost solution for reactive power compensation in power grids. However, the reduced capacitance, and, therefore, faster capacitor voltage dynamics, makes it challenging to control it. Classical cascade control schemes, in which the bandwidths associated with the inner current loop and the outer capacitor voltage loop need to be separated enough, are the most reported approaches. Nevertheless, for the LC-StatCom case, the voltage loop can be almost as fast as that one of the current loop. For this reason, this article proposes a control approach that does not separate voltage and current dynamics. Concretely, we propose a multi-input linear time-variant control law, based on incremental passivity theory for CHB multilevel converters. The proposed control guarantees stability despite saturation in the control signal. In addition, it provides capacitor voltage balance without the need to use a specific balancing stage. This article, first, reviews the average model of the converter and, then, analyses the steady-state dynamic behavior to determine the desired and coherent reference signals. Then, it applies an incremental passivity control approach to drive the LC-StatCom state variables to the desired references. After introducing the proposed control law, experimental results on a seven-level 1-kVA CHB LC-StatCom are shown to demonstrate its excellent performance in steady state and transients.

Finite-Time Incremental Passivity and Output Tracking Control for Switched Nonlinear Systems

This paper studies the finite-time incremental passivity of switched nonlinear systems. Then, the established theory is applied to solve the finite-time output tracking control problem of switched nonlinear systems. First, finite-time incremental passivity is firstly defined for switched nonlinear systems. Each subsystem is finite-time incrementally passive during its active time interval. Unlike incremental passivity, the state trajectories of finite-time incrementally passive system with no external supplied energy can converge to each other in finite time. Second, the criterion of finite-time incremental passivity is established. Third, finite-time incremental passivity is shown to be preserved under the feedback interconnection. A composite switching law design method is provided. Under this switching law, the interconnected switched systems can switch asynchronously. Finally, the finite-time output tracking control problem was solved by the established finite-time incremental passivity theory of the switched nonlinear systems, even if the finite-time output tracking control of individual subsytem is not solvable. The effectiveness of the proposed method is verified by an example.

Compositional Synthesis of Symbolic Models for Networks of Switched Systems

In this letter, we provide a compositional methodology for constructing symbolic models for networks of discrete-time switched systems. We first define a notion of so-called augmented-storage functions to relate switched subsystems and their symbolic models. Then we show that if some dissipativity type conditions are satisfied, one can establish a notion of so-called alternating simulation function as a relation between a network of symbolic models and that of switched subsystems. The alternating simulation function provides an upper bound for the mismatch between the output behavior of the interconnection of switched subsystems and that of their symbolic models. Moreover, we provide an approach to construct symbolic models for discrete-time switched subsystems under some assumptions ensuring incremental passivity of each mode of switched subsystems. Finally, we illustrate the effectiveness of our results through two examples.

Robust trajectory tracking for incrementally passive nonlinear systems

In this paper, we study the robust trajectory tracking problem for a class of nonlinear systems with incremental passivity. The velocity of the desired trajectory and parts of the model information are unknown apart from boundedness assumptions. A velocity observer based method and a sliding mode controller are proposed while the asymptotic tracking result is guaranteed by a zero-state detectability condition for both cases. Unlike previous results, the studied systems are not necessarily feedback linearizable nor in a strict feedback form. The ball and beam system is utilized to illustrate the implementation of the proposed tracking control laws.

Stability analysis and decentralized control of inverter-based ac microgrid

This work considers the problem of decentralized control of inverter-based ac micro-grid in different operation modes. The main objectives are to (i) design decentralized frequency and voltage controllers, to gather with power sharing, without information exchange between microsources (ii) design passive dynamic controllers which ensure stability of the entire microgrid system (iii) capture nonlinear, interconnected and large-scale dynamic of the micro-grid system with meshed topology as a port-Hamiltonian formulation (iv) expand the property of shifted-energy function in the context of decentralized control of ac micro-grid (v) analysis of system stability in large signal point of view. More precisely, to deal with nonlinear, interconnected and large-scale structure of micro-grid systems, the port-Hamiltonian formulation is used to capture the dynamic of micro-grid components including microsource, distribution line and load dynamics as well as interconnection controllers. Furthermore, to deal with large signal stability problem of the microgrid system in the grid-connected and islanded conditions, the shifted-Hamiltonian energy function is served as a storage function to ensure incremental passivity and stability of the microgrid system. Moreover, it is shown that the aggregating of the microgrid dynamic and the decentralized controller dynamics satisfies the incremental passivity. Finally, the effectiveness of the proposed controllers is evaluated through simulation studies. The different scenarios including grid-connected and islanded modes as well as transition between both modes are simulated. The simulation conforms that the decentralized control dynamics are suited to achieve the desired objective of frequency synchronization, voltage control and power sharing in the grid-connected and islanded modes. The simulation results demonstrate the effectiveness of the proposed control strategy.

Optimal regulation of flow networks with transient constraints

This paper investigates the control of flow networks, where the control objective is to regulate the measured output (e.g. storage levels) towards a desired value. We present a distributed controller that dynamically adjusts the inputs and flows, to achieve output regulation in the presence of unknown constant disturbances, while satisfying given input and flow constraints. Optimal coordination among the controllers minimizing a suitable cost function of the inputs at the nodes, is achieved by exchanging information over a communication network. Exploiting an incremental passivity property, the desired steady state is proven to be globally asymptotically attractive under the closed loop dynamics. Two case studies (a district heating system and a super-conducting DC network) show the effectiveness of the proposed solution.

Incremental passivity-based H∞ output tracking control for switched nonlinear systems

This paper is concerned with the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances using incremental passivity, even if the problem of H∞ output tracking control for none of subsystems is solvable. First, an incremental passivity concept of switched nonlinear systems without external disturbances is proposed. This incremental passivity property requires each active subsystem is incrementally passive. Then, sufficient conditions to be incrementally passive are given. Second, by resorting to the established incremental passivity theory, a state-dependent switching law and a set of feedback controllers are designed to solve the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances. This avoids solving Hamilton-Jacobi (HJ) inequality. Third, a composite state-dependent switching law and the state feedback controllers are designed to solve the H∞ output tracking problem for a class of cascaded switched nonlinear systems with external disturbances. The designed composite switching law allows the driven switched system and the driving switched system switch asynchronously. Finally, two examples are provided to verify the effectiveness of the proposed method.

A Passivity-Based Approach to Nash Equilibrium Seeking Over Networks

In this paper we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information. We start from a continuous-time gradient-play dynamics that converges to an NE under strict monotonicity of the pseudo-gradient and assumes perfect information, i.e., instantaneous all-to-all player communication. We consider how to modify this gradient-play dynamics in the case of partial, or networked information between players. We propose an augmented gradient-play dynamics with correction in which players communicate locally only with their neighbours to compute an estimate of the other players' actions. We derive the new dynamics based on the reformulation as a multi-agent coordination problem over an undirected graph. We exploit incremental passivity properties and show that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbours. Under a strict monotonicity property of the pseudo-gradient, we show that the augmented gradient-play dynamics converges to consensus on the NE of the game. We further discuss two cases that highlight the tradeoff between properties of the game and the communication graph.

Distributed Optimal Frequency Control Considering a Nonlinear Network-Preserving Model

This paper addresses the distributed optimal frequency control of power systems considering a network-preserving model with nonlinear power flows and excitation voltage dynamics. Salient features of the proposed distributed control strategy are fourfold, first, nonlinearity is considered to cope with large disturbances, second, only a part of generators are controllable, third, no load measurement is required, fourth, communication connectivity is required only for the controllable generators. To this end, benefiting from the concept of “virtual load demand,” we first design the distributed controller for the controllable generators by leveraging the primal-dual decomposition technique. We then propose a method to estimate the virtual load demand of each controllable generator based on local frequencies. We derive incremental passivity conditions for the uncontrollable generators. Finally, we prove that the closed-loop system is asymptotically stable and its equilibrium attains the optimal solution to the associated economic dispatch problem. Simulations, including small and large-disturbance scenarios, are carried on the New England system, demonstrating the effectiveness of our design.

Distributed Optimal Load Frequency Control with Non-Passive Dynamics

Motivated by an increase of renewable energy sources, we propose a distributed optimal load frequency control scheme achieving frequency regulation and economic dispatch. Based on an energy function of the power network, we derive an incremental passivity property for a well-known nonlinear structure preserving network model, differentiating between generator and load buses. Exploiting this property, we design distributed controllers that adjust the power generation. Notably, we explicitly include the turbine-governor dynamics, where first-order and the widely used second-order dynamics are analyzed in a unifying way. Due to the non-passive nature of the second-order turbine-governor dynamics, incorporating them is challenging, and we develop a suitable dissipation inequality for the interconnected generator and turbine-governor. This allows us to include the generator side more realistically in the stability analysis of optimal load frequency control than was previously possible.