Hybrid System Framework Research Articles

Robust parameter estimation for hybrid dynamical systems with linear parametric uncertainty

We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems – that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution – with dynamics that depend linearly on the unknown parameters. Using a hybrid systems framework, we propose a hybrid estimation algorithm that can operate during both flows and jumps that, under a notion of hybrid persistence of excitation, guarantees convergence of the parameter estimate to the true value. Furthermore, we show that the parameter estimate is input-to-state stable with respect to a class of hybrid disturbances. Simulation results including a spacecraft application show the merits of our proposed approach.

Contingency detection in modern power systems: A stochastic hybrid system method

This paper introduces a new stochastic hybrid system (SHS) framework for contingency detection in modern power systems (MPS). The framework uses stochastic hybrid system representations in state space models to expand and facilitate capability of contingency detection. In typical microgrids (MGs), buses may contain various synchronous generators, renewable generators, controllable loads, battery systems, regular loads, etc. For development of SHS models in power systems, this paper introduces the concept of dynamic and non-dynamic buses. By converting a physical power grid into a virtual linearized state space model and representing contingencies as random switching of system structures and parameters, this paper formulates the contingency detection problem as a joint estimation problem of discrete events and continuous states in stochastic hybrid systems. This method offers unique advantages, including using common measurement signals on voltage and current synchrophasors to detect different types and locations of contingencies, avoiding expensive local direct fault measurements and detecting certain contingencies that cannot be directly measured. The method employs a small and suitably-designed probing signal to sustain the ability of persistent contingency detection. Joint estimation algorithms are presented with their proven convergence and reliability properties. Examples that use an IEEE 5-Bus system demonstrate the main ideas and derivation steps. Simulation case studies on an IEEE 33-Bus system are used for detecting transmission line faults and sensor interruptions.

Hybrid dynamic event-triggered leader-following consensus for multi-agent systems with external disturbances

Herein, we address the leader-following consensus for multi-agent systems with a directed graph while considering external disturbances. To optimize resource utilization, we propose a hybrid dynamic event-triggered mechanism (HDETM) that minimizes the inter-agent communication and reduces the frequency of controller updates. Furthermore, regularization techniques are employed to ensure that the considered system maintains a Zeno-free behavior even in the presence of an external disturbance by guaranteeing a strictly positive inter-event time. Additionally, we propose a hybrid system framework incorporating auxiliary variables to depict both flow and jump dynamics. A Lyapunov consensus analysis is performed within this framework to verify finite-gain L2 stability. Finally, we validate the efficacy of the HDETM design method through numerical simulations.

A Stochastic Hybrid Framework for Event-Triggered Nonlinear Control Systems With Stochastic Denial of Service Attacks

In this paper, the stability problem for event-triggered nonlinear control systems is addressed in the presence of stochastic denial of service (DoS) attacks on the communication network. Dynamic event-triggered control (DETC) and periodic event-triggered control (PETC) are considered under the stochastic attacks. The stochastic attacks are modeled by a stochastic hybrid timer and a logic variable which is used to identify whether the network is attacked or not. Then the entire closed-loop system can be modeled into the framework of stochastic hybrid systems. Uniform global asymptotic stability in probability is concluded for the resulting stochastic system by proving that the equilibrium set is uniformly globally stable in probability and each neighborhood of the equilibrium set is uniformly globally recurrent. A nonlinear system example is provided to illustrate the effectiveness of the proposed results.

Verification of Compositional Frameworks in Coq

In this paper we aim to verify in Coq basic properties of compositional behavioural frameworks for dynamic systems. We analyse systems by their external behaviour rather than a state space model, and use the parallel composition operator to build complex systems from simpler subsystems. It is important that the composition is well-defined and avoids undesirable behaviour such as deadlocks. To ensure the our framework is correct, we formulate and prove the results in the proof assistant Coq. We consider discrete-time deterministic systems and timed-event systems, with a view to eventually proving results on a framework for hybrid systems.

Periodic Event-Triggered Consensus Using Relative-State Measurements: A Hybrid System Approach

Often in practical applications, such as coordinated motion of autonomous vehicles, multi-agent systems (MASs) utilize information obtained from sensors to accomplish complex tasks, asynchronously. In this work, we consider the problem of consensus where the agents obtain relative-state measurements, at their own sampling frequencies, and employ a distributed event-triggered protocol to dictate when to update control. For the designed event-triggered protocol, only local intermittent relative-state measurements are utilized, where they are obtained and evaluated only at pre-determined event-monitoring instants; these instants are governed by sampling periods whose bounds are explicitly pre-computed, individually, for each agent. Hence, the designed protocol is inherently asynchronous and avoid Zeno behaviour by construction. To cope with the continuous-time dynamics of the agents and discrete-time sensing and controller updates, the overall MAS is modelled using the hybrid system framework. A numerical example is provided to clearly demonstrate the effectiveness of the designed protocol.

Hybrid impedance and admittance control for optimal robot–environment interaction

AbstractCompliant interaction between robots and the environment is crucial for completing contact-rich tasks. However, obtaining and implementing optimal interaction behavior in complex unknown environments remains a challenge. This article develops a hybrid impedance and admittance control (HIAC) scheme for robots subjected to the second-order unknown environment. To obtain the second-order target impedance model that represents the optimal interaction behavior without the accurate environment dynamics and acceleration feedback, an impedance adaptation method with virtual inertia is proposed. Since impedance control and admittance control have complementary structures and result in unsatisfactory performance in a wide range of environmental stiffness due to their fixed causality, a hybrid system framework suitable for the second-order environment is proposed to generate a series of intermediate controllers which interpolate between the responses of impedance and admittance controls by using a switching controller and adjusting its switching duty cycle. In addition, the optimal intermediate controller is selected using a mapping of the optimal duty cycle to provide the optimal implementation performance for the target impedance model. The proposed HIAC scheme can achieve the desired interaction and impedance implementation performance while ensuring system stability. Simulation and experimental studies are performed to verify the effectiveness of our scheme with a 2-DOF manipulator and a 7-DOF Franka EMIKA panda robot, respectively.

Fault estimation for cyber–physical systems with intermittent measurement transmissions via a hybrid observer approach

This paper investigates the problem of fault estimation for cyber–physical systems (CPSs) with intermittent measurement transmissions. A novel hybrid observer-based fault estimation scheme is proposed to generate estimations of the system state and the fault. Specifically, the correction terms of the designed observer are updated while new output measurements are available. Moreover, the estimation performance of the designed observer is analyzed within a framework of hybrid systems, and sufficient conditions are established to guarantee exponential input-to-state stability with a prescribed convergence rate based on the elaborately constructed Lyapunov function candidate. In contrast to the existing estimation schemes, the requirements of continuous or periodical communication are eliminated, and therefore the proposed one is more applicable for the modern industrial systems integrated with data communication networks. Finally, the application to an aircraft model is presented to illustrate the effectiveness of the developed methods.

A filter for tracking non-cooperative low-thrust satellites using surveillance radar data

Numerous satellites with electric propulsion perform long duration maneuvers during their orbit acquisition phase. This poses a challenge to space object cataloging activities if no information regarding the maneuver plan is known a priori. Various works have been devoted to maneuver detection and tracking of space objects using radar and optical surveillance data, but the special case of unknown dynamics, analogous to a maneuver spanning several days or months, has received less attention. Herein, we propose a methodology to maintain custody of uncooperative low-thrust spacecraft under the special characteristics of surveillance radar observations. Based on the stochastic hybrid systems framework, a multi-hypothesis algorithm leverages information derived from measurements and the dynamical characteristics of the object. The latter is accomplished in an efficient manner by means of a low-thrust control metric that relies on the Thrust Fourier Coefficients approximation. To improve filter robustness, the maneuver transition density is assumed to be uniform within the set of reachable states, whose outer bound is approximated via the proposed control measure. The algorithm is applied to the orbit acquisition phase of a LEO satellite using synthetic data from a simulated surveillance radar network, and its shown to be capable of maintaining custody throughout the entire three-month transfer.

Distributed Dynamic Event-Triggered Secon- dary Control for Islanded Microgrids With Disturbances and Communication De- lays: A Hybrid Systems Approach

This paper investigates the secondary control problem of islanded microgrid (MG) under hybrid systems framework. Owing to network-induced imperfections caused by communication and limited communication resources, we consider the event-triggered secondary control problem under time-varying delays. A hybrid dynamic event-triggering mechanism (DETM) is proposed to reduce the usage of communication resources, the event triggering interval is enforced to be lower bounded by strictly positive value. A hybrid closed-loop model is constructed, that incorporates the communication delays and event-triggering mechanism (ETM), and it facilitates stability and performance analysis. Lyapunov-based stability conditions are proposed, while the maximum allowable delay can be determined. Moreover, the proposed hybrid DETM ensures that the minimum event-triggering interval (METI) can be designable and pre-specified, even in the presence of disturbances, which is important for control implementation. Finally, the effectiveness of the proposed control strategy is illustrated by simulation examples.

Hybrid Event-Triggered Bipartite Consensus Control of Multiagent Systems and Application to Satellite Formation

This work studies event-triggered bipartite consensus problem of multi-agent systems (MAS) with structurally balanced signed graph. A hybrid system approach is proposed to deal with the leaderless and leader-following bipartite consensus problems in a unified framework, and a novel hybrid event-triggering mechanism (ETM) is proposed to reduce the usage of communication resources. By appropriately defining closed-loop states, a unified hybrid model is constructed for both leaderless and leader-following MAS. Then, stability analysis and ETM design results are given under hybrid systems framework. It is worth noting that the designed hybrid ETM is in decentralized form rather than distributed form. Moreover, the lower bound of triggering intervals can be pre-selected, i.e., Zeno-freeness is guaranteed, that is important for control implementation. The proposed method is applied to satellite formation system in simulation results to show the effectiveness. <i>Note to Practitioners</i>&#x2014;This paper considers bipartite consensus control problem of MAS, which can be applied to some practical systems, e.g., bidirectional formation of unmanned air vehicles, since the control objective in these applications can be transformed into bipartite consensus control problem of MAS. Compared with the existing results, a hybrid system approach is proposed for consensus analysis of MAS with or without leader, and a novel event-triggering mechanism is proposed, which is more easier to be implemented, so, the proposed approach is more friendly for control engineers. The obtained results are applied to satellite formation control problem and the effectiveness is verified, and it is expected that the proposed approach can be extended to MAS with more realistic network-induced constraints and applied to more practical engineering systems.

Leaderless and Leader-Following Bipartite Consensus of Multiagent Systems With Sampled and Delayed Information.

This article proposes a hybrid systems approach to address the sampled-data leaderless and leader-following bipartite consensus problems of multiagent systems (MAS) with communication delays. First, distributed asynchronous sampled-data bipartite consensus protocols are proposed based on estimators. Then, by introducing appropriate intermediate variables and internal auxiliary variables, a unified hybrid model, consisting of flow dynamics and jump dynamics, is constructed to describe the closed-loop dynamics of both leaderless and leader-following MAS. Based on this model, the leaderless and leader-following bipartite consensus is equivalent to stability of a hybrid system, and Lyapunov-based stability results are then developed under hybrid systems framework. With the proposed method, explicit upper bounds of sampling periods and communication delays can be calculated. Finally, simulation examples are given to show the effectiveness.

A Hybrid Systems Approach to Event-Triggered Consensus of Multiagent Systems With Packet Losses

This article addresses the event-triggered consensus problem of multiagent systems (MASs) with packet losses. The packet losses are not restricted to be identical, and a hybrid systems framework is proposed to handle the considered problem with or without leader in a unified framework. Distributed control law is constructed based on an estimator, whose dynamics are related to whether packet losses occur. A novel hybrid event-triggering mechanism (ETM) is proposed, and a lower bound of the interevent times is enforced to guarantee Zeno-freeness. For stability analysis, a unified hybrid model is constructed to describe the dynamics of MAS with or without leader. In accordance to this model, how to design the hybrid ETM and consensus analysis are formally developed, and the maximum allowable successive packet losses can be explicitly computed. Moreover, even if there exist nonlinearities and disturbances in system dynamics, and the leader has nonzero input, the proposed method can still be applied. Finally, examples are provided to illustrate the superiority of the proposed method.

Distribution of the Age of Gossip in Networks.

We study a general setting of gossip networks in which a source node forwards its measurements (in the form of status updates) about some observed physical process to a set of monitoring nodes according to independent Poisson processes. Furthermore, each monitoring node sends status updates about its information status (about the process observed by the source) to the other monitoring nodes according to independent Poisson processes. We quantify the freshness of the information available at each monitoring node in terms of Age of Information (AoI). While this setting has been analyzed in a handful of prior works, the focus has been on characterizing the average (i.e., marginal first moment) of each age process. In contrast, we aim to develop methods that allow the characterization of higher-order marginal or joint moments of the age processes in this setting. In particular, we first use the stochastic hybrid system (SHS) framework to develop methods that allow the characterization of the stationary marginal and joint moment generating functions (MGFs) of age processes in the network. These methods are then applied to derive the stationary marginal and joint MGFs in three different topologies of gossip networks, with which we derive closed-form expressions for marginal or joint high-order statistics of age processes, such as the variance of each age process and the correlation coefficients between all possible pairwise combinations of age processes. Our analytical results demonstrate the importance of incorporating the higher-order moments of age processes in the implementation and optimization of age-aware gossip networks rather than just relying on their average values.

Reset control and ℒ2-gain analysis of piecewise-affine systems

This paper is concerned with reset controller design and L 2 -gain stability of piecewise-affine systems under the framework of hybrid systems. Firstly, stability conditions of piecewise-affine systems under dynamic state-feedback control are established through bilinear matrix inequality conditions. Secondly, a reset controller with reset rules under the hybrid systems framework is proposed in the sense of Lyapunov and sufficient conditions for exponential and L 2 -gain stability of the closed-loop systems are provided. Different from the piecewise-affine systems with the dynamic state-feedback controller, the reset controller is designed such that the L 2 -gain performance of piecewise-affine systems can be enhanced. Thirdly, an LMI approach is proposed to avoid the difficulty of solving the bilinear matrix inequalities. Furthermore, robustness to inflations of the flow and jump sets is established, and robustness to the norm-bounded uncertainties is proposed. Finally, numerical simulations including a robot arm system, an inverted pendulum system and the Chua's circuit system are provided to illustrate the results.

Sliding Mode Control of Quadratic Boost Converters Based on Min-Type Control Strategy

The paper deals with the control of a quadratic boost converter supplied by low-voltage energy sources, such as photovoltaic panels, fuel cells, or batteries. The control scheme consists of two control loops. A min-type controller governs the inner loop to force the current state of the nominal model to converge in a neighborhood of the equilibrium state. The external loop processes the output tracking error using an integrator, and it allows reconfiguring the converter’s working point by changing the equilibrium state given in the input to the internal loop. This configuration assures both zero tracking error of the output voltage and robustness against load and input voltage variations and converter parameter uncertainties. The stability of the whole system is investigated using the hybrid system framework. The proposed control technique has been tested experimentally in a suitably developed (low-cost) setup, and the results show the effectiveness of the proposed approach.

Event-Triggered Consensus of Nonlinear Agents with Quantized Broadcasts: A Hybrid System Approach

Information exchange among agents operating over a network, in practice, is restrained by limited communication bandwidth; this concern is often addressed by employing quantized broadcasts. In this paper, we study the problem of consensus of nonlinear multi-agent systems (MASs) over a directed network where the agents employ: a) encoders, that quantize relevant information prior to broadcasting, and b) decoders, that process this information upon arrival. The decision on the broadcast instant itself is made with the help of a dynamic event-triggering mechanism (ETM) in that the agents evaluate their respective event-triggering conditions intermittently at pre-designed sampling instants (which may be both aperiodic and asynchronous). Subsequently, the agents utilize model-based propagates of the decoded neighbor states in their control protocols to achieve consensus. The overall MAS is modeled using hybrid systems framework and the results are demonstrated through an illustrative example.

Control design under actuator saturation and multi-rate sampling

The problem of designing a stabilizing feedback controller in the presence of saturating actuators and multi-rate (asynchronous) aperiodic state measurements is studied. Specifically, we consider a scenario in which measurements of the plant states are collected at the controller end in a sporadic and asynchronous fashion. A hybrid controller is used to perform a fusion of measurements sampled at different times. In between sampling events, the controller behaves as a copy of the plant and provides a feedback control signal based on the reconstruction of the plant state. The presence of saturation at the plant input limits the value of the components of this signal to a bounded range. When a new measurement is available, the controller state undergoes an instantaneous jump. The resulting system is augmented with a set of timers triggering the arrival of new measurements and analyzed in a hybrid systems framework. Relying on Lyapunov tools for hybrid systems and techniques for control design under saturation, we propose sufficient conditions in the form of matrix inequalities to ensure regional exponential stability of a closed-set containing the origin of the plant, i.e., exponential stability with a guaranteed region of attraction. Specifically, explicit estimates of the basin of attraction are provided in the form of ellipsoidal sets. Leveraging those conditions, a design procedure based on semidefinite programming is proposed to design a stabilizing controller with maximized size of the basin attraction. The effectiveness of the proposed methodology is shown in an example.

Distributed dynamic event-triggered communication and control for multi-agent consensus: A hybrid system approach

This paper investigates the output-based event-triggered communication and control for linear multi-agent consensus under a directed graph based on a co-design method. The communication among the agents, as well as the controller updates, are determined by some new event-triggering mechanisms, in order to reduce the use of the network resources. To simultaneously guarantee the significant properties including the asymptotic consensus, and strong Zeno-freeness (strictly positive inter-event times), a novel distributed dynamic event-triggered protocol is proposed. Unlike the most-existing emulation-based approaches in which the control gain is previously decided, a systematic co-design procedure is proposed to design the controller gain, the observer gain, and the event-triggering mechanisms altogether in terms of solving a linear matrix inequality optimization problem. Based on the resulting hybrid system framework, a hybrid model is established for the distributed closed-loop system and the asymptotic consensus is achieved. Finally, a numerical example is presented to verify our systematic design methodology.

L 2-gain analysis of reset control for piecewise-affine systems with input saturation

This paper is concerned with reset control and -gain stability of piecewise-affine systems with input saturation and external disturbance under the framework of hybrid systems. Firstly, we present a reset controller and establish exponential stability conditions of piecewise-affine systems with input saturation under the reset controller. Secondly, sufficient conditions for -gain stability of the closed-loop systems with input saturation and external disturbance are provided and a reset controller is designed to enhance the -gain performance of piecewise-affine systems with input saturation. Furthermore, robustness to inflations of the flow and jump sets is established. Finally, a numerical simulation is provided to illustrate the results.