Backward Recursive Riccati Difference Equations Research Articles

Fault-tolerant formation consensus control for time-varying multi-agent systems with stochastic communication protocol

Article Fault-tolerant formation consensus control for time-varying multi-agent systems with stochastic communication protocol Chunyu Li, Yifan Liu, Ming Gao, and Li Sheng * 1 College of Control Science and Engineering, China University of Petroleum (East China), Qingdao 266580, China * Correspondence: E-mail: shengli@upc.edu.cn Received: 4 September 2023 Accepted: 8 November 2023 Published: 26 March 2024 Abstract: This paper is concerned with the problem of fault-tolerant formation consensus control for linear time-varying (LTV) multi-agent systems (MASs) with stochastic communication protocol (SCP). The SCP is introduced to schedule the signal transmission, and only one neighbouring agent is allowed to transmit data at one instant. The purpose of this work is to design a fault-tolerant controller for each agent, so that, for all probabilistic scheduling behaviors, MASs can achieve the formation consensus performance. The state and fault are augmented into a new vector, meanwhile, each agent system is written as a singular one and a state observer is designed. By utilizing the estimated information of states and faults, the designed time-varying compensation term can reduce the impacts of unknown external disturbances and faults. Then, a sufficient condition is obtained to guarantee the performance constraint over the finite horizon for closed-loop systems. The parameters of observers and controllers are derived by solving coupled backward recursive Riccati difference equations. Finally, a numerical example is given to validate the effectiveness of the proposed fault-tolerant control scheme.

Optimal Attack Strategy Against Fault Detectors for Linear Cyber-Physical Systems

This paper is concerned with the design of false data injection attacks (FDIAs) against fault detectors (FD) for linear cyber-physical systems (CPSs). The purpose of the attacker is to design an stealthy attack scheme such that the defenders cannot detect the faults in time or fail to detect the faults, and at the same time the robustness of the CPS is deteriorated. Unlike the existing optimal attack strategies (OASs) that are established based on sufficient conditions, necessary and sufficient conditions (NASCs) are established to maximize the degradation of the FD performance and robustness of CPS while maintaining stealth. Subsequently, an OAS is constructed by solving coupled backward recursive Riccati difference equations (RDEs). Finally, two simulation examples are employed to show the effectiveness of the designed attack scheme.

Finite-horizon H ∞ state estimation for time-varying complex networks based on the outputs of partial nodes

In this paper, the partial-nodes-based resilient filtering problem for a class of discrete time-varying complex networks is investigated. In order to reduce the effect of imprecision of filter parameters on estimation performance, a set of resilient filters is proposed. The measurement output from all network nodes may not be available in the actual system, but only from a fraction of nodes. The state estimators are designed for the time-varying complex network based on partial nodes to make the estimation error achieve the performance constraint over a finite horizon. By employing the completing-the-square technique and the backward recursive Riccati difference equations, the sufficient conditions for the existence of the estimator are derived. Then the gain of the estimator is calculated. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Finite-Horizon H∞ Bipartite Consensus Control of Cooperation-Competition Multiagent Systems With Round-Robin Protocols.

This article focuses on the finite-horizon H∞ bipartite consensus control problem for a class of discrete time-varying cooperation-competition multiagent systems (DTV-CCMASs) with the round-robin (RR) protocol. The cooperation-competition relationship among agents is characterized by a signed graph, whose edges are with positive or negative connection weights. Specifically, a positive weight corresponds to an allied relationship between two agents and a negative one means an adversary relationship. The data exchange between each agent and its neighbors is orchestrated by an RR protocol, where only one neighboring agent is authorized to transmit the data packet at each time instant, and therefore, the data collision is prevented. This article aims to design a bipartite consensus controller for DTV-CCMASs with the RR protocol such that the predetermined H∞ bipartite consensus is satisfied over a given finite horizon. A sufficient condition is first established to guarantee the desired H∞ bipartite consensus by resorting to the completing square method. With the help of an auxiliary cost combined with the Moore-Penrose pseudoinverse method, a design scheme of the bipartite consensus controller is obtained by solving two coupled backward recursive Riccati difference equations (BRRDEs). Finally, a simulation example is given to verify the effectiveness of the proposed scheme of the bipartite consensus controller.

H ∞ Control for Time-Varying Cyber-Physical System Under Randomly Occurring Hybrid Attacks: The Output Feedback Case

In this paper, the H ∞ control problem for a class of linear time-varying cyber-physical system (CPS) under randomly occurring hybrid attacks in a finite horizon is investigated. The hybrid attacks, including denial of service (DoS) attacks on both sensor-to-controller and controller-to-actuator communication channels and false data injection (FDI) attacks on sensors and actuators, aim to destroy the measurement data and control data in order to endanger the functionality of the closed-loop system. The purpose of this paper is to study the relationship between the attack injected signals and the controlled output, and to design the output feedback controller gains so that the H ∞ performance of the closed-loop system is guaranteed over a given finite horizon, meanwhile, the impact of attack signals in the worst case on the linear quadratic performance can be reduced. In order to solve the above problems, both the methods of stochastic analysis and completing squares are utilized to establish the sufficient conditions for the existence of the desired controller, and a finite-horizon controller design algorithm is presented by solving two coupled backward recursive Riccati difference equations (RDEs) subject to some scheduled conditions. At last, the numerical simulation and experimental results are given out to demonstrate the effectiveness of the proposed approach.

Finite‐horizon fault estimation for time‐varying systems with multiple fading measurements under torus‐event–based protocols

SummaryIn this paper, the issue of the finite‐horizon H∞ fault estimation is dealt with for a class of discrete time‐varying systems subject to randomly occurring faults and multiple fading measurements. The missing phenomena may occur in a random way from different sensors, which is represented by an individual stochastic variable meeting a certain probability distribution. Furthermore, in order to alleviate the communication burden, the torus‐event–based protocols are adopted to schedule the data transmissions only when some significant events occur. Our aim of the presented issue is to estimate the fault such that, with multiple fading measurements via the received information governed by torus‐event–based protocols, the H∞ index is satisfied over a given finite horizon. Sufficient conditions are obtained for the desired time‐varying estimator in terms of the technique of stochastic analysis and the methods of completing squares. The desired estimator gains are calculated by working out two backward recursive Riccati difference equations. Finally, a numerical simulation is given to verify the usefulness of our designed fault estimation approach.

Observer-based control of vehicle platoons with random network access

This paper investigates cooperative control of vehicle platoons, focusing on the effect of medium access control (MAC) protocol and unreliable measurement on acceleration information. A Markov chain is used to describe the randomness in vehicular network access under a MAC protocol; a reduced-order observer is proposed to estimate the relative acceleration of neighboring vehicles. Based on stochastic system techniques, a series of sufficient conditions for the existence of the observer-based controller are given in the form of backward recursive Riccati Difference Equations (RDE). A controller–estimator design algorithm is derived to determine the controller and observer gains with which the disturbance of the preceding vehicle acceleration can be eliminated and string stability and zero steady-state velocity error performance can be guaranteed. Both numerical simulations and experiments with laboratory-scale Arduino cars are given to verify the effectiveness and practicability of the proposed algorithm.

Robust Protocol‐Based ℋ∞ Consensus Control of Time‐Varying Uncertain Multiagent Systems Subject to Missing Measurements

In this paper, we consider the design problem of a robust ℋ∞ consensus controller for discrete time‐varying uncertain multiagent systems (DTVUMASs) with stochastic communication protocol (SCP) and missing measurements. The SCP is described by a set of random variables with a known probability to arrange signal transmission of addressed multiagent systems. Moreover, we depict the missing measurement phenomenon by a sequence of Bernoulli‐distributed random variables having known probabilities. The controller parameters are designed to ensure that the closed‐loop DTVUMASs satisfy the ℋ∞ performance with the satisfactory consensus criterion. Together with the completing squares approach and the stochastic analysis methodology, some sufficient conditions are proposed by solving coupled backward recursive Riccati difference equations (BRRDEs) to guarantee the ℋ∞ consensus performance. Finally, we present a numerical simulation example to illustrate the effectiveness of the designed controller design scheme.

H∞ Containment Control of Multiagent Systems Under Event-Triggered Communication Scheduling: The Finite-Horizon Case.

This paper investigates the finite-horizon H∞ containment control issue for a general discrete time-varying linear multiagent systems with multileaders. All followers in such a system are driven into a convex hull spanned by multiple leaders, which can be transformed into a problem of tracking a virtual trajectory generated by these leaders. For this purpose, a local state observer is put forward to estimate the state of each agent itself. Then, the estimated state is transmitted to corresponding neighbors governing by an innovation-based event-triggered scheduling protocol. The purpose of the addressed problem is to design both an event-based distributed controller and a state observer such that a prescribed H∞ containment index can be achieved over a given finite horizon. First, with the help of the completing the square method, a sufficient condition is established to ensure the desired H∞ containment performance. Then, by resort to a novel nominal energy cost index combined with Moore-Penrose pseudoinverse method, the desired controller and observer parameters are obtained by solving two coupled backward recursive Riccati difference equations. Two positive scalars in proposed nominal energy cost index provide a tradeoff among the controlled tracking errors, the energy of transformed control inputs, and the precision of estimated states. Finally, a simulation example is given to illustrate the usefulness of the proposed theoretical results.

Finite-horizon state estimation for time-varying complex networks with random coupling strengths under Round-Robin protocol

In this paper, the problem of finite-horizon H∞ state estimation is investigated for a class of discrete time-varying complex networks with multiplicative noises and random coupling strengths. The network nodes and estimators are connected via a constrained communication network which allows only one node to send measurement data at each transmission instant. The Round-Robin protocol is introduced to determine which node obtains the access to the network at certain transmission instant. The aim of the addressed problem is to design a set of time-varying estimator parameters such that the prescribed H∞ performance is guaranteed over a finite horizon. By using the stochastic analysis approach and completing-the-square method, sufficient conditions are derived for the existence of the desired estimators in terms of the solution to backward recursive Riccati difference equations. Finally, a numerical example is provided to validate the feasibility and effectiveness of the proposed results.

Output-feedback [formula omitted] consensus control for stochastic time-varying multi-agent systems with [formula omitted]-dependent noises

In this paper, the output feedback H2∕H∞ consensus control problem is investigated for discrete time-varying stochastic multi-agent systems with state, control and disturbance-dependent noises (also called (x,u,v)-dependent noises). Two new concepts for the H2 and H∞ consensus requirements are proposed to quantify the transient behavior of the consensus, over a finite horizon, for the addressed time-varying multi-agent systems. We aim to design an output feedback consensus controller such that the closed-loop multi-agent systems achieve the prescribed H2 and H∞ consensus performances over a finite horizon. By using the completing squares method and stochastic analysis techniques, sufficient conditions are derived for the existence of the desired output-feedback H2∕H∞ consensus controller in terms of the solution to two coupled backward recursive Riccati difference equations (RDEs). Moreover, an iterative algorithm is proposed for solving the RDEs by resorting to the Moore–Penrose pseudo inverse. A numerical example is utilized to illustrate the effectiveness of the proposed H2∕H∞ consensus control strategy.

Finite-Horizon ${\mathcal H}_{\infty }$ Consensus Control of Time-Varying Multiagent Systems With Stochastic Communication Protocol.

This paper is concerned with the distributed ℋ∞ consensus control problem for a discrete time-varying multiagent system with the stochastic communication protocol (SCP). A directed graph is used to characterize the communication topology of the multiagent network. The data transmission between each agent and the neighboring ones is implemented via a constrained communication channel where only one neighboring agent is allowed to transmit data at each time instant. The SCP is applied to schedule the signal transmission of the multiagent system. A sequence of random variables is utilized to capture the scheduling behavior of the SCP. By using the mapping technology combined with the Hadamard product, the closed-loop multiagent system is modeled as a time-varying system with a stochastic parameter matrix. The purpose of the addressed problem is to design a cooperative controller for each agent such that, for all probabilistic scheduling behaviors, the ℋ∞ consensus performance is achieved over a given finite horizon for the closed-loop multiagent system. A necessary and sufficient condition is derived to ensure the ℋ∞ consensus performance based on the completing squares approach and the stochastic analysis technique. Then, the controller parameters are obtained by solving two coupled backward recursive Riccati difference equations. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design scheme.

Event-Based $H_\infty $ State Estimation for Time-Varying Stochastic Dynamical Networks With State- and Disturbance-Dependent Noises.

In this paper, the event-based finite-horizon H∞ state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called (x,v) -dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed H∞ performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.

Observer-based [formula omitted] control of networked systems with stochastic communication protocol: The finite-horizon case

This paper is concerned with the H∞ control problem for a class of linear time-varying networked control systems (NCSs) with stochastic communication protocol (SCP). The sensor-to-controller network (the controller-to-actuator network) is considered where only one sensor (one actuator) obtains access to the communication network at each transmission instant. The SCP is applied to determine which sensor (actuator) should be given the access to the network at a certain instant. The aim of the problem addressed is to design an observer-based controller such that the H∞ performance of the closed-loop system is guaranteed over a given finite horizon. For the purpose of simplifying the NCS model, a new Markov chain is constructed to model the SCP scheduling of communication networks. Then, both the methods of stochastic analysis and completing squares are utilized to establish the sufficient conditions for the existence of the desired controller. The controller parameters are characterized by solving two coupled backward recursive Riccati difference equations subject to the scheduled SCP. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design scheme.

Finite-Horizon ${\cal H}_{\infty}$ Control for Discrete Time-Varying Systems With Randomly Occurring Nonlinearities and Fading Measurements

This technical note deals with the ${\cal H}_{\infty}$ control problem for a class of discrete time-varying nonlinear systems with both randomly occurring nonlinearities and fading measurements over a finite-horizon. The system measurements are transmitted through fading channels described by a modified stochastic Rice fading model. The purpose of the addressed problem is to design a set of time-varying controllers such that, in the presence of channel fading and randomly occurring nonlinearities, the ${\cal H}_{\infty}$ performance is guaranteed over a given finite-horizon. The model transformation technique is first employed to simplify the addressed problem, and then the stochastic analysis in combination with the completing squares method are carried out to obtain necessary and sufficient conditions of an auxiliary index which is closely related to the finite-horizon ${\cal H}_{\infty}$ performance. Moreover, the time-varying controller parameters are characterized via solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the usefulness of the proposed controller design scheme.

Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems

This paper is concerned with the finite-horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time-varying. The faults are assumed to occur in a random way governed by two sets of Bernoulli distributed white sequences. The stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well-studied nonlinearities. The aim of the problem is to estimate the random faults, over a finite horizon, such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an H∞-norm in the mean square sense. By using the completing squares method and stochastic analysis techniques, necessary and sufficient conditions are established for the existence of the desired finite-horizon H∞ fault estimator whose parameters are then obtained by solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method.

Formula omitted] consensus control for multi-agent systems with missing measurements: The finite-horizon case

This paper deals with the H∞ consensus control problem for a class of discrete time-varying multi-agent systems with both missing measurements and parameter uncertainties. A directed graph is used to represent the communication topology of the multi-agent network, and a binary switching sequence satisfying a conditional probability distribution is employed to describe the missing measurements. The purpose of the addressed problem is to design a time-varying controller such that, for all probabilistic missing observations and admissible parameter uncertainties, the H∞ consensus performance is guaranteed over a given finite horizon for the closed-loop networked multi-agent systems. According to the given topology, the measurement output available for the controller is not only from the individual agent but also from its neighboring agents. By using the completing squares method and stochastic analysis techniques, necessary and sufficient conditions are derived for the H∞ consensus to be ensured, and then the time-varying controller parameters are designed by solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the usefulness of the proposed control protocol.

Distributed [formula omitted] state estimation with stochastic parameters and nonlinearities through sensor networks: The finite-horizon case

This paper deals with the distributed H∞ state estimation problem for a class of discrete time-varying nonlinear systems with both stochastic parameters and stochastic nonlinearities. The system measurements are collected through sensor networks with sensors distributed according to a given topology. The purpose of the addressed problem is to design a set of time-varying estimators such that the average estimation performance of the networked sensors is guaranteed over a given finite-horizon. Through available output measurements from not only the individual sensor but also its neighboring sensors, a necessary and sufficient condition is established to achieve the H∞ performance constraint, and then the estimator design scheme is proposed via a certain H2-type criterion. The desired estimator parameters can be obtained by solving coupled backward recursive Riccati difference equations (RDEs). A numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed estimator design approach.