Robust output consensus of homogeneous multi-agent systems with negative imaginary dynamics

Skeik, Ola; Lanzon, Alexander

doi:10.1016/j.automatica.2019.108799

Cited by 12 publications

(6 citation statements)

References 24 publications

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“…Negative Imaginary (NI) systems' theory provides one such technique that can provide stability and robustness against uncertainties. This has been used beneficially in different applications including large flexible structures [1], multi-link robotic arms [2] and aerial robotics [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Robust Fuzzy Q-Learning-Based Strictly Negative Imaginary Tracking Controllers for the Uncertain Quadrotor Systems

Tran¹,

Mabrok²,

Anavatti³

et al. 2022

Preprint

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Quadrotors are one of the popular unmanned aerial vehicles (UAVs) due to their versatility and simple design. However, the tuning of gains for quadrotor flight controllers can be laborious, and accurately stable control of trajectories can be difficult to maintain under exogenous disturbances and uncertain system parameters. This paper introduces a novel robust and adaptive control synthesis methodology for a quadrotor robot's attitude and altitude stabilization. The developed method is based on the fuzzy reinforcement learning and Strictly Negative Imaginary (SNI) property. The first stage of our control approach is to transform a nonlinear quadrotor system into an equivalent Negative-Imaginary (NI) linear model by means of the feedback linearization (FL) technique. The second phase is to design a control scheme that adapts online the Strictly Negative Imaginary (SNI) controller gains via fuzzy Q-learning, inspired by biological learning. The proposed controller does not require any prior training. The performance of the designed controller is compared with that of a fixed-gain SNI controller, a fuzzy-SNI controller, and a conventional PID controller in a series of numerical simulations. Furthermore, the stability of the proposed controller and the adaptive laws are proofed using the NI theorem.

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Section: Introductionmentioning

confidence: 99%

Robust Fuzzy Q-Learning-Based Strictly Negative Imaginary Tracking Controllers for the Uncertain Quadrotor Systems

Tran¹,

Mabrok²,

Anavatti³

et al. 2022

Preprint

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“…Consensus of multi-agent systems (MASs) has been extensively studied in theory and practice for the past few decades (Gao et al, 2020;Meng et al, 2019;Wang et al, 2020). Up to now, a large number of excellent research results have been obtained on the state consensus of homogeneous MASs (Mondal et al, 2018;Skeik and Lanzon, 2020;Valcher and Zorzan, 2017), in which all agents have the same dynamic model. However, in actual engineering systems, the more common pattern of agents is heterogeneous, which means that agents in an MAS have different dynamic models.…”

Section: Introductionmentioning

confidence: 99%

Leader-following consensus of heterogeneous linear multi-agent systems: New results based on linear transformation method

Chen

Zhan

2021

Transactions of the Institute of Measurement and Control

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This paper studies the leader-following state consensus problem for heterogeneous linear multi-agent systems under fixed directed communication topologies. First, we propose a consensus protocol consisting of four parts for high-order multi-agent systems, in which different agents are allowed to have different gain matrices so as to increase the degree of design freedom. Then, we adopt a state linear transformation, which is constructed based on the incidence matrix of a directed spanning tree of the communication topology, to equivalently transform the state consensus problem into a partial variable stability problem. Meanwhile, the results of the partial variable stability theory are used to derive a sufficient and necessary consensus criterion, expressed as the Hurwitz stability of a real matrix. Then, this criterion is further expressed as a bilinear matrix inequality condition, and, based on this condition, an iterative algorithm is proposed to find the gain matrices of the protocol. Finally, numerical examples are provided to verify the effectiveness of the proposed protocol design method.

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“…Many literatures enrich NI systems, including extensions to marginally stable systems [2][3][4], output strictly NI systems [5,6], nonrational symmetric systems [7,8], and infinite dimensional systems [9], besides, including the study of NI stability [1][2][3]10], the integral controllability and decentralized integral controllability of stable NI systems [11,12], and solution to NI control [13]. The applications of NI systems can be found in nano-positioning [14,15], vehicle platoons [16], multi-agent systems (MAS) [17][18][19][20], and so forth. Moreover, lightly damped structures with colocated position sensors and force actuators can be modeled as an NI system [1,4].…”

Section: Introductionmentioning

confidence: 99%

“…Some methods to construct IQC multipliers are proposed in several studies [27][28][29]. As we know, a variety of conditions have been depicted to solve the robust output consensus problem of continuous-time networked systems with homogeneous or heterogeneous NI dynamics [17][18][19][20]. The motivation of robust output consensus of networked NI systems is that an individual NI system cannot accomplish a specific goal on its own, for example, control and guarantee the stability of large vehicle platoons.…”

Section: Introductionmentioning

confidence: 99%

“…The dc loop gain condition for robust output consensus is also obtained in Wang et al [19] by using the internal stability result in Xiong et al [4], but two assumptions at infinite frequency are required. In Skeik and Lanzon [17], the dc loop gain result is extended according to the NI stability results in Lanzon and Chen [10]. The restrictions of the network graph play important roles, such as ensure the networked systems with NI properties.…”

Section: Introductionmentioning

confidence: 99%

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Robust output consensus of discrete‐time networked negative imaginary systems

Zhang

Liu

2021

Asian Journal of Control

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This paper considers robust output consensus of discrete-time networked homogeneous negative imaginary (NI) systems under 𝓁 2 external disturbances via integral quadratic constraints (IQCs). A necessary and sufficient condition for robust output consensus of discrete-time networked NI systems without poles at ±1 is obtained by the IQC-based discrete-time NI (D-NI) stability result.Moreover, the robust output consensus problem can be solved by designing an unstable controller whose poles are related to transmission zeros of D-NI systems. The case of discrete-time networked NI systems with poles at 1 is also studied. These main results are related to all eigenvalues of the Laplacian matrix of the network graph as well as the corresponding complementary IQCs at ±1 frequencies. Some corollaries are given by constructing appropriate IQC multipliers in order to simplify the main results. Finally, three examples are shown to explain the validity of the main results.

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Robust output consensus of homogeneous multi-agent systems with negative imaginary dynamics

Cited by 12 publications

References 24 publications

Robust Fuzzy Q-Learning-Based Strictly Negative Imaginary Tracking Controllers for the Uncertain Quadrotor Systems

Robust Fuzzy Q-Learning-Based Strictly Negative Imaginary Tracking Controllers for the Uncertain Quadrotor Systems

Leader-following consensus of heterogeneous linear multi-agent systems: New results based on linear transformation method

Robust output consensus of discrete‐time networked negative imaginary systems

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