Mean Square Stability Analysis of Stochastic Continuous-Time Linear Networked Systems

Nandanoori, Sai Pushpak; Diwadkar, Amit; Vaidya, Umesh

doi:10.1109/tac.2018.2830882

Cited by 10 publications

(20 citation statements)

References 43 publications

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“…is intractable. The difficulty, however, can be handily resolved owing to the methods used in the average-consensus analysis of multiagent systems [24], [25] and second moment performance analysis of stochastic differential equations [47], [58]. Referring to the averageconsensus studies [24], [25], let us define…”

Section: A Main Resultsmentioning

confidence: 99%

Formation-Control Stability and Communication Capacity of Multiagent Systems: A Joint Analysis

Qian

Duan

et al. 2021

IEEE Trans. Control Netw. Syst.

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The focus of this study is a joint analysis of the stability of formation control and the capacity of wireless communications between agents moving in a formation. The main results derived in this study show a connection between the second moment stability/convergence of formation control and the expected capacity of the data communications for multiagent systems in which the collective behavior of the multiple agents is dominated by formation control with random errors. More specifically, by developing a joint control-communication framework for the performance analysis, we investigate whether random errors in the formation control have a destructive influence on the data communications between agents. We prove that the expected capacity of the multiagent data communication link has a nonvanishing lower bound that can be evaluated through second moment performance analysis. The results from simulations indicate that the theoretical analysis provides reasonable lower bounds for different system parameters.

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Section: A Main Resultsmentioning

confidence: 99%

Formation-Control Stability and Communication Capacity of Multiagent Systems: A Joint Analysis

Qian

Duan

et al. 2021

IEEE Trans. Control Netw. Syst.

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“…Mean square stability analysis of a stochastic power network where the uncertainty in system inertia appears multiplicative to the system dynamics is studied in [22]. Recent efforts have looked into the problem of control synthesis with closedloop stochastic stability guarantees in dynamical systems with both multiplicative and additive uncertainties [23]- [26]. Specifically, the work in [23] provides sufficient and necessary conditions for mean square exponentially stability (MSES) for stochastic dynamical systems with multiplicative uncertainties.…”

Section: Introductionmentioning

confidence: 99%

“…Recent efforts have looked into the problem of control synthesis with closedloop stochastic stability guarantees in dynamical systems with both multiplicative and additive uncertainties [23]- [26]. Specifically, the work in [23] provides sufficient and necessary conditions for mean square exponentially stability (MSES) for stochastic dynamical systems with multiplicative uncertainties. In addition, a static full-state feedback control synthesis was proposed in [23] for the special case of single-input channel uncertainty, with a quantification on the maximum allowable (critical) uncertainty level.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, the work in [23] provides sufficient and necessary conditions for mean square exponentially stability (MSES) for stochastic dynamical systems with multiplicative uncertainties. In addition, a static full-state feedback control synthesis was proposed in [23] for the special case of single-input channel uncertainty, with a quantification on the maximum allowable (critical) uncertainty level. The approach in [23], however, has limited applicability in realistic power systems because of the assumptions placed on the nature of the uncertainty (singleinput) and the availability of the measurements (full-state); and the non-consideration of design concerns such as sparsity, control efforts and closed-loop transient performance.…”

Section: Introductionmentioning

confidence: 99%

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Sparse Control Synthesis for Uncertain Responsive Loads with Stochastic Stability Guarantees

Nandanoori¹,

Kundu²,

Lian³

et al. 2021

Preprint

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Recent studies have demonstrated the potential of flexible loads in providing frequency response services. However, uncertainty and variability in various weather-related and enduse behavioral factors often affect the demand-side control performance. This work addresses this problem with the design of a demand-side control to achieve frequency response under load uncertainties. Our approach involves modeling the load uncertainties via stochastic processes that appear as both multiplicative and additive to the system states in closed-loop power system dynamics. Extending the recently developed mean square exponential stability (MSES) results for stochastic systems, we formulate multi-objective linear matrix inequality (LMI)-based optimal control synthesis problems to not only guarantee stochastic stability, but also promote sparsity, enhance closed-loop transient performance, and maximize allowable uncertainties. The fundamental trade-off between the maximum allowable (critical) uncertainty levels and the optimal stochastic stabilizing control efforts is established. Moreover, the sparse control synthesis problem is generalized to the realistic power systems scenario in which only partial-state measurements are available. Detailed numerical studies are carried out on IEEE 39-bus system to demonstrate the closed-loop stochastic stabilizing performance of the sparse controllers in enhancing frequency response under load uncertainties; as well as illustrate the fundamental trade-off between the allowable uncertainties and optimal control efforts.

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“…The stochastic disturbance is more and more obvious, the power system stability is affected to some extent. [8][9][10][11] Some literatures use the improved probability method to analyze the dynamic stability under different operating modes, 12 some propose an evaluation. 13 A feasible method for calculating the influence of parameter uncertainty on the dynamic behavior of power systems are developed.…”

Section: Introductionmentioning

confidence: 99%

Stable bounded value analysis of disturbance in stochastic linear power systems

Tong

Gao

2020

Measurement and Control

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Stochastic disturbances play a profound problem in the power system, which have an important impact on the stability of the power system. The paper proposes the stability analysis of stochastic disturbance bounded value of linear power system, and presents that the stability of power system has bounded value under stochastic disturbance and additional disturbance, and gives the analysis process in combination with stochastic differentiation. The equation theory proposes a numerical solution based on mean stability to calculate the boundedness of infinite systems under the influence of stochastic disturbance and additional disturbance. The results show that the system has bounded value stability under the disturbance.

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Mean Square Stability Analysis of Stochastic Continuous-Time Linear Networked Systems

Cited by 10 publications

References 43 publications

Formation-Control Stability and Communication Capacity of Multiagent Systems: A Joint Analysis

Formation-Control Stability and Communication Capacity of Multiagent Systems: A Joint Analysis

Sparse Control Synthesis for Uncertain Responsive Loads with Stochastic Stability Guarantees

Stable bounded value analysis of disturbance in stochastic linear power systems

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