arXiv subjects

Nima Monshizadeh

Publications and source records attributed to Nima Monshizadeh.

At least 37 records · Page 2Linked to original sources

arXiv2022

Dynamic interventions with limited knowledge in network games

This paper studies the problem of intervention design for steering the actions of noncooperative players in quadratic network games to the social optimum. The players choose their actions with the aim of maximizing their individual payoff functions, while a central regulator uses interventions to modify their marginal returns and maximize the social welfare function. This work builds on the key observation that the solution to the steering problem depends on the knowledge of the regulator on the players' parameters and the underlying network. We, therefore, consider different scenarios based on limited knowledge and propose suitable static, dynamic and adaptive intervention protocols. We formally prove convergence to the social optimum under the proposed mechanisms. We demonstrate our theoretical findings on a case study of Cournot competition with differentiated goods.

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arXiv2021

Exponential Stability and Tuning for a Class of Mechanical Systems

In this paper, we prove the exponential stability property of a class of mechanical systems represented in the port-Hamiltonian framework. To this end, we propose a Lyapunov candidate function different from the Hamiltonian of the system. Moreover, we study how the proposed analysis can be used to determine the exponential stability and the rate of convergence of some (nonlinear)-mechanical systems stabilized by two passivity-based control techniques, namely, PID passivity-based control and interconnection and damping assignment. We implement the former control approach to stabilize a three degrees-of-freedom robotic arm at the desired equilibrium point to illustrate the mentioned analysis.

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arXiv2021

PID passivity-based droop control of power converters: Large-signal stability, robustness and performance

We present a full review of PID passivity-based controllers (PBC) applied to power electronic converters, discussing limitations, unprecedented merits and potential improvements in terms of large-signal stability, robustness and performance. We provide four main contributions. The nominal case is first considered and it is shown, under the assumption of perfect knowledge of the system parameters, that the PID-PBC is able to guarantee global exponential stability of a desired operating point for any positive gains. Second, we analyze robustness of the controller to parameters uncertainty for a specific class of power converters, by establishing precise stability margins. Third, we propose a modification of the controller by introducing a leakage, in order to overcome some of the intrinsic performance and robustness limitations. Interestingly, such controller can be interpreted at steady-state as a droop between the input and the passive output, similar to traditional primary controllers. Fourth, we robustify the design against saturation of the control input via an appropriate monotone transformation of the controller. The obtained results are thoroughly discussed and validated by simulations on two relevant power applications: a dc/dc boost converter and an HVDC grid-connected voltage source converter.

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arXiv2021

Steering the aggregative behavior of noncooperative agents: a nudge framework

This paper considers the problem of steering the aggregative behavior of a population of noncooperative price-taking agents towards a desired behavior. Different from conventional pricing schemes where the price is fully available for design, we consider the scenario where a system regulator broadcasts a price prediction signal that can be different from the actual price incurred by the agents. The resulting reliability issues are taken into account by including trust dynamics in our model, implying that the agents will not blindly follow the signal sent by the regulator, but rather follow it based on the history of its accuracy, i.e, its deviation from the actual price. We present several nudge mechanisms to generate suitable price prediction signals that are able to steer the aggregative behavior of the agents to stationary as well as temporal desired aggregative behaviors. We provide analytical convergence guarantees for the resulting multi-components models. In particular, we prove that the proposed nudge mechanisms earn and maintain full trust of the agents, and the aggregative behavior converges to the desired one. The analytical results are complemented by a numerical case study of coordinated charging of plug-in electric vehicles.

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arXiv2021

Diagonal Stability of Systems with Rank-1 Interconnections and Application to Automatic Generation Control in Power Systems

We study a class of matrices with a rank-1 interconnection structure, and derive a simple necessary and sufficient condition for diagonal stability. The underlying Lyapunov function is used to provide sufficient conditions for diagonal stability of approximately rank-1 interconnections. The main result is then leveraged as a key step in a larger stability analysis problem arising in power systems control. Specifically, we provide the first theoretical stability analysis of automatic generation control (AGC) in an interconnected nonlinear power system. Our analysis is based on singular perturbation theory, and provides theoretical justification for the conventional wisdom that AGC is stabilizing under the typical time-scales of operation. We illustrate how our main analysis results can be leveraged to provide further insight into the tuning and dynamic performance of AGC.

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arXiv2021

Primary frequency regulation in power grids with on-off loads: chattering, limit cycles and convergence to optimality

Load side participation can provide valuable support to the power network in case of urgencies. On many occasions, loads are naturally represented by on and off states. However, the use of on-off loads for frequency control can lead to chattering and undesirable limit cycle behavior, which are issues that need to be resolved for such loads to be used for network support. This paper considers the problem of primary frequency regulation with ancillary service from on-off loads in power networks and establishes conditions that lead to convergence guarantees and an appropriate power allocation within the network. In particular, in order to assist existing frequency control mechanisms, we consider loads that switch when prescribed frequency thresholds are exceeded. Such control policies are prone to chattering, which limits their practicality. To resolve this issue, we consider loads that follow a decentralized hysteretic on-off policy, and show that chattering is not observed within such a setting. Hysteretic loads may exhibit, however, limit cycle behavior, which is undesirable. To address this, we propose an adapted hysteretic control scheme for which we provide convergence guarantees. Furthermore, we consider a mixed-integer optimization problem for power allocation and propose a suitable design of the control policy such that the cost incurred at equilibrium is within $ε$ from the optimal cost, providing a non conservative value for $ε$. The practicality of our analytic results is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system.

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arXiv2021

Optimal intervention strategies to mitigate the COVID-19 pandemic effects

Governments across the world are currently facing the task of selecting suitable intervention strategies to cope with the effects of the COVID-19 pandemic. This is a highly challenging task, since harsh measures may result in economic collapse while a relaxed strategy might lead to a high death toll. Motivated by this, we consider the problem of forming intervention strategies to mitigate the impact of the COVID-19 pandemic that optimize the trade-off between the number of deceases and the socio-economic costs. We demonstrate that the healthcare capacity and the testing rate highly affect the optimal intervention strategies. Moreover, we propose an approach that enables practical strategies, with a small number of policies and policy changes, that are close to optimal. In particular, we provide tools to decide which policies should be implemented and when should a government change to a different policy. Finally, we consider how the presented results are affected by uncertainty in the initial reproduction number and infection fatality rate and demonstrate that parametric uncertainty has a more substantial effect when stricter strategies are adopted.

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arXiv2020

A distributed scheme for secondary frequency control with stability guarantees and optimal power allocation

We consider the problem of distributed secondary frequency regulation in power networks such that stability and an optimal power allocation are attained. This is a problem that has been widely studied in the literature, and two main control schemes have been proposed, usually referred to as 'primal-dual' and 'distributed averaging proportional-integral (DAPI)' respectively. However, each has its limitations, with the former requiring knowledge of uncontrollable demand, which can be difficult to obtain in real time, and with the existing literature on the latter being based on static models for generation and demand. We propose a novel control scheme that overcomes these issues by making use of generation measurements in the control policy. In particular, our analysis allows distributed stability and optimality guarantees to be deduced with practical measurement requirements and permits a broad range of linear generation dynamics, that can be of higher order, to be incorporated in the power network. We show how the controller parameters can be selected in a computationally efficient way by solving appropriate linear matrix inequalities (LMIs). Furthermore, we demonstrate how the proposed analysis applies to several examples of turbine governor models. The practicality of our analysis is demonstrated with simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system that verify that our proposed controller achieves convergence to the nominal frequency and an economically optimal power allocation.

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arXiv2020

Quadratic Performance Analysis of Secondary Frequency Controllers

This paper investigates the input-output performance of secondary frequency controllers through the control-theoretic notion of $H_2$ norms. We consider a quadratic objective accounting for the cost of reserve procurement and provide exact analytical formulae for the performance of continuous-time aggregated averaging controllers. Then, we contrast it with distributed averaging controllers -- seeking optimality conditions such as identical marginal costs -- and primal-dual controllers which have gained attention as systematic techniques to design distributed algorithms solving convex optimization problems. Our conclusion is that while the performance of aggregated averaging controllers, such as gather & broadcast, is independent of the system size and driven predominantly by the control gain, the plain vanilla closed-loop primal-dual controllers scale poorly with size and do not offer any improvement over feedforward primal-dual controllers. Finally, distributed averaging-based controllers scale sub-linearly with size and are independent of system size in the high-gain limit.

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arXiv2020

Amidst data-driven model reduction and control

In this note, we explore a middle ground between data-driven model reduction and data-driven control. In particular, we use snapshots collected from the system to build reduced models that can be expressed in terms of data. We illustrate how the derived family of reduced models can be used for data-driven control of the original system under suitable conditions. Finding a control law that stabilizes certain solutions of the original system as well as the one that reaches any desired state in final time are studied in detail.

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arXiv2019

Privacy and Robustness Guarantees in Distributed Dynamics for Aggregative Games

This paper considers the problem of Nash equilibrium (NE) seeking in aggregative games, where the payoff function of each player depends on an aggregate of all players' actions. We present a distributed continuous time algorithm such that the actions of the players converge to NE by communicating to each other through a connected network. A major concern in communicative schemes among strategic agents is that their private information may be revealed to other agents or to a curious third party who can eavesdrop the communications. We address this concern for the presented algorithm and show that private information of the players cannot be reconstructed even if all the communicated variables are compromised. As agents may deviate from their optimal strategies dictated by the NE seeking protocol, we investigate robustness of the proposed algorithm against time-varying disturbances. In particular, we provide rigorous robustness guarantees by proving input to state stability (ISS) properties of the NE seeking dynamics. Finally, we demonstrate practical applications of our theoretical findings on two case studies; namely, on an energy consumption game and a charging coordination problem of electric vehicles.

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arXiv2019

Secondary frequency control with on-off load side participation in power networks

We study the problem of decentralized secondary frequency regulation in power networks where ancillary services are provided via on-off load-side participation. We initially consider on-off loads that switch when prescribed frequency thresholds are exceeded, together with a large class of passive continuous dynamics for generation and demand. The considered on-off loads are able to assist existing secondary frequency control mechanisms and return to their nominal operation when the power system is restored to its normal operation, a highly desirable feature which minimizes users disruption. We show that system stability is not compromised despite the switching nature of the loads. However, such control policies are prone to chattering, which limits the practicality of these schemes. As a remedy to this problem, we propose a hysteretic on-off policy where loads switch on and off at different frequency thresholds and show that stability guarantees are retained when the same decentralized passivity conditions for continuous generation and demand hold. Several relevant examples are discussed to demonstrate the applicability of the proposed results. Furthermore, we verify our analytic results with numerical investigations on the Northeast Power Coordinating Council (NPCC) 140-bus system.

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arXiv2019

Bias estimation in sensor networks

This paper investigates the problem of estimating biases affecting relative state measurements in a sensor network. Each sensor measures the relative states of its neighbors and this measurement is corrupted by a constant bias. We analyse under what conditions on the network topology and the maximum number of biased sensors the biases can be correctly estimated. We show that for non-bipartite graphs the biases can always be determined even when all the sensors are corrupted, while for bipartite graphs more than half of the sensors should be unbiased to ensure the correctness of the bias estimation. If the biases are heterogeneous, then the number of unbiased sensors can be reduced to two. Based on these conditions, we propose some algorithms to estimate the biases.

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arXiv2019

Secant and Popov-like Conditions in Power Network Stability

The problem of decentralized frequency control in power networks has received an increasing attention in recent years due to its significance in modern power systems and smart grids. Nevertheless, generation dynamics including turbine-governor dynamics, in conjunction with nonlinearities associated with generation and power flow, increase significantly the complexity in the analysis, and are not adequately addressed in the literature. In this paper we show how incremental secant gain conditions can be used in this context to deduce decentralized stability conditions with reduced conservatism. Furthermore, for linear generation dynamics, we establish Popov-like conditions that are able to reduce the conservatism even further by incorporating additional local information associated with the coupling strength among the bus dynamics. Various examples are discussed throughout the paper to demonstrate the significance of the results presented.

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arXiv2018

Input-Output Performance of Linear-Quadratic Saddle-Point Algorithms with Application to Distributed Resource Allocation Problems

Saddle-point or primal-dual methods have recently attracted renewed interest as a systematic technique to design distributed algorithms which solve convex optimization problems. When implemented online for streaming data or as dynamic feedback controllers, these algorithms become subject to disturbances and noise; convergence rates provide incomplete performance information, and quantifying input-output performance becomes more important. We analyze the input-output performance of the continuous-time saddle-point method applied to linearly constrained quadratic programs, providing explicit expressions for the saddle-point H2 norm under a relevant input-output configuration. We then proceed to derive analogous results for regularized and augmented versions of the saddle-point algorithm. We observe some rather peculiar effects -- a modest amount of regularization significantly improves the transient performance, while augmentation does not necessarily offer improvement. We then propose a distributed dual version of the algorithm which overcomes some of the performance limitations imposed by augmentation. Finally, we apply our results to a resource allocation problem to compare the input-output performance of various centralized and distributed saddle-point implementations and show that distributed algorithms may perform as well as their centralized counterparts.

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arXiv2018

Output Impedance Diffusion into Lossy Power Lines

Output impedances are inherent elements of power sources in the electrical grids. In this paper, we give an answer to the following question: What is the effect of output impedances on the inductivity of the power network? To address this question, we propose a measure to evaluate the inductivity of a power grid, and we compute this measure for various types of output impedances. Following this computation, it turns out that network inductivity highly depends on the algebraic connectivity of the network. By exploiting the derived expressions of the proposed measure, one can tune the output impedances in order to enforce a desired level of inductivity on the power system. Furthermore, the results show that the more "connected" the network is, the more the output impedances diffuse into the network. Finally, using Kron reduction, we provide examples that demonstrate the utility and validity of the method.

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arXiv2018

Permanent Magnet Synchronous Motors are Globally Asymptotically Stabilizable with PI Current Control

This note shows that the industry standard desired equilibrium for permanent magnet synchronous motors (i.e., maximum torque per Ampere) can be globally asymptotically stabilized with a PI control around the current errors, provided some viscous friction (possibly small) is present in the rotor dynamics and the proportional gain of the PI is suitably chosen. Instrumental to establish this surprising result is the proof that the map from voltages to currents of the incremental model of the motor satisfies some passivity properties. The analysis relies on basic Lyapunov theory making the result available to a wide audience.

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arXiv2018

A feedback control algorithm to steer networks to a Cournot-Nash equilibrium

We propose a distributed feedback control that steers a dynamical network to a prescribed equilibrium corresponding to the so-called Cournot-Nash equilibrium. The network dynamics considered here are a class of passive nonlinear second-order systems, where production and demands act as external inputs to the systems. While productions are assumed to be controllable at each node, the demand is determined as a function of local prices according to the utility of the consumers. Using reduced information on the demand, the proposed controller guarantees the convergence of the closed loop system to the optimal equilibrium point dictated by the Cournot-Nash competition.

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