arXiv subjects

Seddik Djouadi

Publications and source records attributed to Seddik Djouadi.

15 recordsLinked to original sources

arXiv2026

Private & Common Information States in Decentralized Team Equilibrium via Dynamic Programming for POMDPs with Delayed Sharing

Witsenhausen, in his seminal 1971 paper [1], introduced decentralized partially observable Markov decision problems (POMDPs), with multiple agents or controls operating under T-step delayed sharing information patterns. A fundamental problem in [1] is the identification of structural properties of optimal strategies that compress the information patterns into multiple information states. In this paper, we develop such structural properties of optimal strategies and associated dynamic programming (DP) equations, using the concept of decentralized sequential team equilibrium (a generalization of person-by-person optimality from static team theory). Within this framework, each strategy is assigned an individual value function conditioned on its delayed sharing information pattern, while the strategies of all other agents are held fixed. The resulting DP framework yields several new DP equations and characterizations of decentralized team equilibrium. Moreover, these DP equations exhibit fundamental properties analogous to those of centralized DP of POMDPs: the optimization in each agent's DP equations is performed over the agent's action space rather than over strategy spaces; each agent's multiple information states satisfy Markov recursions; and a separation principle holds. The DP equations reveal a structural compression property of optimal strategies: each agent compresses its delayed sharing information pattern into three components: 1) a private posterior distribution conditioned on the agent's delayed sharing information pattern, 2) a centralized posterior distribution conditioned on the common information shared by all agents, and 3) the agent's private information component. This structural result substantially extends Witsenhausen's Assertion 8 in [1].

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arXiv2026

Comments and Corrections on the DP Equations of Paper "On Team Decision Problems With Nonclassical Information Structures"

The 2023 paper ``On Team Decision Problems With Nonclassical Information Structures'' [1] presented information states and dynamic programming (DP) equations for delayed sharing information patterns, based on the concept of person-by-person (PbP) optimality of static team theory. In particular, [Section IV, 1], Theorem 5 presents recursions of the information states and Theorem 7, eqn(57), eqn(58), presents DP equations, of each team member. In this note we show that the proof of Theorem 5 and the DP eqn(57), eqn(58) of Theorem 7 of [1] are incorrect. Consequently, Lemma 8, Theorem 6, and the full statement of Theorem 7 in [1] are invalid, because their proofs rely on erroneous information states and the optimality of separated strategies (i.e., functions of the information states). We further provide the correct DP equations for PbP optimality, thereby highlighting the subtleties and challenges inherent in the analysis of delayed sharing information patterns.

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arXiv2026

Private and Common Information States in Decentralized Parallel Dynamic Programming for Delayed Sharing Patterns

This paper develops a dynamic programming (DP) approach for decentralized stochastic optimal control problems with delayed sharing information patterns, which exhibits the fundamental Properties of classical DP of centralized partially observable Markov decision problems (POMDPs): the value functions and information states depend on the actions of the minimizing controls and not their strategies. This is achieved by invoking the concept of Person-by-Person (PbP) optimality, in which each control strategy is associated with a value function conditioned on its assigned delayed sharing information pattern, when all other strategies are fixed to their optimal responses. The value functions satisfy generalized and simplified DP equations. These are used to derive necessary and sufficient conditions for PbP optimality. The simplified DP equations are obtained by invoking the structural property that optimal strategies are separated and functionals of two information states: 1) a private a posteriori probability distribution based on the information pattern of the strategy, and 2) a centralized a posteriori probability distribution based on the shared or common information to all strategies, each satisfying a Markov recursion. The DP approach of this paper, settles a long standing open problem since the appearance of T-step delayed sharing patterns in [1, Section IV.G], in terms of generalizing the fundamental properties of classical DP approach.

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arXiv2025

General Decentralized Stochastic Optimal Control via Change of Measure: Applications to the Witsenhausen Counterexample

In this paper we present global and person-by-person (PbP) optimality conditions for general decentralized stochastic dynamic optimal control problems, using a discrete-time version of Girsanov's change of measure. The PbP optimality conditions are applied to the Witsenhausen counterexample to show that the two strategies satisfy two coupled nonlinear integral equations. Further, we prove a fixed point theorem in a function space, establishing existence and uniqueness of solutions to the integral equations. We also provide numerical solutions of the two integral equations using the Gauss Hermite Quadrature scheme, and include a detail comparison to other numerical methods of the literature. The numerical solutions confirm Witsehausen's observation that, for certain choices of parameters, linear or affine strategies are optimal, while for other choices of parameters nonlinear strategies outperformed affine strategies.

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arXiv2022

A Novel Framework for Decentralized Dynamic Resource Allocation Using Voronoi Tessellations

In this work, we approach the problem of resource allocation in a team of agents through the framework of Centroidal Voronoi Tessellations. CVTs provide a natural way to embed a desired global trend in the team through probability distributions, and in one-dimensional spaces, CVTs offer an inherent line structure allowing for a simple communication graph and scalability. We first consider the amount of resource to be allocated to be a constant and provide an analytical solution to such static resource allocation problem by embedding the allocation constraint within the distribution through a system of nonlinear equations. Using the solution of such a constrained CVT minimization problem as an initialization step, we propose a decentralized dynamic resource allocation solution that employs a one-step update when the desired distribution is Gaussian. We introduce a "civility model" for negotiations between the agents to allow for flexibility in local preferences and maintaining robustness against local disturbances. We demonstrate the effectiveness of the proposed method by considering the application of demand-response in smart grids through the problem of power allocation in a group of building thermal loads.

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arXiv2022

Computation of Centroidal Voronoi Tessellations in High Dimensional spaces

Owing to the natural interpretation and various desirable mathematical properties, centroidal Voronoi tessellations (CVT) have found a wide range of applications and correspondingly a vast development in their literature. However the computation of CVT in higher dimensional spaces still remains difficult. In this paper, we exploit the non-uniqueness of CVTs in higher dimensional spaces for their computation. We construct such high dimensional tessellations from CVTs in one-dimensional spaces. We then prove that such a tessellation is centroidal under the condition of independence among densities over the one-dimensional spaces considered. Various numerical evaluations backup the theoretical result through the low energy of the tessellations. The resulting grid-like tessellations are obtained efficiently with minimal computation time.

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arXiv2020

Numerical Evaluation of Exact Person-by-Person Optimal Nonlinear Control Strategies of the Witsenhausen Counterexample

Witsenhausen's 1968 counterexmaple is a simple two-stage decentralized stochastic control problem that highlighted the difficulties of sequential decision problems with non-classical information structures. Despite extensive prior efforts, what is known currently, is the exact Person-by-Person (PbP) optimal nonlinear strategies, which satisfy two nonlinear integral equations, announced in 2014, and obtained using Girsanov's change of measure transformations. In this paper, we provide numerical solutions to the two exact nonlinear PbP optimal control strategies, using the Gauss Hermite Quadrature to approximate the integrals and then solve a system of non-linear equations to compute the signaling levels. Further, we analyse and compare our numerical results to existing results previously reported in the literature.

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arXiv2020

Review on Set-Theoretic Methods for Safety Verification and Control of Power System

Increasing penetration of renewable energy introduces significant uncertainty into power systems. Traditional simulation-based verification methods may not be applicable due to the unknown-but-bounded feature of the uncertainty sets. Emerging set-theoretic methods have been intensively investigated to tackle this challenge. The paper comprehensively reviews these methods categorized by underlying mathematical principles, that is, set operation-based methods and passivity-based methods. Set operation-based methods are more computationally efficient, while passivity-based methods provide semi-analytical expression of reachable sets, which can be readily employed for control. Other features between different methods are also discussed and illustrated by numerical examples. A benchmark example is presented and solved by different methods to verify consistency.

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arXiv2018

Privacy-Preserving Aggregation of Controllable Loads to Compensate Fluctuations in Solar Power

Cybersecurity and privacy are of the utmost importance for safe, reliable operation of the electric grid. It is well known that the increased connectivity/interoperability between all stakeholders (e.g., utilities, suppliers, and consumers) will enable personal information collection. Significant advanced metering infrastructure (AMI) deployment and demand response (DR) programs across the country, while enable enhanced automation, also generate energy data on individual consumers that can potentially be used for exploiting privacy. Inspired by existing works which consider DR, battery-based perturbation, and differential privacy noise adding, we novelly consider the aggregator (cluster) level privacy issue in the DR framework of solar photovoltaic (PV) generation following. Different from most of the existing works which mainly rely on the charging/discharging scheduling of rechargeable batteries, we utilize controllable building loads to serve as virtual storage devices to absorb a large portion of the PV generation while delicately keeping desired noisy terms to satisfy the differential privacy for the raw load profiles at the aggregator level. This not only ensures differential privacy, but also improves the DR efficiency in load following since part of the noisy signal in solar PV generation has been filtered out. In particular, a mixed integer quadratic optimization problem is formulated to optimally dispatch a population of on/off controllable loads to achieve this privacy preserving DR service.

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arXiv2018

Regions of Attraction Approximation Using Individual Invariance

Approximating regions of attraction in nonlinear systems require extensive computational and analytical efforts. In this paper, nonlinear vector fields are recasted as sum of vectors where each individual vector is used to construct an artificial system. The theoretical foundation is provided for a theorem in individual invariance to relate regions of attraction of artificial systems to the original vector field's region of attraction which leads to significant simplification in approximating regions of attraction. Several second order examples are used to demonstrate the effectiveness of this theorem. It is also proposed to use this theorem for the transient stability problem in power systems where an algorithm is presented to identify the critical clearing time through sequences of function evaluations. The algorithm is successfully applied on the 3-machine 9-bus system as well as the IEEE 39-bus New England system giving accurate and realistic estimations of the critical clearing time.

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arXiv2018

Synthesizing Distributed Energy Resources in Microgrids with Temporal Logic Specifications

Grid supportive (GS) modes integrated within distributed energy resources (DERs) can improve the frequency response. However, synthesis of GS modes for guaranteed performance is challenging. Moreover, a tool is needed to handle sophisticated specifications from grid codes and protection relays. This paper proposes a model predictive control (MPC)-based mode synthesis methodology, which can accommodate the temporal logic specifications (TLSs). The TLSs allow richer descriptions of control specifications addressing both magnitude and time at the same time. The proposed controller will compute a series of Boolean control signals to synthesize the GS mode of DERs by solving the MPC problem under the normal condition, where the frequency response predicted by a reduced-order model satisfies the defined specifications. Once a sizable disturbance is detected, the pre-calculated signals are applied to the DERs. The proposed synthesis methodology is verified on the full nonlinear model in Simulink. A robust factor is imposed on the specifications to compensate the response mismatch between the reduce-order model and nonlinear model so that the nonlinear response satisfies the required TLS.

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arXiv2018

Battery Energy Storage Scheduling for Optimal Load Variance Minimization

Generation portfolio can be significantly altered due to the deployment of distributed energy resources (DER) in distribution networks and the concept of microgrid. Generally, distribution networks can operate in a more resilient and economic fashion through proper coordination of DER. However, due to the partially uncontrollable and stochastic nature of some DER, the variance of net load of distribution systems increases, which raises the operational cost and complicates operation for transmission companies. This motivates peak shaving and valley filling using energy storage units deployed in distribution systems. This paper aims at theoretical formulation of optimal load variance minimization, where the infinity norm of net load is minimized. Then, the problem is reformulated equivalently as a linear program. A case study is performed with capacity-limited battery energy storage model and the simplified power flow model of a radial distribution network. The influence of capacity limit and deployment location are studied.

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arXiv2018

Performance Guaranteed Inertia Emulation for Diesel-Wind System Feed Microgrid via Model Reference Control

In this paper, a model reference control based inertia emulation strategy is proposed. Desired inertia can be precisely emulated through this control strategy so that guaranteed performance is ensured. A typical frequency response model with parametrical inertia is set to be the reference model. A measurement at a specific location delivers the information of disturbance acting on the diesel-wind system to the reference model. The objective is for the speed of the diesel-wind system to track the reference model. Since active power variation is dominantly governed by mechanical dynamics and modes, only mechanical dynamics and states, i.e., a swing-engine-governor system plus a reduced-order wind turbine generator, are involved in the feedback control design. The controller is implemented in a three-phase diesel-wind system feed microgrid. The results show exact synthetic inertia is emulated, leading to guaranteed performance and safety bounds.

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arXiv2017

Model-free Load Control for High Penetration of Solar Photovoltaic Generation

This paper presents a new model-free control (MFC) mechanism that enables the local distribution level circuit consumption of the photovoltaic (PV) generation by local building loads, in particular, distributed heating, ventilation and air conditioning (HVAC) units. The local consumption of PV generation will help minimize the impact of PV generation on the distribution grid, reduce the required battery storage capacity for PV penetration, and increase solar PV generation penetration levels. The proposed MFC approach with its corresponding intelligent controllers does not require any precise model for buildings, where a reliable modeling is a demanding task. Even when assuming the availability of a good model, the various building architectures would compromise the performance objectives of any model-based control strategy. The objective is to consume most of the PV generation locally while maintaining occupants comfort and physical constraints of HVAC units. That is, by enabling proper scheduling of responsive loads temporally and spatially to minimize the difference between demand and PV production, it would be possible to reduce voltage variations and two-way power flow. Computer simulations show promising results where a significant proportion of the PV generation can be consumed by building HVAC units with the help of intelligent control.

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arXiv2017

Immune Therapeutic Strategies Using Optimal Controls with $L^1$ and $L^2$ Type Objectives

Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory response to a pathogenic insult with two therapeutic control inputs which have either a direct pro- or anti-inflammatory effect in the given system. We use Pontryagin's maximum principle and discuss necessary optimality conditions. We consider both an $L^1$ type objective functional as well as an $L^2$ type objective. For the former, the presence of singular control will be addressed. For each case, numerical simulations using a nonlinear programming optimization solver to acquire different drug treatment strategies are presented and discussed. The results provide insight for possible treatment strategies and the methods could be a relevant tool for future practice to assist in better prediction of clinical outcomes and subsequently better treatment for patients.

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