arXiv subjects

Mohammad H. Mamduhi

Publications and source records attributed to Mohammad H. Mamduhi.

13 recordsLinked to original sources

arXiv2026

Safe Packetized Control for Stochastic Constrained Networked Systems

This work develops a formal framework for the synthesis of packetized safety controllers for discrete-time polynomial stochastic networked control systems (dt-PSNCS) operating under communication constraints, including uplink delays (plant-to-controller) and downlink packet losses (controller-to-actuator). In this setting, the controller is deployed remotely and exchanges information with the plant over an imperfect wireless communication network. Our proposed approach treats the downlink channel as an erasure channel, with packet losses characterized by an independent Bernoulli process. To systematically manage both uplink delays and downlink packet loss, we first introduce a buffer collocated with the plant that accommodates the packetized safety control (PSC) mechanism. We augment the plant and buffer states into a unified augmented-state representation that accurately captures the system evolution in the presence of communication imperfections. Our proposed framework synthesizes safety controllers based on control barrier certificates (CBCs), providing probabilistic safety guarantees that remain robust in the presence of both communication delays and packet losses. To achieve this, we reformulate the safety constraints as a sum-of-squares (SOS) optimization program, thereby facilitating the systematic construction of CBCs and their corresponding safety controllers. We validate the proposed framework through three (physical) case studies, demonstrating its effectiveness and practical applicability.

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arXiv2026

Barrier Certificates for Uncertain Temporal Specifications

This paper studies satisfying temporal logic specifications on stochastic dynamical systems, where the predicates evolve randomly over time. Such randomness may arise from uncertain environment models or external stochastic processes causing the sets associated with predicate satisfaction to vary in a non-deterministic manner. As a result, verifying whether a stochastic dynamical system satisfies a temporal specification depends also on the uncertainty in the predicates. We develop a certificate-based framework to bound the probability of satisfying temporal logic specifications with randomly evolving predicates. We first show that temporal logic specifications with stochastic predicates can be transformed to specifications with deterministic predicates on an augmented space which is extended to include the stochastic space of predicate's uncertainty. We then utilize barrier certificates on an augmented space to provide tractable optimization-based conditions and to avoid the computational burden of dynamic programming. Focusing on linear dynamics and safety-type specifications, we derive analytical conditions under which barrier certificates guarantee bounds on the probability of violating the stochastic safety predicates. The approach is demonstrated on numerical case studies.

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arXiv2025

Safety Controller Synthesis for Stochastic Networked Systems under Communication Constraints

This paper develops a framework for synthesizing safety controllers for discrete-time stochastic linear control systems (dt-SLS) operating under communication imperfections. The control unit is remote and communicates with the sensor and actuator through an imperfect wireless network. We consider a constant delay in the sensor-to-controller channel (uplink), and data loss in both sensor-to-controller and controller-to-actuator (downlink) channels. In our proposed scheme, data loss in each channel is modeled as an independent Bernoulli-distributed random process. To systematically handle the uplink delay, we first introduce an augmented discrete-time stochastic linear system (dt-ASLS) by concatenating all states and control inputs that sufficiently represent the state-input evolution of the original dt-SLS under the delay and packet loss constraints. We then leverage control barrier certificates for dt-ASLS to synthesize a controller that ensures the stochastic safety of dt-SLS, guaranteeing that all trajectories remain outside unsafe regions with a quantified probabilistic bound. Our approach translates safety constraints into matrix inequalities, leading to an optimization problem that eventually quantifies the probability of satisfying the safety specification in the presence of communication imperfections. We validate our results on an RLC circuit subject to both constant delay and probabilistic data loss.

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arXiv2024

Average Communication Rate for Event-Triggered Stochastic Control Systems

Quantifying the average communication rate (ACR) of a networked event-triggered stochastic control system (NET-SCS) with deterministic thresholds is challenging due to the non-stationary nature of the system's stochastic processes. For a NET-SCS, the nonlinear statistics propagation of the network communication status brought up by deterministic thresholds makes the precise computation of ACR difficult. Previous work used to over-simplify the computation using a Gaussian distribution without incorporating this nonlinearity, leading to sacrificed precision. This paper proposes both analytical and numerical approaches to predict the exact ACR for a NET-SCS using a recursive model. We use theoretical analysis and a numerical study to qualitatively evaluate the deviation gap of the conventional approach that ignores the side information. The accuracy of our proposed method, alongside its comparison with the simplified results of the conventional approach, is validated by experimental studies. Our work is promising to benefit the efficient resource planning of networked control systems with limited communication resources by providing accurate ACR computation.

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arXiv2023

Stochastic Stability of Discrete-time Phase-coupled Oscillators over Uncertain and Random Networks

This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. Stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators coupled with 2π-periodic odd functions over underlying undirected graphs subject to both multiplicative and additive stochastic uncertainties. We prove stochastic phase-cohesiveness of the network with respect to two specific, namely in-phase and anti-phase, sets by deriving sufficient coupling conditions. We show the dependency of these conditions on the size of the mean values of additive and multiplicative uncertainties, as well as the sign of the mean values of multiplicative uncertainties. Furthermore, we discuss the results under a relaxation of the odd property of the coupling function. Second, we study an uncertain network in which the multiplicative uncertainties are governed by the Bernoulli process representing the well-known Erdos-Renyi network. We assume constant exogenous frequencies and derive sufficient conditions for achieving both stochastic phase-cohesive and phase-locked solutions, i.e., stochastic phase-cohesiveness with respect to the origin. For the latter case, where identical exogenous frequencies are assumed, we prove that any positive probability of connectivity leads to phase-locking. Thorough analyses are provided, and insights obtained from stochastic analysis are discussed, along with numerical simulations to validate the analytical results.

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arXiv2023

Distributed State Estimation for Linear Time-Varying Systems with Sensor Network Delays

Distributed sensor networks often include a multitude of sensors, each measuring parts of a process state space or observing the operations of a system. Communication of measurements between the sensor nodes and estimator(s) cannot realistically be considered delay-free due to communication errors and transmission latency in the channels. We propose a novel stability-based method that mitigates the influence of sensor network delays in distributed state estimation for linear time-varying systems. Our proposed algorithm efficiently selects a subset of sensors from the entire sensor nodes in the network based on the desired stability margins of the distributed Kalman filter estimates, after which, the state estimates are computed only using the measurements of the selected sensors. We provide comparisons between the estimation performance of our proposed algorithm and a greedy algorithm that exhaustively selects an optimal subset of nodes. We then apply our method to a simulative scenario for estimating the states of a linear time-varying system using a sensor network including 2000 sensor nodes. Simulation results demonstrate the performance efficiency of our algorithm and show that it closely follows the achieved performance by the optimal greedy search algorithm.

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arXiv2022

Controller-Aware Dynamic Network Management for Industry 4.0

In this paper, we consider a cyber-physical manufacturing system (CPMS) scenario containing physical components (robots, sensors, and actuators), operating in a digitally connected, constrained environment to perform industrial tasks. The CPMS has a centralized control plane with digital twins (DTs) of the physical resources, computational resources, and a network manager that allocates network resources. Existing approaches for allocation of network resources are typically fixed with respect to controller-dependent run-time specifications, which may impact the performance of physical processes. We propose a dynamic network management framework, where the network resource allocation schemes are controller-aware. The information about the controllers of the physical resources is implemented at the DT level, and metrics, such as regret bounds, take the process performance measures into account. The proposed network management schemes optimize physical system performance by balancing the shared resources between the physical assets on the plant floor, and by considering their control requirements, providing a new perspective for dynamic resource allocation. A simulation study is provided to illustrate the performance of the proposed network management approaches and compare their efficiencies.

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arXiv2020

Delay-sensitive Joint Optimal Control and Resource Management in Multi-loop Networked Control Systems

In the operation of networked control systems, where multiple processes share a resource-limited and time-varying cost-sensitive network, communication delay is inevitable and primarily influenced by, first, the control systems deploying intermittent sensor sampling to reduce the communication cost by restricting non-urgent transmissions, and second, the network performing resource management to minimize excessive traffic and eventually data loss. In a heterogeneous scenario, where control systems may tolerate only specific levels of sensor-to-controller latency, delay sensitivities need to be considered in the design of control and network policies to achieve the desired performance guarantees. We propose a cross-layer optimal co-design of control, sampling and resource management policies for an NCS consisting of multiple stochastic linear time-invariant systems which close their sensor-to-controller loops over a shared network. Aligned with advanced communication technology, we assume that the network offers a range of latency-varying transmission services for given prices. Local samplers decide either to pay higher cost to access a low-latency channel, or to delay sending a state sample at a reduced price. A resource manager residing in the network data-link layer arbitrates channel access and re-allocates resources if link capacities are exceeded. The performance of the local closed-loop systems is measured by a combination of linear-quadratic Gaussian cost and a suitable communication cost, and the overall objective is to minimize a defined social cost by all three policy makers. We derive optimal control, sampling and resource allocation policies under different cross-layer awareness models, including constant and time-varying parameters, and show that higher awareness generally leads to performance enhancement at the expense of higher computational complexity.

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arXiv2019

Event-triggered Add-on Safety for Connected and Automated Vehicles Using Road-side Network Infrastructure

This paper proposes an event-triggered add-on safety mechanism to adjust the control parameters for timely braking in a networked vehicular system while maintaining maneuverability. Passenger vehicle maneuverability is significantly affected by the combined-slip friction effect, in which larger longitudinal tire slips result in considerable drop in lateral tire forces. This is of higher importance when unexpected dangerous situations occur on the road and immediate actions, such as braking, need to be taken to avoid collision. Harsh braking can lead to high-slip and loss of maneuverability, hence, timely braking is essential to reduce high-slip scenarios. In addition to the vehicles own active safety systems, the proposed event-triggered add-on safety is activated upon being informed about dangers by the road-side infrastructure. The aim is to incorporate the add-on safety feature to adjust the automatic control parameters for smooth and timely braking such that a collision is avoided while vehicle's maneuverability is maintained. We study two different wireless technologies for communication between the infrastructure and the vehicles, the Long-Term Evolution (LTE) and the fifth generation (5G) schemes. The framework is validated through high-fidelity software simulations and the advantages of including the add-on feature to augment the safety margins for each communication technology is evaluated.

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arXiv2019

Joint Cross-layer Optimization in Real-Time Networked Control Systems

Networked control system (NCS) refer to a set of control loops that are closed over a communication network. In this article, the joint operation of control and networking for NCS is investigated wherein the network serves the sensor-to-controller communication links for multiple stochastic linear time-invariant (LTI) sub-systems. The sensors sample packets based on the observed plant state, which they send over a shared multi-hop network. The network has limited communication resources, which need to be assigned to competing links to support proper control loop operation. In this set-up, we formulate an optimization problem to minimize the weighted-sum linear-quadratic-Gaussian (LQG) cost of all loops, taking into account the admissible sampling, control, congestion control and scheduling policies. Under some mild assumptions on the sampling frequencies of the control loops and the communication network, we find the joint optimal solution to be given by a certainty equivalence control with threshold-based sampling policy, as well as a back-pressure type scheduler with a simple pass-through congestion control. The interface between network and control loops is identified to be the buffer state of the sensor node, which can be interpreted as network price for sampling a packet from control perspective. We validate our theoretical claims by simulating NCSs comprising of multiple LTI stochastic control loops communicating over a two-hop cellular network.

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arXiv2019

Performance Characterization Using AoI in a Single-loop Networked Control System

The joint design of control and communication scheduling in a Networked Control System (NCS) is known to be a hard problem. Several research works have successfully designed optimal sampling and/or control strategies under simplified communication models, where transmission delays/times are negligible or fixed. However, considering sophisticated communication models, with random transmission times, result in highly coupled and difficult-to-solve optimal design problems due to the parameter inter-dependencies between estimation/control and communication layers. To tackle this problem, in this work, we investigate the applicability of Age-of-Information (AoI) for solving control/estimation problems in an NCS under i.i.d. transmission times. Our motivation for this investigation stems from the following facts: 1) recent results indicate that AoI can be tackled under relatively sophisticated communication models, and 2) a lower AoI in an NCS may result in a lower estimation/control cost. We study a joint optimization of sampling and scheduling for a single-loop stochastic LTI networked system with the objective of minimizing the time-average squared norm of the estimation error. We first show that under mild assumptions on information structure the optimal control policy can be designed independently from the sampling and scheduling policies. We then derive a key result that minimizing the estimation error is equivalent to minimizing a function of AoI when the sampling decisions are independent of the state of the LTI system. Noting that minimizing the function of AoI is a stochastic combinatorial optimization problem and is hard to solve, we resort to heuristic algorithms obtained by extending existing algorithms in the AoI literature. We also identify a class of LTI system dynamics for which minimizing the estimation error is equivalent to minimizing the expected AoI.

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arXiv2019

Stochastic phase-cohesiveness of discrete-time Kuramoto oscillators in a frequency-dependent tree network

This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the exogenous frequencies of the oscillators are combined with random variables representing uncertainties. A bidirectional tree network is considered such that each oscillator is coupled to its neighbors with a coupling law which depends on its own noisy exogenous frequency. In addition, an undirected tree network is studied. For both cases, a sufficient condition for the common coupling strength and a necessary condition for the sampling-period are derived such that the stochastic phase-cohesiveness is achieved. The analysis is performed within the stochastic systems framework and validated by means of numerical simulations.

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arXiv2018

Optimal LQG Control under Delay-dependent Costly Information

In the design of closed-loop networked control systems (NCSs), induced transmission delay between sensors and the control station is an often-present issue which compromises control performance and may even cause instability. A very relevant scenario in which network-induced delay needs to be investigated is costly usage of communication resources. More precisely, advanced communication technologies, e.g. 5G, are capable of offering latency-varying information exchange for different prices. Therefore, induced delay becomes a decision variable. It is then the matter of decision maker's willingness to either pay the required cost to have low-latency access to the communication resource, or delay the access at a reduced price. In this article, we consider optimal price-based bi-variable decision making problem for single-loop NCS with a stochastic linear time-invariant system. Assuming that communication incurs cost such that transmission with shorter delay is more costly, a decision maker determines the switching strategy between communication links of different delays such that an optimal balance between the control performance and the communication cost is maintained. In this article, we show that, under mild assumptions on the available information for decision makers, the separation property holds between the optimal link selecting and control policies. As the cost function is decomposable, the optimal policies are efficiently computed.

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