We introduce the framework of performative control, where the policy chosen by the controller affects the underlying dynamics of the control system. This results in a sequence of policy-dependent system state data with policy-dependent temporal correlations. Following the recent literature on performative prediction \cite{perdomo2020performative}, we introduce the concept of a performatively stable control (PSC) solution. We first propose a sufficient condition for the performative control problem to admit a unique PSC solution with a problem-specific structure of distributional sensitivity propagation and aggregation. We further analyze the impacts of system stability on the existence of the PSC solution. Specifically, for {almost surely strongly stable} policy-dependent dynamics, the PSC solution exists if the sum of the distributional sensitivities is small enough. However, for almost surely unstable policy-dependent dynamics, the existence of the PSC solution will necessitate a temporally backward decaying of the distributional sensitivities. We finally provide a repeated stochastic gradient descent scheme that converges to the PSC solution and analyze its non-asymptotic convergence rate. Numerical results validate our theoretical analysis.

This article studies a sequential task offloading problem for a multiuser mobile-edge computing (MEC) system. While most of the existing works consider static one-shot offloading optimization with fixed wireless channel conditions and fixed computational tasks, we consider a dynamic optimization approach, which embraces wireless channel fluctuations and random deep neural network (DNN) task arrivals over an infinite horizon. Specifically, we introduce a local CPU workload queue (WD-QSI) and a MEC server workload queue (MEC-QSI) to model the dynamic workload of DNN tasks at each wireless device (WD) and the MEC server, respectively. The transmit power and the partitioning of the local DNN task at each WD are dynamically determined based on the instantaneous channel conditions (to capture the transmission opportunities) and the instantaneous WD-QSI and MEC-QSI (to capture the dynamic urgency of the tasks) to minimize the average latency of the DNN tasks. The joint optimization can be formulated as an ergodic Markov decision process (MDP), in which the optimality condition is characterized by a centralized Bellman equation. However, the brute force solution of the MDP is not viable due to the curse of dimensionality as well as the requirement for knowledge of the global state information. To overcome these issues, we first decompose the MDP into multiple lower dimensional sub-MDPs, each of which can be associated with a WD or the MEC server. Next, we further develop a parametric online$Q$-learning algorithm, so that each sub-MDP is solved locally at its associated WD or the MEC server. The proposed solution is completely decentralized in the sense that the transmit power for sequential offloading and the DNN task partitioning can be determined based on the local channel state information (CSI) and the local WD-QSI at the WD only. Additionally, no prior knowledge of the distribution of the DNN task arrivals or the channel statistics will be needed for the MEC server. The proposed solution can achieve the superb performance over various state-of-the-art baselines.

With the rapid development of mobile computing, mission-critical Internet of Things (IoT) systems have become popular. Typical mission-critical IoT systems may contain complicated unknown and unstable elements and it is of particular importance to identify and stabilize them as unstable systems may experience catastrophic consequences. We consider the identification and optimal control for a mission-critical IoT system over multiple-input–multiple-output (MIMO) fading channels. First, we focus on the optimal control of the mission-critical IoT system, assuming that the system dynamics are known, and propose a novel stochastic-approximation-based algorithm to learn the optimal control solution for the IoT controller in an online manner. Second, we extend the optimal control framework to deal with the unknown mission-critical IoT system and propose a novel normalized-stochastic-gradient-descent-based algorithm to simultaneously identify and control the system in an online manner. Using the Lyapunov stability analysis, we theoretically show the asymptotic optimality of the proposed learning algorithms. Numerical results are analyzed for our proposed scheme and for several state-of-the-art learning schemes in terms of the computational complexity, convergence, and stability performance. Specifically, the proposed scheme can be implemented more than 50% faster than the state-of-the-art learning schemes. Moreover, the system identification performance of the proposed scheme can achieve a normalized system identification mean square error (MSE) of around 0.01 in 100 iterations. This is a substantial improvement compared to the baseline algorithms, where the normalized system identification MSE diverges.

In this article, we consider the remote state estimation for nonlinear dynamic systems with known linear dynamics and unknown nonlinear perturbations. The nonlinear dynamic plant is monitored by multiple distributed sensors over a random access wireless network with shared common radio channel. We focus on the communication strategy and remote state estimation algorithm design so as to achieve a remote state estimation stability subject to unknown nonlinearities in plant and various wireless impairments, such as multisensor interference, wireless fading, and additive channel noise. By exploiting the additive properties of the physical wireless channels, we propose a novel information fusion over-the-air mechanism to address the signal collision and interference among the sensors. Utilizing the partial knowledge on the linear dynamics of the plant, we also propose a novel recurrent neural network (RNN)-based remote state estimator aided by a virtual state estimation mean-square-error (MSE) process. We further propose a novel online training algorithm such that the RNN at the remote estimator can effectively learn the unknown plant nonlinearities. Using the Lyapunov drift analysis approach, we establish closed-form sufficient requirements on the communication resources needed to achieve almost sure stability of both state estimation and RNN online training in high signal-to-noise ratio (SNR) regime. As a result, our proposed scheme is asymptomatic optimal for large SNR in the sense that both the plant state and the unknown plant nonlinearities can be perfectly recovered at the remote estimator. The proposed scheme is also compared with various baselines and we show that significant performance gains can be achieved.

We consider the recurrent neural network (RNN)-based remote state estimation for nonlinear dynamic systems with unknown state dynamics. The nonlinear dynamic plant is monitored by multiple distributed IIoT sensors over a random access wireless network with shared common spectrum. We focus on the remote state estimation algorithm design so as to achieve remote state estimation stability subject to noninvertible nonlinear sensor state observations, imperfect channel state information (CSI) at the remote estimator, and various wireless impairments, such as multisensor interference, wireless fading, and additive channel noise. Utilizing a state diffeomorphism, the original system is transformed into a canonical form with a linear rank deficient observation matrix. We propose a novel RNN remote state estimator based on the pole placement design associated with the transformed rank deficient state measurement matrices. We further propose a novel online training algorithm such that the RNN at the remote estimator can not only address the divergence issue over wireless networks but also effectively learn the unknown nonlinear plant dynamics despite rank deficiency and imperfect CSI. Using the Lyapunov drift analysis approach, we establish closed-form sufficient requirements on the communication resources needed to achieve almost sure stability of both state estimation and RNN online training in the high signal-to-noise ratio (SNR) regime. As a result, our proposed scheme is asymptomatic optimal for large SNR in the sense that both the plant state and the unknown plant nonlinearity can be perfectly recovered at the remote estimator. The proposed scheme is also compared with various baselines and we show that significant performance gains can be achieved.

We consider remote state estimation for an industrial Internet-of-Things (IoT) system, where the plant dynamics are monitored by a number of distributed industrial IoT sensors. We propose an “estimation friendly” remote state estimation framework, which not only maintains low computational complexity but also provides better estimation stability performance. Specifically, we propose a novel over-the-air-aggregation-based multiple access, which enhances the observability performance of the state estimation system and hence, provides better estimation stability. Additionally, exploiting the sparsity in the observation matrix induced by the over-the-air-aggregation-based multiple access, we propose a low-complexity 2-D message passing state estimation algorithm, where the cyclic loops in the 2-D factor graphs are removed based on the quasi-diagonal transformation of the aggregated channel matrix of the IoT sensors. As a result, the proposed state estimation scheme is of low complexity and can achieve exact maximum a posterior estimation. Using the Lyapunov drift analysis, we derive the closed-form necessary and sufficient conditions for stability of the mission-critical remote state estimation system. The numerical results demonstrate that the proposed scheme has a low computational complexity. Furthermore, it is scalable with the number of sensors and has a low power consumption.

In this paper, we consider a mission-critical remote state estimation system with asynchronous massive access of the IoT sensors. We focus on remote state estimation stability of the system in the presence of asynchronous access of the sensors. Exploiting the sparsity in the observation matrix induced by the asynchronous access, we propose a low complexity 2-D message passing state estimation algorithm, where the cyclic loops in the 2-D factor graphs are removed based on the Gaussian-elimination-based quasi-diagonalization of the oversampled aggregated channel matrix of the IoT sensors. As a result, the proposed state estimation scheme is of low complexity and can achieve exact MAP estimation. Using Lyapunov drift analysis, we derive closed-form necessary and sufficient conditions for stability of the mission-critical remote state estimation system. We show that our proposed scheme can achieve significant performance gain over various state-of-the-art baselines for the large-scale system under asynchronous massive access.

In this paper, we consider a mission-critical control system, where an unstable dynamic plant is monitored by multiple distributed IoT sensors over a wireless communication network with shared common spectrum. To reduce the complexity of Kalman filtering, we consider a constant gain filter at the remote controller. We propose a decentralized dynamic scheduling and information fusion of the IoT sensors to stabilize the unstable dynamic plant. The proposed scheme has a state-driven multiple access structure, where a large state estimation MSE (high transmission urgency) and good wireless channel conditions (good transmission opportunities) promote the active mode of the sensors. Using the Lyapunov techniques, we provide the closed-form sufficient condition for stability and closed-form characterizations on the trade-off between the state estimation MSE and average power consumption of the sensors. We also propose a design guideline for the constant filter gain via minimizing the state estimation MSE. The proposed scheme is also compared with various representative literature and we show that significant performance gains can be achieved.

In this paper, we consider the stabilization of multiagent dynamic systems. We propose a novel cloud-assisted information sharing solution for the mission-critical Internet of Things control applications. In the proposed design, the sensors and controllers communicate with the cloud network using modulation-free transmissions. Via exploiting the additive properties of the physical wireless channels, signal collision, and interference among the agents is utilized for multiagent stabilization by means of information fusion over the air (AirFuse). Utilizing the proposed AirFuse mechanism, the cloud provides observation side-information and control side-information efficiently to the sensor and the controller in each agent, respectively, which substantially enhance the stabilization performance of the multiagent dynamic system. Using the Lyapunov drift analysis approach, we further establish closed-form sufficient requirements on the communication resources needed to achieve stabilization of the multiagent dynamic system. Compared with the conventional multiagent dynamic systems without cloud assistance, we explicitly quantify the benefits of the cloud assistance in terms of stability performance and show that the proposed cloud-assisted solution enjoys superior scalability performance with ultra low access latency.