P. R. Kumar

Abhishek Halder, Xinbo Geng, P. R. Kumar et al.

Motivated by the growing importance of demand response in modern power system's operations, we propose an architecture and supporting algorithms for privacy preserving thermal inertial load management as a service provided by the load serving entity (LSE). We focus on an LSE managing a population of its customers' air conditioners, and propose a contractual model where the LSE guarantees quality of service to each customer in terms of keeping their indoor temperature trajectories within respective bands around the desired individual comfort temperatures. We show how the LSE can price the contracts differentiated by the flexibility embodied by the width of the specified bands. We address architectural questions of (i) how the LSE can strategize its energy procurement based on price and ambient temperature forecasts, (ii) how an LSE can close the real time control loop at the aggregate level while providing individual comfort guarantees to loads, without ever measuring the states of an air conditioner for privacy reasons. Control algorithms to enable our proposed architecture are given, and their efficacy is demonstrated on real data.

Xueying Guo, Rahul Singh, P. R. Kumar et al.

In cyber-physical systems such as in-vehicle wireless sensor networks, a large number of sensor nodes continually generate measurements that should be received by other nodes such as actuators in a regular fashion. Meanwhile, energy-efficiency is also important in wireless sensor networks. Motivated by these, we develop scheduling policies which are energy efficient and simultaneously maintain "regular" deliveries of packets. A tradeoff parameter is introduced to balance these two conflicting objectives. We employ a Markov Decision Process (MDP) model where the state of each client is the time-since-last-delivery of its packet, and reduce it into an equivalent finite-state MDP problem. Although this equivalent problem can be solved by standard dynamic programming techniques, it suffers from a high-computational complexity. Thus we further pose the problem as a restless multi-armed bandit problem and employ the low-complexity Whittle Index policy. It is shown that this problem is indexable and the Whittle indexes are derived. Also, we prove the Whittle Index policy is asymptotically optimal and validate its optimality via extensive simulations.

Bharadwaj Satchidanandan, P. R. Kumar

The coming decades may see the large scale deployment of networked cyber-physical systems to address global needs in areas such as energy, water, healthcare, and transportation. However, as recent events have shown, such systems are vulnerable to cyber attacks. Being safety critical, their disruption or misbehavior can cause economic losses or injuries and loss of life. It is therefore important to secure such networked cyber-physical systems against attacks. In the absence of credible security guarantees, there will be resistance to the proliferation of cyber-physical systems, which are much needed to meet global needs in critical infrastructures and services. This paper addresses the problem of secure control of networked cyber-physical systems. This problem is different from the problem of securing the communication network, since cyber-physical systems at their very essence need sensors and actuators that interface with the physical plant, and malicious agents may tamper with sensors or actuators, as recent attacks have shown. We consider physical plants that are being controlled by multiple actuators and sensors communicating over a network, where some sensors could be "malicious," meaning that they may not report the measurements that they observe. We address a general technique by which the actuators can detect the actions of malicious sensors in the system, and disable closed-loop control based on their information. This technique, called "watermarking," employs the technique of actuators injecting private excitation into the system which will reveal malicious tampering with signals. We show how such an active defense can be used to secure networked systems of sensors and actuators.

Tong Huang, Bharadwaj Satchidanandan, P. R. Kumar et al.

We propose an online framework to detect cyber attacks on Automatic Generation Control (AGC). A cyber at- tack detection algorithm is designed based on the approach of Dynamic Watermarking. The detection algorithm provides a theoretical guarantee of detection of cyber attacks launched by sophisticated attackers possessing extensive knowledge of the physical and statistical models of targeted power systems. The proposed framework is practically implementable, as it needs no hardware update on generation units. The efficacy of the proposed framework is validated in both four-area system and 140-bus system.

Kyoung-Dae Kim, Sayan Mitra, P. R. Kumar

We define a special class of hybrid automata, called Deterministic and Transversal Linear Hybrid Automata (DTLHA), whose continuous dynamics in each location are linear time-invariant (LTI) with a constant input, and for which every discrete transition up to a given bounded time is deterministic and, importantly, transversal. For such a DTLHA starting from an initial state, we show that it is possible to compute an approximation of the reach set of a DTLHA over a finite time interval that is arbitrarily close to the exact reach set, called a bounded epsilon-reach set, through sampling and polyhedral over-approximation of sampled states. We propose an algorithm and an attendant architecture for the overall bounded epsilon-reach set computation process.

Yu-Heng Hung, Ping-Chun Hsieh, Akshay Mete et al.

We consider the infinite-horizon linear Markov Decision Processes (MDPs), where the transition probabilities of the dynamic model can be linearly parameterized with the help of a predefined low-dimensional feature mapping. While the existing regression-based approaches have been theoretically shown to achieve nearly-optimal regret, they are computationally rather inefficient due to the need for a large number of optimization runs in each time step, especially when the state and action spaces are large. To address this issue, we propose to solve linear MDPs through the lens of Value-Biased Maximum Likelihood Estimation (VBMLE), which is a classic model-based exploration principle in the adaptive control literature for resolving the well-known closed-loop identification problem of Maximum Likelihood Estimation. We formally show that (i) VBMLE enjoys $\widetilde{O}(d\sqrt{T})$ regret, where $T$ is the time horizon and $d$ is the dimension of the model parameter, and (ii) VBMLE is computationally more efficient as it only requires solving one optimization problem in each time step. In our regret analysis, we offer a generic convergence result of MLE in linear MDPs through a novel supermartingale construct and uncover an interesting connection between linear MDPs and online learning, which could be of independent interest. Finally, the simulation results show that VBMLE significantly outperforms the benchmark method in terms of both empirical regret and computation time.

Min Cheng, Ruida Zhou, P. R. Kumar et al.

We study Markov potential games under the infinite horizon average reward criterion. Most previous studies have been for discounted rewards. We prove that both algorithms based on independent policy gradient and independent natural policy gradient converge globally to a Nash equilibrium for the average reward criterion. To set the stage for gradient-based methods, we first establish that the average reward is a smooth function of policies and provide sensitivity bounds for the differential value functions, under certain conditions on ergodicity and the second largest eigenvalue of the underlying Markov decision process (MDP). We prove that three algorithms, policy gradient, proximal-Q, and natural policy gradient (NPG), converge to an $ε$-Nash equilibrium with time complexity $O(\frac{1}{ε^2})$, given a gradient/differential Q function oracle. When policy gradients have to be estimated, we propose an algorithm with $\tilde{O}(\frac{1}{\min_{s,a}π(a|s)δ})$ sample complexity to achieve $δ$ approximation error w.r.t~the $\ell_2$ norm. Equipped with the estimator, we derive the first sample complexity analysis for a policy gradient ascent algorithm, featuring a sample complexity of $\tilde{O}(1/ε^5)$. Simulation studies are presented.

Yu-Heng Hung, Ping-Chun Hsieh, Xi Liu et al.

Modifying the reward-biased maximum likelihood method originally proposed in the adaptive control literature, we propose novel learning algorithms to handle the explore-exploit trade-off in linear bandits problems as well as generalized linear bandits problems. We develop novel index policies that we prove achieve order-optimality, and show that they achieve empirical performance competitive with the state-of-the-art benchmark methods in extensive experiments. The new policies achieve this with low computation time per pull for linear bandits, and thereby resulting in both favorable regret as well as computational efficiency.

Priyanka Mahesh, Akash Tiwari, Chenglu Jin et al.

The Industry 4.0 concept promotes a digital manufacturing (DM) paradigm that can enhance quality and productivity, that reduces inventory and the lead-time for delivering custom, batch-of-one products based on achieving convergence of Additive, Subtractive, and Hybrid manufacturing machines, Automation and Robotic Systems, Sensors, Computing, and Communication Networks, Artificial Intelligence, and Big Data. A DM system consists of embedded electronics, sensors, actuators, control software, and inter-connectivity to enable the machines and the components within them to exchange data with other machines, components therein, the plant operators, the inventory managers, and customers. This paper presents the cybersecurity risks in the emerging DM context, assesses the impact on manufacturing, and identifies approaches to secure DM.

Xi Liu, Ping-Chun Hsieh, Anirban Bhattacharya et al.

Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE -- a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential family, we show that RBMLE yields an index policy. To choose the bias-growth rate $α(t)$ in RBMLE, we reveal the nontrivial interplay between $α(t)$ and the regret bound that generally applies in both the Exponential Family as well as the sub-Gaussian/Exponential family bandits. To quantify the finite-time performance, we prove that RBMLE attains order-optimality by adaptively estimating the unknown constants in the expression of $α(t)$ for Gaussian and sub-Gaussian bandits. Extensive experiments demonstrate that the proposed RBMLE achieves empirical regret performance competitive with the state-of-the-art methods, while being more computationally efficient and scalable in comparison to the best-performing ones among them.

Xi Liu, Ping-Chun Hsieh, P. R. Kumar

Most recent studies on establishing intersection safety focus on the situation where all vehicles are fully autonomous. However, currently most vehicles are human-driven and so we will need to transition through regimes featuring a varying proportion of human-driven vehicles ranging from 100\% to 0\% before realizing such a fully autonomous future -- if ever. We will, therefore, need to address the safety of hybrid systems featuring an arbitrary mixture of human-driven and autonomous vehicles. In fact, recent incidents involving autonomous vehicles have already highlighted the need to study the safety of autonomous vehicles co-existing with human-driven vehicles. Motivated by this we address the design of provably safe intersection management for mixed traffic consisting of a mix of human-driven vehicles (HVs) as well as autonomous vehicles (AVs). To analyze such mixed traffic, we model HVs as nearsighted and with relatively loose constraints, permitting worst-case behavior while AVs are considered as capable of following much tighter constraints. HVs are allowed freedom to change their speed at any time while AVs are only allowed to change their speed beginning of a time slot through a Model Predictive Controller (MPC). AVs are assumed to possess a shorter response time and stronger braking capability than HVs in collision avoidance. Moreover, AVs obtain the permissions of passing through the intersection through vehicle-to-infrastructure (V2I) communication, while HVs achieve the same objective by following traffic lights. Taking the above differences into consideration, we propose a provably safe intersection management for mixed traffic comprised of an MPC-based protocol for AVs along with a coordination protocol for traffic lights...

Mohammadhussein Rafieisakhaei, Suman Chakravorty, P. R. Kumar

We consider nonlinear stochastic systems that arise in path planning and control of mobile robots. As is typical of almost all nonlinear stochastic systems, the optimally solving problem is intractable. We provide a design approach which yields a tractable design that is quantifiably near-optimal. We exhibit a "separation" principle under a small noise assumption consisting of the optimal open-loop design of nominal trajectory followed by an optimal feedback law to track this trajectory, which is different from the usual effort of separating estimation from control. As a corollary, we obtain a trajectory-optimized linear quadratic regulator design for stochastic nonlinear systems with Gaussian noise.

Mohammadhussein Rafieisakhaei, Suman Chakravorty, P. R. Kumar

Planning under motion and observation uncertainties requires solution of a stochastic control problem in the space of feedback policies. In this paper, we reduce the general (n^2+n)-dimensional belief space planning problem to an (n)-dimensional problem by obtaining a Linear Quadratic Gaussian (LQG) design with the best nominal performance. Then, by taking the underlying trajectory of the LQG controller as the decision variable, we pose a coupled design of trajectory, estimator, and controller design through a Non-Linear Program (NLP) that can be solved by a general NLP solver. We prove that under a first-order approximation and a careful usage of the separation principle, our approximations are valid. We give an analysis on the existing major belief space planning methods and show that our algorithm has the lowest computational burden. Finally, we extend our solution to contain general state and control constraints. Our simulation results support our design.

Mohammadhussein Rafieisakhaei, Amirhossein Tamjidi, Suman Chakravorty et al.

Planning under process and measurement uncertainties is a challenging problem. In its most general form it can be modeled as a Partially Observed Markov Decision Process (POMDP) problem. However POMDPs are generally difficult to solve when the underlying spaces are continuous, particularly when beliefs are non-Gaussian, and the difficulty is further exacerbated when there are also non-convex constraints on states. Existing algorithms to address such challenging POMDPs are expensive in terms of computation and memory. In this paper, we provide a feedback policy in non-Gaussian belief space via solving a convex program for common non-linear observation models. The solution involves a Receding Horizon Control strategy using particle filters for the non-Gaussian belief representation. We develop a way of capturing non-convex constraints in the state space and adapt the optimization to incorporate such constraints, as well. A key advantage of this method is that it does not introduce additional variables in the optimization problem and is therefore more scalable than existing constrained problems in belief space. We demonstrate the performance of the method on different scenarios.