arXiv subjects

Karl H. Johansson

Publications and source records attributed to Karl H. Johansson.

At least 127 records · Page 7Linked to original sources

arXiv2024

Small-Scale Testbed for Evaluating C-V2X Applications on 5G Cellular Networks

In this work, we present a small-scale testbed for evaluating the real-life performance of cellular V2X (C-V2X) applications on 5G cellular networks. Despite the growing interest and rapid technology development for V2X applications, researchers still struggle to prototype V2X applications with real wireless networks, hardware, and software in the loop in a controlled environment. To help alleviate this challenge, we present a testbed designed to accelerate development and evaluation of C-V2X applications on 5G cellular networks. By including a small-scale vehicle platform into the testbed design, we significantly reduce the time and effort required to test new C-V2X applications on 5G cellular networks. With a focus around the integration of small-scale vehicle platforms, we detail the design decisions behind the full software and hardware setup of commonly needed intelligent transport system agents (e.g. sensors, servers, vehicles). Moreover, to showcase the testbed's capability to produce industrially-relevant, real world performance evaluations, we present an evaluation of a simple test case inspired from shared situational awareness. Finally, we discuss the upcoming use of the testbed for evaluating 5G cellular network-based shared situational awareness and other C-V2X applications.

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arXiv2024

Guaranteed Completion of Complex Tasks via Temporal Logic Trees and Hamilton-Jacobi Reachability

In this paper, we present an approach for guaranteeing the completion of complex tasks with cyber-physical systems (CPS). Specifically, we leverage temporal logic trees constructed using Hamilton-Jacobi reachability analysis to (1) check for the existence of control policies that complete a specified task and (2) develop a computationally-efficient approach to synthesize the full set of control inputs the CPS can implement in real-time to ensure the task is completed. We show that, by checking the approximation directions of each state set in the temporal logic tree, we can check if the temporal logic tree suffers from the "leaking corner issue," where the intersection of reachable sets yields an incorrect approximation. By ensuring a temporal logic tree has no leaking corners, we know the temporal logic tree correctly verifies the existence of control policies that satisfy the specified task. After confirming the existence of control policies, we show that we can leverage the value functions obtained through Hamilton-Jacobi reachability analysis to efficiently compute the set of control inputs the CPS can implement throughout the deployment time horizon to guarantee the completion of the specified task. Finally, we use a newly released Python toolbox to evaluate the presented approach on a simulated driving task.

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arXiv2024

Achieving violation-free distributed optimization under coupling constraints

Constraint satisfaction is a critical component in a wide range of engineering applications, including but not limited to safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed optimization techniques for problems characterized by separable objective functions and coupling constraints. First, we incorporate auxiliary decision variables together with a network-dependent linear mapping to each coupling constraint. For the reformulated problem, we show that the projection of its feasible set onto the space of primal variables is identical to that of the original problem, which is the key to achieving all-time constraint satisfaction. Upon treating the reformulated problem as a min-min optimization problem with respect to auxiliary and primal variables, we demonstrate that the gradients in the outer minimization problem have a locally computable closed-form. Then, two violation-free distributed optimization algorithms are developed and their convergence under reasonable assumptions is analyzed. Finally, the proposed algorithm is applied to implement a control barrier function based controller in a distributed manner, and the results verify its effectiveness.

math.OC↗

arXiv2024

Formal Verification of Linear Temporal Logic Specifications Using Hybrid Zonotope-Based Reachability Analysis

In this paper, we introduce a hybrid zonotope-based approach for formally verifying the behavior of autonomous systems operating under Linear Temporal Logic (LTL) specifications. In particular, we formally verify the LTL formula by constructing temporal logic trees (TLT)s via backward reachability analysis (BRA). In previous works, TLTs are predominantly constructed with either highly general and computationally intensive level set-based BRA or simplistic and computationally efficient polytope-based BRA. In this work, we instead propose the construction of TLTs using hybrid zonotope-based BRA. By using hybrid zonotopes, we show that we are able to formally verify LTL specifications in a computationally efficient manner while still being able to represent complex geometries that are often present when deploying autonomous systems, such as non-convex, disjoint sets. Moreover, we evaluate our approach on a parking example, providing preliminary indications of how hybrid zonotopes facilitate computationally efficient formal verification of LTL specifications in environments that naturally lead to non-convex, disjoint geometries.

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arXiv2024

Risk-averse Learning with Non-Stationary Distributions

Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative impact of change to avoid potentially risky situations. In this paper, we investigate risk-averse online optimization where the distribution of the random cost changes over time. We minimize risk-averse objective function using the Conditional Value at Risk (CVaR) as risk measure. Due to the difficulty in obtaining the exact CVaR gradient, we employ a zeroth-order optimization approach that queries the cost function values multiple times at each iteration and estimates the CVaR gradient using the sampled values. To facilitate the regret analysis, we use a variation metric based on Wasserstein distance to capture time-varying distributions. Given that the distribution variation is sub-linear in the total number of episodes, we show that our designed learning algorithm achieves sub-linear dynamic regret with high probability for both convex and strongly convex functions. Moreover, theoretical results suggest that increasing the number of samples leads to a reduction in the dynamic regret bounds until the sampling number reaches a specific limit. Finally, we provide numerical experiments of dynamic pricing in a parking lot to illustrate the efficacy of the designed algorithm.

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arXiv2024

Non-convex potential games for finding global solutions to sensor network localization

Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results.

math.OC↗

arXiv2024

Policy Evaluation in Distributional LQR (Extended Version)

Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard reinforcement learning. Meanwhile, a challenge in DRL is that the policy evaluation typically relies on the representation of the return distribution, which needs to be carefully designed. In this paper, we address this challenge for the special class of DRL problems that rely on a discounted linear quadratic regulator (LQR), which we call \emph{distributional LQR}. Specifically, we provide a closed-form expression for the distribution of the random return, which is applicable for all types of exogenous disturbance as long as it is independent and identically distributed (i.i.d.). We show that the variance of the random return is bounded if the fourth moment of the exogenous disturbance is bounded. Furthermore, we investigate the sensitivity of the return distribution to model perturbations. While the proposed exact return distribution consists of infinitely many random variables, we show that this distribution can be well approximated by a finite number of random variables. The associated approximation error can be analytically bounded under mild assumptions. When the model is unknown, we propose a model-free approach for estimating the return distribution, supported by sample complexity guarantees. Finally, we extend our approach to partially observable linear systems. Numerical experiments are provided to illustrate the theoretical results.

math.OC↗

arXiv2024

Relation between Value and Age of Information in Feedback Control

In this chapter, we investigate the value of information as a more comprehensive instrument than the age of information for optimally shaping the information flow in a networked control system. In particular, we quantify the value of information based on the variation in a value function, and discuss the structural properties of this metric. Through our analysis, we establish the mathematical relation between the value of information and the age of information. We prove that the value of information is in general a function of an estimation discrepancy that depends on the age of information and the primitive variables. In addition, we prove that there exists a condition under which the value of information becomes completely expressible in terms of the age of information. Nonetheless, we show that this condition is not achievable without a degradation in the performance of the system.

cs.IT↗

arXiv2024

Foundations of Value of Information: A Semantic Metric for Networked Control Systems Tasks

In this chapter, we present our recent invention, i.e., the notion of the value of information$\unicode{x2014}$a semantic metric that is fundamental for networked control systems tasks. We begin our analysis by formulating a causal tradeoff between the packet rate and the regulation cost, with an encoder and a decoder as two distributed decision makers, and show that the valuation of information is conceivable and quantifiable grounded on this tradeoff. More precisely, we characterize an equilibrium, and quantify the value of information there as the variation in a value function with respect to a piece of sensory measurement that can be communicated from the encoder to the decoder at each time. We prove that, in feedback control of a dynamical process over a noiseless channel, the value of information is a function of the discrepancy between the state estimates at the encoder and the decoder, and that a data packet containing a sensory measurement at each time should be exchanged only if the value of information at that time is nonnegative. Finally, we prove that the characterized equilibrium is in fact globally optimal.

cs.IT↗

arXiv2024

Consistency of Value of Information: Effects of Packet Loss and Time Delay in Networked Control Systems Tasks

In this chapter, we study the consistency of the value of information$\unicode{x2014}$a semantic metric that claims to determine the right piece of information in networked control systems tasks$\unicode{x2014}$in a lossy and delayed communication regime. Our analysis begins with a focus on state estimation, and subsequently extends to feedback control. To that end, we make a causal tradeoff between the packet rate and the mean square error. Associated with this tradeoff, we demonstrate the existence of an optimal policy profile, comprising a symmetric threshold scheduling policy based on the value of information for the encoder and a non-Gaussian linear estimation policy for the decoder. Our structural results assert that the scheduling policy is expressible in terms of $3d-1$ variables related to the source and the channel, where $d$ is the time delay, and that the estimation policy incorporates no residual related to signaling. We then construct an optimal control policy by exploiting the separation principle.

cs.IT↗

arXiv2024

Learning of Nash Equilibria in Risk-Averse Games

This paper considers risk-averse learning in convex games involving multiple agents that aim to minimize their individual risk of incurring significantly high costs. Specifically, the agents adopt the conditional value at risk (CVaR) as a risk measure with possibly different risk levels. To solve this problem, we propose a first-order risk-averse leaning algorithm, in which the CVaR gradient estimate depends on an estimate of the Value at Risk (VaR) value combined with the gradient of the stochastic cost function. Although estimation of the CVaR gradients using finitely many samples is generally biased, we show that the accumulated error of the CVaR gradient estimates is bounded with high probability. Moreover, assuming that the risk-averse game is strongly monotone, we show that the proposed algorithm converges to the risk-averse Nash equilibrium. We present numerical experiments on a Cournot game example to illustrate the performance of the proposed method.

math.OC↗

arXiv2024

Rollout-Based Charging Strategy for Electric Trucks with Hours-of-Service Regulations (Extended Version)

Freight drivers of electric trucks need to design charging strategies for where and how long to recharge the truck in order to complete delivery missions on time. Moreover, the charging strategies should be aligned with drivers' driving and rest time regulations, known as hours-of-service (HoS) regulations. This letter studies the optimal charging problems of electric trucks with delivery deadlines under HoS constraints. We assume that a collection of charging and rest stations is given along a pre-planned route with known detours and that the problem data are deterministic. The goal is to minimize the total cost associated with the charging and rest decisions during the entire trip. This problem is formulated as a mixed integer program with bilinear constraints, resulting in a high computational load when applying exact solution approaches. To obtain real-time solutions, we develop a rollout-based approximate scheme, which scales linearly with the number of stations while offering solid performance guarantees. We perform simulation studies over the Swedish road network based on realistic truck data. The results show that our rollout-based approach provides near-optimal solutions to the problem in various conditions while cutting the computational time drastically.

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arXiv2024

Survey of Distributed Algorithms for Resource Allocation over Multi-Agent Systems

Resource allocation and scheduling in multi-agent systems present challenges due to complex interactions and decentralization. This survey paper provides a comprehensive analysis of distributed algorithms for addressing the distributed resource allocation (DRA) problem over multi-agent systems. It covers a significant area of research at the intersection of optimization, multi-agent systems, and distributed consensus-based computing. The paper begins by presenting a mathematical formulation of the DRA problem, establishing a solid foundation for further exploration. Real-world applications of DRA in various domains are examined to underscore the importance of efficient resource allocation, and relevant distributed optimization formulations are presented. The survey then delves into existing solutions for DRA, encompassing linear, nonlinear, primal-based, and dual-formulation-based approaches. Furthermore, this paper evaluates the features and properties of DRA algorithms, addressing key aspects such as feasibility, convergence rate, and network reliability. The analysis of mathematical foundations, diverse applications, existing solutions, and algorithmic properties contributes to a broader comprehension of the challenges and potential solutions for this domain.

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arXiv2024

Gain and Phase: Decentralized Stability Conditions for Power Electronics-Dominated Power Systems

This paper proposes decentralized stability conditions for multi-converter systems based on the combination of the small gain theorem and the small phase theorem. Instead of directly computing the closed-loop dynamics, e.g., eigenvalues of the state-space matrix, or using the generalized Nyquist stability criterion, the proposed stability conditions are more scalable and computationally lighter, which aim at evaluating the closed-loop system stability by comparing the individual converter dynamics with the network dynamics in a decentralized and open-loop manner. Moreover, our approach can handle heterogeneous converters' dynamics and is suitable to analyze large-scale multi-converter power systems that contain grid-following (GFL), grid-forming (GFM) converters, and synchronous generators. Compared with other decentralized stability conditions, e.g., passivity-based stability conditions, the proposed conditions are significantly less conservative and can be generally satisfied in practice across the whole frequency range.

eess.SY↗

arXiv2024

Global solution to sensor network localization: A non-convex potential game approach and its distributed implementation

Consider a sensor network consisting of both anchor and non-anchor nodes. We address the following sensor network localization (SNL) problem: given the physical locations of anchor nodes and relative measurements among all nodes, determine the locations of all non-anchor nodes. The solution to the SNL problem is challenging due to its inherent non-convexity. In this paper, the problem takes on the form of a multi-player non-convex potential game in which canonical duality theory is used to define a complementary dual potential function. After showing the Nash equilibrium (NE) correspondent to the SNL solution, we provide a necessary and sufficient condition for a stationary point to coincide with the NE. An algorithm is proposed to reach the NE and shown to have convergence rate $\mathcal{O}(1/\sqrt{k})$. With the aim of reducing the information exchange within a network, a distributed algorithm for NE seeking is implemented and its global convergence analysis is provided. Extensive simulations show the validity and effectiveness of the proposed approach to solve the SNL problem.

math.OC↗

arXiv2023

Efficient and Reconfigurable Optimal Planning in Large-Scale Systems Using Hierarchical Finite State Machines

In this paper, we consider a planning problem for a large-scale system modelled as a hierarchical finite state machine (HFSM) and develop a control algorithm for computing optimal plans between any two states. The control algorithm consists of two steps: a preprocessing step computing optimal exit costs for each machine in the HFSM, with time complexity scaling linearly with the number of machines, and a query step that rapidly computes optimal plans, truncating irrelevant parts of the HFSM using the optimal exit costs, with time complexity scaling near-linearly with the depth of the HFSM. The control algorithm is reconfigurable in the sense that a change in the HFSM is efficiently handled, updating only needed parts in the preprocessing step to account for the change, with time complexity linear in the depth of the HFSM. We validate our algorithm on a robotic application, comparing it with Dijkstra's algorithm and Contraction Hierarchies. Our algorithm outperforms both.

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arXiv2023

Distributed Optimization with Quantized Gradient Descent

In this paper, we consider the unconstrained distributed optimization problem, in which the exchange of information in the network is captured by a directed graph topology, thus, nodes can only communicate with their neighbors. Additionally, in our problem, the communication channels among the nodes have limited bandwidth. In order to alleviate this limitation, quantized messages should be exchanged among the nodes. For solving this distributed optimization problem, we combine a gradient descent method with a distributed quantized consensus algorithm (which requires the nodes to exchange quantized messages and converges in a finite number of steps). Specifically, at every optimization step, each node (i) performs a gradient descent step (i.e., subtracts the scaled gradient from its current estimate), and (ii) performs a finite-time calculation of the quantized average of every node's estimate in the network. As a consequence, this algorithm approximately mimics the centralized gradient descent algorithm. We show that our algorithm asymptotically converges to a neighborhood of the optimal solution with linear convergence rate. The performance of the proposed algorithm is demonstrated via simple illustrative examples.

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arXiv2023

Transient Behavior of Gossip Opinion Dynamics with Community Structure

We study transient behavior of gossip opinion dynamics, in which agents randomly interact pairwise over a weighted graph with two communities. Edges within a community have identical weights different from edge weights between communities. We first derive an upper bound for the second moment of agent opinions. Using this bound, we obtain upper bounds for probability that a large proportion of agents have opinions close to average ones. The results imply a phase transition of transient behavior of the process: When edge weights within communities are larger than those between communities and those between regular and stubborn agents, most agents in the same community hold opinions close to the average opinion of that community with large probability, at an early stage of the process. However, if the difference between intra- and inter-community weights is small, most of the agents instead hold opinions close to everyone's average opinion at the early stage. In contrast, when the influence of stubborn agents is large, agent opinions settle quickly to steady state. We then conduct numerical experiments to validate the theoretical results. Different from traditional asymptotic analysis in most opinion dynamics literature, the paper characterizes the influences of stubborn agents and community structure on the initial phase of the opinion evolution.

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