Searcharxiv⌕ Search

arXiv subjects

John Lygeros

Publications and source records attributed to John Lygeros.

At least 109 records · Page 6Linked to original sources
arXiv2023

CARMA: Fair and efficient bottleneck congestion management via non-tradable karma credits

This paper proposes a non-monetary traffic demand management scheme, named CARMA, as a fair solution to the morning commute congestion. We consider heterogeneous commuters traveling through a single bottleneck that differ in both the desired arrival time and Value of Time (VOT). We consider a generalized notion of VOT by allowing it to vary dynamically on each day (e.g., according to trip purpose and urgency), rather than being a static characteristic of each individual. In our CARMA scheme, the bottleneck is divided into a fast lane that is kept in free flow and a slow lane that is subject to congestion. We introduce a non-tradable mobility credit, named karma, that is used by commuters to bid for access to the fast lane. Commuters who get outbid or do not participate in the CARMA scheme instead use the slow lane. At the end of each day, karma collected from the bidders is redistributed, and the process repeats day by day. We model the collective commuter behaviors under CARMA as a Dynamic Population Game (DPG), in which a Stationary Nash Equilibrium (SNE) is guaranteed to exist. Unlike existing monetary schemes, CARMA is demonstrated, both analytically and numerically, to achieve a) an equitable traffic assignment with respect to heterogeneous income classes and b) a strong Pareto improvement in the long-term average travel disutility with respect to no policy intervention. With extensive numerical analysis, we show that CARMA is able to retain the same congestion reduction as an optimal monetary tolling scheme under uniform karma redistribution and even outperform tolling under a well-designed redistribution scheme. We also highlight the privacy-preserving feature of CARMA, i.e., its ability to tailor to the private preferences of commuters without centrally collecting the information.

eess.SY↗
arXiv2023

Routing and charging game in ride-hailing service with electric vehicles

This paper studies the routing and charging behaviors of electric vehicles in a competitive ride-hailing market. When the vehicles are idle, they can choose whether to continue cruising to search for passengers, or move a charging station to recharge. The behaviors of individual vehicles are then modeled by a Markov decision process (MDP). The state transitions in the MDP model, however, depend on the aggregate vehicle flows both in service zones and at charging stations. Accordingly, the value function of each vehicle is determined by the collective behaviors of all vehicles. With the assumption of the large population, we formulate the collective routing and charging behaviors as a mean-field Markov game. We characterize the equilibrium of such a game, prove its existence, and numerically show that the competition among vehicles leads to ``inefficient congestion" both in service zones and at charging stations.

eess.SY↗
arXiv2023

Stochastic MPC for energy hubs using data driven demand forecasting

Energy hubs convert and distribute energy resources by combining different energy inputs through multiple conversion and storage components. The optimal operation of the energy hub exploits its flexibility to increase the energy efficiency and reduce the operational costs. However, uncertainties in the demand present challenges to energy hub optimization. In this paper, we propose a stochastic MPC controller to minimize energy costs using chance constraints for the uncertain electricity and thermal demands. Historical data is used to build a demand prediction model based on Gaussian processes to generate a forecast of the future electricity and heat demands. The stochastic optimization problem is solved via the Scenario Approach by sampling multi-step demand trajectories from the derived prediction model. The performance of the proposed predictor and of the stochastic controller is verified on a simulated energy hub model and demand data from a real building.

eess.SY↗
arXiv2023

Sequential Quadratic Programming-based Iterative Learning Control for Nonlinear Systems

Learning-based control methods for industrial processes leverage the repetitive nature of the underlying process to learn optimal inputs for the system. While many works focus on linear systems, real-world problems involve nonlinear dynamics. In this work, we propose an algorithm for the nonlinear iterative learning control problem based on sequential quadratic programming, a well-studied method for nonconvex optimization. We repeatedly solve quadratic subproblems built using approximate nonlinear models and process measurements, to find an optimal input for the original system. We demonstrate our method in a trajectory optimization problem for a precision motion system. We present simulations to illustrate the performance of the proposed method for linear and nonlinear dynamics models.

eess.SY↗
arXiv2023

Degradation-aware data-enabled predictive control of energy hubs

Mitigating the energy use in buildings, together with satisfaction of comfort requirements are the main objectives of efficient building control systems. Augmenting building energy systems with batteries can improve the energy use of a building, while posing the challenge of considering battery degradation during control operation. We demonstrate the performance of a data-enabled predictive control (DeePC) approach applied to a single multi-zone building and an energy hub comprising an electric heat pump and a battery. In a comparison with a standard rule-based controller, results demonstrate that the performance of DeePC is superior in terms of satisfaction of comfort constraints without increasing grid power consumption. Moreover, DeePC achieved two-fold decrease in battery degradation over one year, as compared to a rule-based controller.

eess.SY↗
arXiv2023

On the Guarantees of Minimizing Regret in Receding Horizon

Towards bridging classical optimal control and online learning, regret minimization has recently been proposed as a control design criterion. This competitive paradigm penalizes the loss relative to the optimal control actions chosen by a clairvoyant policy, and allows tracking the optimal performance in hindsight no matter how disturbances are generated. In this paper, we propose the first receding horizon scheme based on the repeated computation of finite horizon regret-optimal policies, and we establish stability and safety guarantees for the resulting closed-loop system. Our derivations combine novel monotonicity properties of clairvoyant policies with suitable terminal ingredients. We prove that our scheme is recursively feasible, stabilizing, and that it achieves bounded regret relative to the infinite horizon clairvoyant policy. Last, we show that the policy optimization problem can be solved efficiently through convex-concave programming. Our numerical experiments show that minimizing regret can outperform standard receding horizon approaches when the disturbances poorly fit classical design assumptions - even when the finite horizon planning is recomputed less frequently.

eess.SY↗
arXiv2023

Stress Flow Guided Non-Planar Print Trajectory Optimization for Additive Manufacturing of Anisotropic Polymers

When manufacturing parts using material extrusion additive manufacturing and anisotropic polymers, the mechanical properties of a manufactured component are strongly dependent on the print trajectory orientation. We conduct non-planar slicing and optimize the print trajectories to maximize the alignment between the material deposition direction and the stress flow induced by a predefined load case. The trajectory optimization framework considers manufacturability constraints in the form of uniform layer height and line spacing. We demonstrate the method by manufacturing a load bearing mechanical bracket using a 5-axis 3D printer and a liquid crystal polymer material. The failure strength and stiffness of the optimized bracket are improved by a factor of 44 and 6 respectively when compared with conventional printing.

math.OC↗
arXiv2023

Efficient sample selection for safe learning

Ensuring safety in industrial control systems usually involves imposing constraints at the design stage of the control algorithm. Enforcing constraints is challenging if the underlying functional form is unknown. The challenge can be addressed by using surrogate models, such as Gaussian processes, which provide confidence intervals used to find solutions that can be considered safe. This in turn involves an exhaustive search on the entire search space. That approach can quickly become computationally expensive. We reformulate the exhaustive search as a series of optimization problems to find the next recommended points. We show that the proposed reformulation allows using a wide range of available optimization solvers, such as derivative-free methods. We show that by exploiting the properties of the solver, we enable the introduction of new stopping criteria into safe learning methods and increase flexibility in trading off solver accuracy and computational time. The results from a non-convex optimization problem and an application for controller tuning confirm the flexibility and the performance of the proposed reformulation.

math.OC↗
arXiv2023

Performance Bounds of Model Predictive Control for Unconstrained and Constrained Linear Quadratic Problems and Beyond

We study unconstrained and constrained linear quadratic problems and investigate the suboptimality of the model predictive control (MPC) method applied to such problems. Considering MPC as an approximate scheme for solving the related fixed point equations, we derive performance bounds for the closed-loop system under MPC. Our analysis, as well as numerical examples, suggests new ways of choosing the terminal cost and terminal constraints, which are \emph{not} related to the solution of the Riccati equation of the original problem. The resulting method can have a larger feasible region, and cause hardly any loss of performance in terms of the closed-loop cost over an infinite horizon.

math.OC↗
arXiv2023

Distributed Multi-Horizon Model Predictive Control for Network of Energy Hubs

The increasing penetration of renewable energy resources has transformed the energy system from traditional hierarchical energy delivery paradigm to a distributed structure. Such development is accompanied with continuous liberalization in the energy sector, giving rise to possible energy trading among networked local energy hub. Joint operation of such hubs can improve energy efficiency and support the integration of renewable energy resource. Acknowledging peer-to-peer trading between hubs, their optimal operation within the network can maximize consumption of locally produced energy. However, for such complex systems involving multiple stakeholders, both computational tractability and privacy concerns need to be accounted for. We investigate both decentralized and centralized model predictive control (MPC) approaches for a network of energy hubs. While the centralized control strategy offers superior performance to the decentralized method, its implementation is computationally prohibitive and raises privacy concerns, as the information of each hub has to be shared extensively. On the other hand, a classical decentralized control approach can ease the implementation at the expense of sub-optimal performance of the overall system. In this work, a distributed scheme based on a consensus alternating direction method of multipliers (ADMM) algorithm is proposed. It combines the performance of the centralized approach with the privacy preservation of decentralized approach. A novel multi-horizon MPC framework is also introduced to increase the prediction horizon without compromising the time discretization or making the problem computationally intractable. A benchmark three-hub network is used to compare the performance of the mentioned methods. The results show superior performance in terms of total cost, computational time, robustness to demand and prices variations.

eess.SY↗
arXiv2023

Designing Optimal Personalized Incentive for Traffic Routing using BIG Hype algorithm

We study the problem of optimally routing plug-in electric and conventional fuel vehicles on a city level. In our model, commuters selfishly aim to minimize a local cost that combines travel time, from a fixed origin to a desired destination, and the monetary cost of using city facilities, parking or service stations. The traffic authority can influence the commuters' preferred routing choice by means of personalized discounts on parking tickets and on the energy price at service stations. We formalize the problem of designing these monetary incentives optimally as a large-scale bilevel game, where constraints arise at both levels due to the finite capacities of city facilities and incentives budget. Then, we develop an efficient decentralized solution scheme with convergence guarantees based on BIG Hype, a recently-proposed hypergradient-based algorithm for hierarchical games. Finally, we validate our model via numerical simulations over the Anaheim's network, and show that the proposed approach produces sensible results in terms of traffic decongestion and it is able to solve in minutes problems with more than 48000 variables and 110000 constraints.

math.OC↗
arXiv2023

Wasserstein Tube MPC with Exact Uncertainty Propagation

We study model predictive control (MPC) problems for stochastic LTI systems, where the noise distribution is unknown, compactly supported, and only observable through a limited number of i.i.d. noise samples. Building upon recent results in the literature, which show that distributional uncertainty can be efficiently captured within a Wasserstein ambiguity set, and that such ambiguity sets propagate exactly through the system dynamics, we start by formulating a novel Wasserstein Tube MPC (WT-MPC) problem, with distributionally robust CVaR constraints. We then show that the WT-MPC problem: (1) is a direct generalization of the (deterministic) Robust Tube MPC (RT-MPC) to the stochastic setting; (2) through a scalar parameter, it interpolates between the data-driven formulation based on sample average approximation and the RT-MPC formulation, allowing us to optimally trade between safety and performance; (3) admits a tractable convex reformulation; and (4) is recursively feasible. We conclude the paper with a numerical comparison of WT-MPC and RT-MPC.

math.OC↗
arXiv2023

Implications of Regret on Stability of Linear Dynamical Systems

The setting of an agent making decisions under uncertainty and under dynamic constraints is common for the fields of optimal control, reinforcement learning, and recently also for online learning. In the online learning setting, the quality of an agent's decision is often quantified by the concept of regret, comparing the performance of the chosen decisions to the best possible ones in hindsight. While regret is a useful performance measure, when dynamical systems are concerned, it is important to also assess the stability of the closed-loop system for a chosen policy. In this work, we show that for linear state feedback policies and linear systems subject to adversarial disturbances, linear regret implies asymptotic stability in both time-varying and time-invariant settings. Conversely, we also show that bounded input bounded state stability and summability of the state transition matrices imply linear regret.

eess.SY↗
arXiv2023

Generalized uncertain Nash games: Reformulation and robust equilibrium seeking -- Extended version

We consider generalized Nash equilibrium problems (GNEPs) with linear coupling constraints affected by both local (i.e., agent-wise) and global (i.e., shared resources) disturbances taking values in polyhedral uncertainty sets. By making use of traditional tools borrowed from robust optimization, for this class of problems we derive a tractable, finite-dimensional reformulation leading to a deterministic ''extended game'', and we show that this latter still amounts to a GNEP featuring generalized Nash equilibria ''in the worst-case''. We then design a fully-distributed, accelerated algorithm based on monotone operator theory, which enjoys convergence towards a Nash equilibrium of the original, uncertain game under weak structural assumptions. Finally, we illustrate the effectiveness of the proposed distributed scheme through numerical simulations

eess.SY↗
arXiv2023

Stability and Robustness of Distributed Suboptimal Model Predictive Control

In distributed model predictive control (MPC), the control input at each sampling time is computed by solving a large-scale optimal control problem (OCP) over a finite horizon using distributed algorithms. Typically, such algorithms require several (virtually, infinite) communication rounds between the subsystems to converge, which is a major drawback both computationally and from an energetic perspective (for wireless systems). Motivated by these challenges, we propose a suboptimal distributed MPC scheme in which the total communication burden is distributed also in time, by maintaining a running solution estimate for the large-scale OCP and updating it at each sampling time. We demonstrate that, under some regularity conditions, the resulting suboptimal MPC control law recovers the qualitative robust stability properties of optimal MPC, if the communication budget at each sampling time is large enough.

eess.SY↗
arXiv2023

Designing Fairness in Autonomous Peer-to-peer Energy Trading

Several autonomous energy management and peer-to-peer trading mechanisms for future energy markets have been recently proposed based on optimization and game theory. In this paper, we study the impact of trading prices on the outcome of these market designs for energy-hub networks. We prove that, for a generic choice of trading prices, autonomous peer-to-peer trading is always network-wide beneficial but not necessarily individually beneficial for each hub. Therefore, we leverage hierarchical game theory to formalize the problem of designing locally-beneficial and network-wide fair peer-to-peer trading prices. Then, we propose a scalable and privacy-preserving price-mediation algorithm that provably converges to a profile of such prices. Numerical simulations on a 3-hub network show that the proposed algorithm can indeed incentivize active participation of energy hubs in autonomous peer-to-peer trading schemes.

eess.SY↗
arXiv2022

Optimal service station design for traffic mitigation via genetic algorithm and neural network

This paper analyzes how the presence of service stations on highways affects traffic congestion. We focus on the problem of optimally designing a service station to achieve beneficial effects in terms of total traffic congestion and peak traffic reduction. Microsimulators cannot be used for this task due to their computational inefficiency. We propose a genetic algorithm based on the recently proposed CTMs, that efficiently describes the dynamics of a service station. Then, we leverage the algorithm to train a neural network capable of solving the same problem, avoiding implementing the CTMs. Finally, we examine two case studies to validate the capabilities and performance of our algorithms. In these simulations, we use real data extracted from Dutch highways.

eess.SY↗