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Christos G. Cassandras

Publications and source records attributed to Christos G. Cassandras.

At least 73 records · Page 4Linked to original sources

Uncertainty-Aware Policy Optimization: A Robust, Adaptive Trust Region Approach

In order for reinforcement learning techniques to be useful in real-world decision making processes, they must be able to produce robust performance from limited data. Deep policy optimization methods have achieved impressive results on complex tasks, but their real-world adoption remains limited because they often require significant amounts of data to succeed. When combined with small sample sizes, these methods can result in unstable learning due to their reliance on high-dimensional sample-based estimates. In this work, we develop techniques to control the uncertainty introduced by these estimates. We leverage these techniques to propose a deep policy optimization approach designed to produce stable performance even when data is scarce. The resulting algorithm, Uncertainty-Aware Trust Region Policy Optimization, generates robust policy updates that adapt to the level of uncertainty present throughout the learning process.

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Asymptotic Analysis for Greedy Initialization of Threshold-Based Distributed Optimization of Persistent Monitoring on Graphs

This paper considers the optimal multi-agent persistent monitoring problem defined for a team of agents on a set of nodes (targets) interconnected according to a fixed network topology. The aim is to control this team so as to minimize a measure of overall node state uncertainty evaluated over a finite time interval. A class of distributed threshold-based parametric controllers has been proposed in prior work to control agent dwell times at nodes and next-node destinations by enforcing thresholds on the respective node states. Under such a Threshold Control Policy (TCP), an on-line gradient technique was used to determine optimal threshold values. However, due to the non-convexity of the problem, this approach often leads to a poor local optima highly dependent on the initial thresholds used. To overcome this initialization challenge, we develop a computationally efficient off-line greedy technique based on the asymptotic analysis of the network system. This analysis is then used to generate a high-performing set of initial thresholds. Extensive numerical results show that such initial thresholds are almost immediately (locally) optimal or quickly lead to optimal values. In all cases, they perform significantly better than the locally optimal solutions known to date.

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Sufficient Conditions for Feasibility of Optimal Control Problems Using Control Barrier Functions

It has been shown that satisfying state and control constraints while optimizing quadratic costs subject to desired (sets of) state convergence for affine control systems can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in this approach is ensuring the feasibility of these QPs, especially under tight control bounds and safety constraints of high relative degree. In this paper, we provide sufficient conditions for guranteed feasibility. The sufficient conditions are captured by a single constraint that is enforced by a CBF, which is added to the QPs such that their feasibility is always guaranteed. The additional constraint is designed to be always compatible with the existing constraints, therefore, it cannot make a feasible set of constraints infeasible - it can only increase the overall feasibility. We illustrate the effectiveness of the proposed approach on an adaptive cruise control problem.

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Comparison of Cooperative Driving Strategies for CAVs at Signal-Free Intersections

The properties of cooperative driving strategies for planning and controlling Connected and Automated Vehicles (CAVs) at intersections range from some that achieve highly efficient coordination performance to others whose implementation is computationally fast. This paper comprehensively compares the performance of four representative strategies in terms of travel time, energy consumption, computation time, and fairness under different conditions, including the geometric configuration of intersections, asymmetry in traffic arrival rates, and the relative magnitude of these rates. Our simulation-based study has led to the following conclusions: 1) the Monte Carlo Tree Search (MCTS)-based strategy achieves the best traffic efficiency, whereas the Dynamic Resequencing (DR)-based strategy is energy-optimal; both strategies perform well in all metrics of interest. If the computation budget is adequate, the MCTS strategy is recommended; otherwise, the DR strategy is preferable; 2) An asymmetric intersection has a noticeable impact on the strategies, whereas the influence of the arrival rates can be neglected. When the geometric shape is asymmetrical, the modified First-In-First-Out (FIFO) strategy significantly outperforms the FIFO strategy and works well when the traffic demand is moderate, but their performances are similar in other situations; and 3) Improving traffic efficiency sometimes comes at the cost of fairness, but the DR and MCTS strategies can be adjusted to realize a better trade-off between various performance metrics by appropriately designing their objective functions.

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A General Framework for Decentralized Safe Optimal Control of Connected and Automated Vehicles in Multi-Lane Intersections

We address the problem of optimally controlling Connected and Automated Vehicles (CAVs) arriving from four multi-lane roads at an intersection where they conflict in terms of safely crossing (including turns) with no collision. The objective is to jointly minimize the travel time and energy consumption of each CAV while ensuring safety. This problem was solved in prior work for single-lane roads. A direct extension to multiple lanes on each road is limited by the computational complexity required to obtain an explicit optimal control solution. Instead, we propose a general framework that first converts a multi-lane intersection problem into a decentralized optimal control problem for each CAV with less conservative safety constraints than prior work. We then employ a method combining optimal control and control barrier functions, which has been shown to efficiently track tractable unconstrained optimal CAV trajectories while also guaranteeing the satisfaction of all constraints. Simulation examples are included to show the effectiveness of the proposed framework under symmetric and asymmetric intersection geometries and different schemes for CAV sequencing.

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Event-Driven Receding Horizon Control For Distributed Persistent Monitoring in Network Systems

We address the multi-agent persistent monitoring problem defined on a set of nodes (targets) interconnected over a network topology. A measure of mean overall node state uncertainty evaluated over a finite period is to be minimized by controlling the motion of a cooperating team of agents. To address this problem, we propose an event-driven receding horizon control approach that is computationally efficient, distributed and on-line. The proposed controller differs from the existing on-line gradient-based parametric controllers and off-line greedy cycle search methods that often lead to either low-performing local optima or computationally intensive centralized solutions. A critical novel element in this controller is that it automatically optimizes its planning horizon length, thus making it parameter-free. We show that explicit globally optimal solutions can be obtained for every distributed optimization problem encountered at each event where the receding horizon controller is invoked. Numerical results are provided showing improvements compared to state of the art distributed on-line parametric control solutions.

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Optimal Minimax Mobile Sensor Scheduling Over a Network

We investigate the problem of monitoring multiple targets using a single mobile sensor, with the goal of minimizing the maximum estimation error among all the targets over long time horizons. The sensor can move in a network-constrained structure, where it has to plan which targets to visit and for how long to dwell at each node. We prove that in an optimal observation time allocation, the peak uncertainty is the same among all the targets. By further restricting the agent policy to only visit each target once every cycle, we develop a scheme to optimize the agent's behavior that is significantly simpler computationally when compared to previous approaches for similar problems.

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Comparison of Centralized and Decentralized Approaches in Cooperative Coverage Problems with Energy-Constrained Agents

A multi-agent coverage problem is considered with energy-constrained agents. The objective of this paper is to compare the coverage performance between centralized and decentralized approaches. To this end, a near-optimal centralized coverage control method is developed under energy depletion and repletion constraints. The optimal coverage formation corresponds to the locations of agents where the coverage performance is maximized. The optimal charging formation corresponds to the locations of agents with one agent fixed at the charging station and the remaining agents maximizing the coverage performance. We control the behavior of this cooperative multi-agent system by switching between the optimal coverage formation and the optimal charging formation. Finally, the optimal dwell times at coverage locations, charging time, and agent trajectories are determined so as to maximize coverage over a given time interval. In particular, our controller guarantees that at any time there is at most one agent leaving the team for energy repletion.

math.OC↗

Bridging the Gap between Optimal Trajectory Planning and Safety-Critical Control with Applications to Autonomous Vehicles

We address the problem of optimizing the performance of a dynamic system while satisfying hard safety constraints at all times. Implementing an optimal control solution is limited by the computational cost required to derive it in real time, especially when constraints become active, as well as the need to rely on simple linear dynamics, simple objective functions, and ignoring noise. The recently proposed Control Barrier Function (CBF) method may be used for safety-critical control at the expense of sub-optimal performance. In this paper, we develop a real-time control framework that combines optimal trajectories generated through optimal control with the computationally efficient CBF method providing safety guarantees. We use Hamiltonian analysis to obtain a tractable optimal solution for a linear or linearized system, then employ High Order CBFs (HOCBFs) and Control Lyapunov Functions (CLFs) to account for constraints with arbitrary relative degrees and to track the optimal state, respectively. We further show how to deal with noise in arbitrary relative degree systems. The proposed framework is then applied to the optimal traffic merging problem for Connected and Automated Vehicles (CAVs) where the objective is to jointly minimize the travel time and energy consumption of each CAV subject to speed, acceleration, and speed-dependent safety constraints. In addition, when considering more complex objective functions, nonlinear dynamics and passenger comfort requirements for which analytical optimal control solutions are unavailable, we adapt the HOCBF method to such problems. Simulation examples are included to compare the performance of the proposed framework to optimal solutions (when available) and to a baseline provided by human-driven vehicles with results showing significant improvements in all metrics.

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Distributed Non-convex Optimization of Multi-agent Systems Using Boosting Functions to Escape Local Optima: Theory and Applications

We address the problem of multiple local optima arising due to non-convex objective functions in cooperative multi-agent optimization problems. To escape such local optima, we propose a systematic approach based on the concept of boosting functions. The underlying idea is to temporarily transform the gradient at a local optimum into a boosted gradient with a non-zero magnitude. We develop a Distributed Boosting Scheme (DBS) based on a gradient-based optimization algorithm using a novel optimal variable step size mechanism so as to guarantee convergence. Even though our motivation is based on the coverage control problem setting, our analysis applies to a broad class of multi-agent problems. Simulation results are provided to compare the performance of different boosting functions families and to demonstrate the effectiveness of the boosting function approach in attaining improved (still generally local) optima.

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Explainability of Intelligent Transportation Systems using Knowledge Compilation: a Traffic Light Controller Case

Usage of automated controllers which make decisions on an environment are widespread and are often based on black-box models. We use Knowledge Compilation theory to bring explainability to the controller's decision given the state of the system. For this, we use simulated historical state-action data as input and build a compact and structured representation which relates states with actions. We implement this method in a Traffic Light Control scenario where the controller selects the light cycle by observing the presence (or absence) of vehicles in different regions of the incoming roads.

cs.AI↗

Decentralized Optimal Control in Multi-lane Merging for Connected and Automated Vehicles

We address the problem of optimally controlling Connected and Automated Vehicles (CAVs) arriving from two multi-lane roads and merging at multiple points where the objective is to jointly minimize the travel time and energy consumption of each CAV subject to speed-dependent safety constraints, as well as speed and acceleration constraints. This problem was solved in prior work for two single-lane roads. A direct extension to multi-lane roads is limited by the computational complexity required to obtain an explicit optimal control solution. Instead, we propose a general framework that converts a multi-lane merging problem into a decentralized optimal control problem for each CAV in a less-conservative way. To accomplish this, we employ a joint optimal control and barrier function method to efficiently get an optimal control for each CAV with guaranteed satisfaction of all constraints. Simulation examples are included to compare the performance of the proposed framework to a baseline provided by human-driven vehicles with results showing significant improvements in both time and energy metrics.

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Multi-Agent Persistent Monitoring of Targets with Uncertain States

We address the problem of persistent monitoring, where a finite set of mobile agents has to persistently visit a finite set of targets. Each of these targets has an internal state that evolves with linear stochastic dynamics. The agents can observe these states, and the observation quality is a function of the distance between the agent and a given target. The goal is then to minimize the mean squared estimation error of these target states. We approach the problem from an infinite horizon perspective, where we prove that, under some natural assumptions, the covariance matrix of each target converges to a limit cycle. The goal, therefore, becomes to minimize the steady state uncertainty. Assuming that the trajectory is parameterized, we provide tools for computing the steady state cost gradient. We show that, in one-dimensional (1D) environments with bounded control and non-overlapping targets, when an optimal control exists it can be represented using a finite number of parameters. We also propose an efficient parameterization of the agent trajectories for multidimensional settings using Fourier curves. Simulation results show the efficacy of the proposed technique in 1D, 2D and 3D scenarios.

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Combined Eco-Routing and Power-Train Control of Plug-In Hybrid Electric Vehicles in Transportation Networks

We study the problem of eco-routing for Plug-In Hybrid Electric Vehicles (PHEVs) to minimize the overall energy consumption cost. We propose an algorithm which can simultaneously calculate an energy-optimal route (eco-route) for a PHEV and an optimal power-train control strategy over this route. In order to show the effectiveness of our method in practice, we use a HERE Maps API to apply our algorithms based on traffic data in the city of Boston with more than 110,000 links. Moreover, we validate the performance of our eco-routing algorithm using speed profiles collected from a traffic simulator (SUMO) as input to a high-fidelity energy model to calculate energy consumption costs. Our results show significant energy savings (around 12%) for PHEVs with a near real-time execution time for the algorithm.

math.OC↗

Joint Pricing and Rebalancing of Autonomous Mobility-on-Demand Systems

This paper studies optimal pricing and rebalancing policies for Autonomous Mobility-on-Demand (AMoD) systems. We take a macroscopic planning perspective to tackle a profit maximization problem while ensuring that the system is load-balanced. We begin by describing the system using a dynamic fluid model to show the existence and stability of an equilibrium (i.e., load balance) through pricing policies. We then develop an optimization framework that allows us to find optimal policies in terms of pricing and rebalancing. We first maximize profit by only using pricing policies, then incorporate rebalancing, and finally we consider whether the solution is found sequentially or jointly. We apply each approach on a data-driven case study using real taxi data from New York City. Depending on which benchmarking solution we use, the joint problem (i.e., pricing and rebalancing) increases profits by 7% to 40%

math.OC↗

Optimal Composition of Heterogeneous Multi-Agent Teams for Coverage Problems with Performance Bound Guarantees

We consider the problem of determining the optimal composition of a heterogeneous multi-agent team for coverage problems by including costs associated with different agents and subject to an upper bound on the maximal allowable number of agents. We formulate a resource allocation problem without introducing additional non-convexities to the original problem. We develop a distributed Projected Gradient Ascent (PGA) algorithm to solve the optimal team composition problem. To deal with non-convexity, we initialize the algorithm using a greedy method and exploit the submodularity and curvature properties of the coverage objective function to derive novel tighter performance bound guarantees on the optimization problem solution. Numerical examples are included to validate the effectiveness of this approach in diverse mission space configurations and different heterogeneous multi-agent collections. Comparative results obtained using a commercial mixed-integer nonlinear programming problem solver demonstrate both the accuracy and computational efficiency of the distributed PGA algorithm.

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Congestion-aware Routing and Rebalancing of Autonomous Mobility-on-Demand Systems in Mixed Traffic

This paper studies congestion-aware route-planning policies for Autonomous Mobility-on-Demand (AMoD) systems, whereby a fleet of autonomous vehicles provides on-demand mobility under mixed traffic conditions. Specifically, we first devise a network flow model to optimize the AMoD routing and rebalancing strategies in a congestion-aware fashion by accounting for the endogenous impact of AMoD flows on travel time. Second, we capture reactive exogenous traffic consisting of private vehicles selfishly adapting to the AMoD flows in a user-centric fashion by leveraging an iterative approach. Finally, we showcase the effectiveness of our framework with two case-studies considering the transportation sub-networks in Eastern Massachusetts and New York City. Our results suggest that for high levels of demand, pure AMoD travel can be detrimental due to the additional traffic stemming from its rebalancing flows, while the combination of AMoD with walking or micromobility options can significantly improve the overall system performance.

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Adaptive Control Barrier Functions for Safety-Critical Systems

Recent work showed that stabilizing affine control systems to desired (sets of) states while optimizing quadratic costs and observing state and control constraints can be reduced to quadratic programs (QP) by using control barrier functions (CBF) and control Lyapunov functions. In our own recent work, we defined high order CBFs (HOCBFs) to accommodating systems and constraints with arbitrary relative degrees, and a penalty method to increase the feasibility of the corresponding QPs. In this paper, we introduce adaptive CBF (AdaCBFs) that can accommodate time-varying control bounds and dynamics noise, and also address the feasibility problem. Central to our approach is the introduction of penalty functions in the definition of an AdaCBF and the definition of auxiliary dynamics for these penalty functions that are HOCBFs and are stabilized by CLFs. We demonstrate the advantages of the proposed method by applying it to a cruise control problem with different road surfaces, tires slipping, and dynamics noise.

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