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We solve the output-feedback stabilization problem for a tank with a liquid modeled by the viscous Saint-Venant PDE system. The control input is the acceleration of the tank and a Control Lyapunov Functional methodology is used. The measurements are the tank position and the liquid level at the tank walls. The control scheme is a combination of a state feedback law with functional observers for the tank velocity and the liquid momentum. Four different types of output feedback stabilizers are proposed. A full-order observer and a reduced-order observer are used in order to estimate the tank velocity while the unmeasured liquid momentum is either estimated by using an appropriate scalar filter or is ignored. The reduced order observer differs from the full order observer because it omits the estimation of the measured tank position. Exponential convergence of the closed-loop system to the desired equilibrium point is achieved in each case. An algorithm is provided that guarantees that a robotic arm can move a glass of water to a pre-specified position no matter how full the glass is, without spilling water out of the glass, without residual end point sloshing and without measuring the water momentum and the glass velocity. Finally, the efficiency of the proposed output feedback laws is validated by numerical examples, obtained by using a simple finite-difference numerical scheme. The properties of the proposed, explicit, finite-difference scheme are determined.

We propose throughput and cost optimal job scheduling algorithms in cloud computing platforms offering Infrastructure as a Service. We first consider online migration and propose job scheduling algorithms to minimize job migration and server running costs. We consider algorithms that assume knowledge of job-size on arrival of jobs. We characterize the optimal cost subject to system stability. We develop a drift-plus-penalty framework based algorithm that can achieve optimal cost arbitrarily closely. Specifically this algorithm yields a trade-off between delay and costs. We then relax the job-size knowledge assumption and give an algorithm that uses readily offered service to the jobs. We show that this algorithm gives order-wise identical cost as the job size based algorithm. Later, we consider offline job migration that incurs migration delays. We again present throughput optimal algorithms that minimize server running cost. We illustrate the performance of the proposed algorithms and compare these to the existing algorithms via simulation.

In this paper, the problem of coordinated transportation of heavy payload by a team of UAVs in a cluttered environment is addressed. The payload is modeled as a rigid body and is assumed to track a pre-computed global flight trajectory from a start point to a goal point. Due to the presence of local dynamic obstacles in the environment, the UAVs must ensure that there is no collision between the payload and these obstacles while ensuring that the payload oscillations are kept minimum. An Integrated Decision Controller (IDC) is proposed, that integrates the optimal tracking control law given by a centralized Model Predictive Controller with safety-critical constraints provided by the Exponential Control Barrier Functions. The entire payload-UAV system is enclosed by a safe convex hull boundary, and the IDC ensures that no obstacle enters this boundary. To evaluate the performance of the IDC, the results for a numerical simulation as well as a high-fidelity Gazebo simulation are presented. An ablation study is conducted to analyze the robustness of the proposed IDC against practical dubieties like noisy state values, relative obstacle safety margin, and payload mass uncertainty. The results clearly show that the IDC achieves both trajectory tracking and obstacle avoidance successfully while restricting the payload oscillations within a safe limit.

Environments with multi-agent interactions often result a rich set of modalities of behavior between agents due to the inherent suboptimality of decision making processes when agents settle for satisfactory decisions. However, existing algorithms for solving these dynamic games are strictly unimodal and fail to capture the intricate multimodal behaviors of the agents. In this paper, we propose MMELQGames (Multimodal Maximum-Entropy Linear Quadratic Games), a novel constrained multimodal maximum entropy formulation of the Differential Dynamic Programming algorithm for solving generalized Nash equilibria. By formulating the problem as a certain dynamic game with incomplete and asymmetric information where agents are uncertain about the cost and dynamics of the game itself, the proposed method is able to reason about multiple local generalized Nash equilibria, enforce constraints with the Augmented Lagrangian framework and also perform Bayesian inference on the latent mode from past observations. We assess the efficacy of the proposed algorithm on two illustrative examples: multi-agent collision avoidance and autonomous racing. In particular, we show that only MMELQGames is able to effectively block a rear vehicle when given a speed disadvantage and the rear vehicle can overtake from multiple positions.

We introduce vector optimization problems with stochastic bandit feedback, which extends the best arm identification problem to vector-valued rewards. We consider $K$ designs, with multi-dimensional mean reward vectors, which are partially ordered according to a polyhedral ordering cone $C$. This generalizes the concept of Pareto set in multi-objective optimization and allows different sets of preferences of decision-makers to be encoded by $C$. Different than prior work, we define approximations of the Pareto set based on direction-free covering and gap notions. We study the setting where an evaluation of each design yields a noisy observation of the mean reward vector. Under subgaussian noise assumption, we investigate the sample complexity of the na\"ive elimination algorithm in an ($\epsilon,\delta$)-PAC setting, where the goal is to identify an ($\epsilon,\delta$)-PAC Pareto set with the minimum number of design evaluations. In order to characterize the difficulty of learning the Pareto set, we introduce the concept of ordering complexity, i.e., geometric conditions on the deviations of empirical reward vectors from their mean under which the Pareto front can be approximated accurately. We show how to compute the ordering complexity of any polyhedral ordering cone. We run experiments to verify our theoretical results and illustrate how $C$ and sampling budget affect the Pareto set, returned ($\epsilon,\delta$)-PAC Pareto set and the success of identification.

We present an algorithm for the maximum matching problem in dynamic (insertion-deletions) streams with *asymptotically optimal* space complexity: for any $n$-vertex graph, our algorithm with high probability outputs an $\alpha$-approximate matching in a single pass using $O(n^2/\alpha^3)$ bits of space. A long line of work on the dynamic streaming matching problem has reduced the gap between space upper and lower bounds first to $n^{o(1)}$ factors [Assadi-Khanna-Li-Yaroslavtsev; SODA 2016] and subsequently to $\text{polylog}{(n)}$ factors [Dark-Konrad; CCC 2020]. Our upper bound now matches the Dark-Konrad lower bound up to $O(1)$ factors, thus completing this research direction. Our approach consists of two main steps: we first (provably) identify a family of graphs, similar to the instances used in prior work to establish the lower bounds for this problem, as the only "hard" instances to focus on. These graphs include an induced subgraph which is both sparse and contains a large matching. We then design a dynamic streaming algorithm for this family of graphs which is more efficient than prior work. The key to this efficiency is a novel sketching method, which bypasses the typical loss of $\text{polylog}{(n)}$-factors in space compared to standard $L_0$-sampling primitives, and can be of independent interest in designing optimal algorithms for other streaming problems.

Multi-agent reinforcement learning (MARL) algorithms often suffer from an exponential sample complexity dependence on the number of agents, a phenomenon known as \emph{the curse of multiagents}. In this paper, we address this challenge by investigating sample-efficient model-free algorithms in \emph{decentralized} MARL, and aim to improve existing algorithms along this line. For learning (coarse) correlated equilibria in general-sum Markov games, we propose \emph{stage-based} V-learning algorithms that significantly simplify the algorithmic design and analysis of recent works, and circumvent a rather complicated no-\emph{weighted}-regret bandit subroutine. For learning Nash equilibria in Markov potential games, we propose an independent policy gradient algorithm with a decentralized momentum-based variance reduction technique. All our algorithms are decentralized in that each agent can make decisions based on only its local information. Neither communication nor centralized coordination is required during learning, leading to a natural generalization to a large number of agents. We also provide numerical simulations to corroborate our theoretical findings.

The arboricity of a graph is the minimum number of forests required to cover all its edges. In this paper, we examine arboricity from a game-theoretic perspective and investigate cost-sharing in the minimum forest cover problem. We introduce the arboricity game as a cooperative cost game defined on a graph. The players are edges, and the cost of each coalition is the arboricity of the subgraph induced by the coalition. We study properties of the core and propose an efficient algorithm for computing the nucleolus when the core is not empty. In order to compute the nucleolus in the core, we introduce the prime partition which is built on the densest subgraph lattice. The prime partition decomposes the edge set of a graph into a partially ordered set defined from minimal densest minors and their invariant precedence relation. Moreover, edges from the same partition always have the same value in a core allocation. Consequently, when the core is not empty, the prime partition significantly reduces the number of variables and constraints required in the linear programs of Maschler's scheme and allows us to compute the nucleolus in polynomial time. Besides, the prime partition provides a graph decomposition analogous to the celebrated core decomposition and the density-friendly decomposition, which may be of independent interest.

We apply computational Game Theory to a unification of physics-based models that represent decision-making across a number of agents within both cooperative and competitive processes. Here the competitors try to both positively influence their own returns, while negatively affecting those of their competitors. Modelling these interactions with the so-called Boyd-Kuramoto-Lanchester (BKL) complex dynamical system model yields results that can be applied to business, gaming and security contexts. This paper studies a class of decision problems on the BKL model, where a large set of coupled, switching dynamical systems are analysed using game-theoretic methods. Due to their size, the computational cost of solving these BKL games becomes the dominant factor in the solution process. To resolve this, we introduce a novel Nash Dominant solver, which is both numerically efficient and exact. The performance of this new solution technique is compared to traditional exact solvers, which traverse the entire game tree, as well as to approximate solvers such as Myopic and Monte Carlo Tree Search (MCTS). These techniques are assessed, and used to gain insights into both nonlinear dynamical systems and strategic decision making in adversarial environments.

Multi-access edge computing (MEC) is a key enabler to reduce the latency of vehicular network. Due to the vehicles mobility, their requested services (e.g., infotainment services) should frequently be migrated across different MEC servers to guarantee their stringent quality of service requirements. In this paper, we study the problem of service migration in a MEC-enabled vehicular network in order to minimize the total service latency and migration cost. This problem is formulated as a nonlinear integer program and is linearized to help obtaining the optimal solution using off-the-shelf solvers. Then, to obtain an efficient solution, it is modeled as a multi-agent Markov decision process and solved by leveraging deep Q learning (DQL) algorithm. The proposed DQL scheme performs a proactive services migration while ensuring their continuity under high mobility constraints. Finally, simulations results show that the proposed DQL scheme achieves close-to-optimal performance.