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We develop an Integral Transformation Method (ITM) for the study of suitable optimal control and differential game models. This allows for a solution to such dynamic problems to be found through solving a family of optimization problems…
In this work, we develop a scalable, local trajectory optimization algorithm that enables robots to interact with other robots. It has been shown that agents' interactions can be successfully captured in game-theoretic formulations, where…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
We present a robust framework with computational algorithms to support decision makers in sequential games. Our framework includes methods to solve games with complete information, assess the robustness of such solutions and, finally,…
We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally…
This paper investigates the synthesis of distributed economic control algorithms under which dynamically coupled physical systems are regulated to a variational equilibrium of a constrained convex game. We study two complementary cases: (i)…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…
Learning algorithms are essential for the applications of game theory in a networking environment. In dynamic and decentralized settings where the traffic, topology and channel states may vary over time and the communication between agents…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
We present a novel algorithm for game-theoretic trajectory planning, tailored for settings in which agents can only observe one another in specific regions of the state space. Such problems arise naturally in the context of multi-robot…
Multi-agent interactions are increasingly important in the context of reinforcement learning, and the theoretical foundations of policy gradient methods have attracted surging research interest. We investigate the global convergence of…
This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…
The goal of agents in multi-agent environments is to maximize total reward against the opposing agents that are encountered. Following a game-theoretic solution concept, such as Nash equilibrium, may obtain a strong performance in some…
We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…
This paper proposes a new method for finding closed-loop saddle points in zero-sum linear-quadratic stochastic differential games by decoupling their inherent structure. Specifically, we develop a nested iterative scheme that constructs a…
In this paper I present several algorithmic techniques for improving the decision process of multiple types of agents behaving in environments where their interests are in conflict. The interactions between the agents are modelled by using…
Neuro-dynamic programming is a class of powerful techniques for approximating the solution to dynamic programming equations. In their most computationally attractive formulations, these techniques provide the approximate solution only…
In this paper, we consider a learning problem among non-cooperative agents interacting in a time-varying system. Specifically, we focus on repeated linear quadratic network games, in which the network of interactions changes with time and…
Stochastic optimal control and games have a wide range of applications, from finance and economics to social sciences, robotics, and energy management. Many real-world applications involve complex models that have driven the development of…