Related papers: A Minimum Discounted Reward Hamilton-Jacobi Formul…
This paper studies optimal consensus tracking problem of heterogeneous linear multi-agent systems. By introducing tracking error dynamics, the optimal tracking problem is reformulated as finding a Nash-equilibrium solution of a multi-player…
We present a fast planning architecture called Hamilton-Jacobi-based bidirectional A* (HJBA*) to solve general tight parking scenarios. The algorithm is a two-layer composed of a high-level HJ-based reachability analysis and a lower-level…
This article presents a Hamilton--Jacobi (HJ) reachability framework for a two--satellite collision avoidance problem operating in the same circular orbit, where relative motion is modeled in the radial--tangential--normal (RTN) frame using…
Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for dynamical systems, but solving high-dimensional HJ partial differential equations limits its use in real-time planning. This paper presents a contingency-aware…
We propose a hybrid approach that combines Hamilton-Jacobi (HJ) reachability and mixed-integer optimization for solving a reach-avoid game with multiple attackers and defenders. The reach-avoid game is an important problem with potential…
This paper investigates the so-called reward-balancing methods, a novel class of algorithms for solving discounted-return reinforcement learning (RL) problems. These methods consist of iteratively adjusting the reward function to transform…
A learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is involved when the feedback law is constructed by…
This paper addresses the model-free nonlinear optimal problem with generalized cost functional, and a data-based reinforcement learning technique is developed. It is known that the nonlinear optimal control problem relies on the solution of…
We study reward design strategies for incentivizing a reinforcement learning agent to adopt a policy from a set of admissible policies. The goal of the reward designer is to modify the underlying reward function cost-efficiently while…
This paper introduces a reinforcement learning-based tracking control approach for a class of nonlinear systems using neural networks. In this approach, adversarial attacks were considered both in the actuator and on the outputs. This…
Reach-avoid problems involve driving a system to a set of desirable configurations while keeping it away from undesirable ones. Providing mathematical guarantees for such scenarios is challenging but have numerous potential practical…
A control theoretic approach is presented in this paper for both batch and instantaneous updates of weights in feed-forward neural networks. The popular Hamilton-Jacobi-Bellman (HJB) equation has been used to generate an optimal weight…
Computing tasks may often be posed as optimization problems. The objective functions for real-world scenarios are often nonconvex and/or nondifferentiable. State-of-the-art methods for solving these problems typically only guarantee…
In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraints for the cost function where the cost function is described by the solution of one reflected backward stochastic differential…
In this article, we consider the infinite-horizon reach-avoid (RA) and stabilize-avoid (SA) zero-sum game problems for general nonlinear continuous-time systems, where the goal is to find the set of states that can be controlled to reach or…
Real-world autonomous systems often employ probabilistic predictive models of human behavior during planning to reason about their future motion. Since accurately modeling human behavior a priori is challenging, such models are often…
A tenet of reinforcement learning is that the agent always observes rewards. However, this is not true in many realistic settings, e.g., a human observer may not always be available to provide rewards, sensors may be limited or…
Hamilton-Jacobi (HJ) Reachability is widely used to compute value functions for states satisfying specific control objectives. However, it becomes intractable for high-dimensional problems due to the curse of dimensionality. Dimensionality…
This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…
We present a simple algorithm to approximate the viscosity solution of Hamilton-Jacobi (HJ) equations by means of an artificial deep neural network. The algorithm uses a stochastic gradient descent-based method to minimize the least square…