相关论文: Time-Optimal Collaborative Guidance Using the Gene…

We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…

This paper presents a hierarchical planning algorithm for racing with multiple opponents. The two-stage approach consists of a high-level behavioral planning step and a low-level optimization step. By combining discrete and continuous…

We consider an optimal control on networks in the spirit of the works of Achdou et al. (2013) and Imbert et al. (2013). The main new feature is that there are entry (or exit) costs at the edges of the network leading to a possible…

In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…

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…

Stability under model predictive control (MPC) schemes is frequently ensured by terminal ingredients. Employing a (control) Lyapunov function as the terminal cost constitutes a common choice. Learning-based methods may be used to construct…

This paper presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The method is inverse optimal because…

Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…

This paper addresses the design of an optimization-based cooperative path-following control law for multiple robotic vehicles that optimally balances the transient trade-off between coordination and path-following errors. To this end, we…

The minimization of a multiobjective Lagrangian with non-constant discount is studied. The problem is embedded into a set-valued framework and a corresponding definition of the value function is given. Bellman's optimality principle and…

We study a constrained stochastic control problem with jumps; the jump times of the controlled process are given by a Poisson process. The cost functional comprises quadratic components for an absolutely continuous control and the…

The merging area of highway ramps faces multiple challenges, including traffic congestion, collision risks, speed mismatches, driver behavior uncertainties, limited visibility, and bottleneck effects. However, autonomous vehicles engaging…

We address two major challenges in scientific machine learning (SciML): interpretability and computational efficiency. We increase the interpretability of certain learning processes by establishing a new theoretical connection between…

Safety is an important topic in autonomous driving since any collision may cause serious injury to people and damage to property. Hamilton-Jacobi (HJ) Reachability is a formal method that verifies safety in multi-agent interaction and…

This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…

In this paper, we address a coordination problem for connected and autonomous vehicles (CAVs) in mixed traffic settings with human-driven vehicles (HDVs). The main objective is to have a safe and optimal crossing order for vehicles…

We consider an optimal control problem with ergodic (long term average) reward for a McKean-Vlasov dynamics, where the coefficients of a controlled stochastic differential equation depend on the marginal law of the solution. Starting from…

Hybrid dynamical systems with nonlinear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of nonlinear…

Designing controllers that are both safe and performant is inherently challenging. This co-optimization can be formulated as a constrained optimal control problem, where the cost function represents the performance criterion and safety is…

The optimal \(H_{\infty}\) control problem over an infinite time horizon, which incorporates a performance function with a discount factor \(e^{-\alpha t}\) (\(\alpha > 0\)), is important in various fields. Solving this optimal…