Related papers: Solving Optimal Control Problems of Rigid-Body Dyn…
The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid…
Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…
This paper presents a new model-based algorithm that computes predictive optimal controls on-line and in closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive,…
We study the problem of robust global stabilization in control-affine systems, focusing on dynamic uncertainties in the control directions \emph{and} the presence of topological obstructions that prevent the existence of smooth global…
We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…
This paper studies the problem of control strategy synthesis for dynamical systems with differential constraints to fulfill a given reachability goal while satisfying a set of safety rules. Particular attention is devoted to goals that…
This paper considers the problem of real-time mode scheduling in linear time-varying switched systems subject to a quadratic cost functional. The execution time of hybrid control algorithms is often prohibitive for real-time applications…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
Robust optimal or min-max model predictive control (MPC) approaches aim to guarantee constraint satisfaction over a known, bounded uncertainty set while minimizing a worst-case performance bound. Traditionally, these methods compute a…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
This paper investigates the collision-free control problem for multi-agent systems. For such multi-agent systems, it is the typical situation where conventional methods using either the usual centralized model predictive control (MPC), or…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
We present non-convex maximal dissipation principle (NMDP), a time integration scheme for articulated bodies with simultaneous contacts. Our scheme resolves contact forces via the maximal dissipation principle (MDP). Prior MDP solvers…
In this paper, we introduce a novel parallel contact algorithm designed to run efficiently in High-Performance Computing based supercomputers. Particular emphasis is put on its computational implementation in a multiphysics finite element…
Optimal control is ubiquitous in many fields of engineering. A common technique to find candidate solutions is via Pontryagin's maximum principle. An unfortunate aspect of this method is that the dimension of system doubles. When the system…
This paper details an approach to linearise differentiable but non-convex collision avoidance constraints tailored to convex shapes. It revisits introducing differential collision avoidance constraints for convex objects into an optimal…
The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal…
This paper presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
We develop a methodology for performing approximate optimal control simulations for quantum systems with multiple interacting degrees of freedom. The quantum dynamics are modeled using the first-order Magnus approximation in the interaction…