Related papers: Constrained Trajectory Optimization for Hybrid Dyn…
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
In this paper, we design a theoretical framework allowing to apply model predictive control on hybrid systems. For this, we develop a theory of approximate dynamic programming by leveraging the concept of alternating simulation. We show how…
This paper presents a Lagrangian approach to simulating multibody dynamics in a tensegrity framework with an ability to tackle holonomic constraint violations in an energy-preserving scheme. Governing equations are described using…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
Risk-sensitive control balances performance with resilience to unlikely events in uncertain systems. This paper introduces ergodic-risk criteria, which capture long-term cumulative risks through probabilistic limit theorems. By ensuring the…
In this paper we address the problem of information-constrained optimal control for an interconnected system subject to one-step communication delays and power constraints. The goal is to minimize a finite-horizon quadratic cost by…
The convergence of policy gradient algorithms hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of linear quadratic control.…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each…
Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum…
For various typical cases and situations where the formulation results in an optimal control problem, the Linear Quadratic Regulator (LQR) approach and its variants continue to be highly attractive. In certain scenarios, it can happen that…
Developing controllers for obstacle avoidance between polytopes is a challenging and necessary problem for navigation in tight spaces. Traditional approaches can only formulate the obstacle avoidance problem as an offline optimization…
Interior point methods for solving linearly constrained convex programming involve a variable projection matrix at each iteration to deal with the linear constraints. This matrix often becomes ill-conditioned near the boundary of the…
We present a numerically tractable formulation for computing the optimal control of the class of hybrid dynamical systems whose trajectories are continuous. Our formulation, an extension of existing relaxed-control techniques for switched…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
This thesis presents new mathematical algorithms for the numerical solution of a mathematical problem class called \emph{dynamic optimization problems}. These are mathematical optimization problems, i.e., problems in which numbers are…
In many real world applications, reinforcement learning agents have to optimize multiple objectives while following certain rules or satisfying a list of constraints. Classical methods based on reward shaping, i.e. a weighted combination of…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
This paper investigates the performance of Newton's method, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP) in solving discrete-time optimal control problems. We offer a unified perspective on these…