Related papers: Policy Optimization in Control: Geometry and Algor…
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…
One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the deterministic case is to provide the desired feedback controls for linear quadratic…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
Policy gradients methods apply to complex, poorly understood, control problems by performing stochastic gradient descent over a parameterized class of polices. Unfortunately, even for simple control problems solvable by standard dynamic…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
In this paper, we present a geometric framework for the reachability analysis of attitude control systems. We model the attitude dynamics on the product manifold $\mathrm{SO}(3) \times \mathbb{R}^3$ and introduce a novel parametrized family…
A large body of animation research focuses on optimization of movement control, either as action sequences or policy parameters. However, as closed-form expressions of the objective functions are often not available, our understanding of…
The Linear Quadratic Gaussian (LQG) regulator is a cornerstone of optimal control theory, yet its performance can degrade significantly when the noise distributions deviate from the assumed Gaussian model. To address this limitation, this…
We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
The connection between control algorithms for Markov decision processes and optimization algorithms has been implicitly and explicitly exploited since the introduction of dynamic programming algorithm by Bellman in the 1950s. Recently, this…
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
We consider the problem of synthesizing optimal linear feedback policies subject to arbitrary convex constraints on the feedback matrix. This is known to be a hard problem in the usual formulations ($\Htwo,\Hinf,\LQR$) and previous works…
Computational constraints permeate the controller design process, and yet are rarely treated as explicit design constraints. Towards addressing this gap, we propose a quantitative framework that captures the effects of common design…
This paper presents policy-based motion planning for robotic systems. The motion planning literature has been mostly focused on open-loop trajectory planning which is followed by tracking online. In contrast, we solve the problem of path…
We address the challenge of dimension reduction in the discrete-time optimal control problem which is solved repeatedly online within the framework of model predictive control. Our study demonstrates that a reduced-order approach, aimed at…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
Deep reinforcement learning agents for continuous control are known to exhibit significant instability in their performance over time. In this work, we provide a fresh perspective on these behaviors by studying the return landscape: the…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
We present a novel approach to control design for nonlinear systems which leverages model-free policy optimization techniques to learn a linearizing controller for a physical plant with unknown dynamics. Feedback linearization is a…