Related papers: Controlled Optimization of Quadratic Functions in …
Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…
We introduce a novel algorithm for the task of coherently controlling a quantum mechanical system to implement any chosen unitary dynamics. It performs faster than existing state of the art methods by one to three orders of magnitude…
In this paper, we consider a linear quadratic (LQ) optimal control problem in both finite and infinite dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon T tends to infinity. The leading term in…
We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while respecting the…
In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control.…
We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's function, we show an…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
We consider policy gradient algorithms for the indefinite least squares stationary optimal control, e.g., linear-quadratic-regulator (LQR) with indefinite state and input penalization matrices. Such a setup has important applications in…
Time delays are ubiquitous in industrial processes, and they must be accounted for when designing control algorithms because they have a significant effect on the process dynamics. Therefore, in this work, we propose a simultaneous approach…
In this work we consider a flow network for which the goal is to solve a practical optimal regulation problem in the presence of input saturation. Based on Lyapunov arguments we propose distributed controllers which guarantee global…
We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…
We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential…
The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly…
Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of…
We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method…