Related papers: Towards Global Optimal Control via Koopman Lifts
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in…
This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system. The Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system,…
This paper is concerned with data-driven optimal control of nonlinear systems. We present a convex formulation to the optimal control problem (OCP) with a discounted cost function. We consider OCP with both positive and negative discount…
A tracking type optimal control problem for a nonlinear and nonlocal kinetic Fokker-Planck equation which arises as the mean field limit of an interacting particle systems that is subject to distance dependent random fluctuations is…
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…
Solving real-world optimal control problems are challenging tasks, as the complex, high-dimensional system dynamics are usually unrevealed to the decision maker. It is thus hard to find the optimal control actions numerically. To deal with…
The Koopman operator framework enables global analysis of nonlinear systems through its inherent linearity. This study aims to clarify spectral properties of the Koopman operators for nonlinear systems with control inputs. To this end, we…
This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…
This research presents a novel, analytical, Koopman Operator based formulation for position and attitude dynamics which can be used to derive control strategies for underactuated systems. Compared to data driven Koopman based techniques,…
In this paper, we derive a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. Our framework is actually much more general, and we treat optimal control problems for…
The aim of this paper is to provide improvments to Pontryagin principles in infinite-horizon discrete-time framework when the space of states and of space of controls are infinite-dimensional. We use the method of reduction to finite…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
We propose the application of Koopman operator theory for the design of stabilizing feedback controller for a nonlinear control system. The proposed approach is data-driven and relies on the use of time-series data generated from the…
This paper studies the decay of an objective functional using a new control technique within Pontryagin's framework. Convergence analysis is carried out on the infinite-dimensional space of Tokamak plasma dynamical state as described by…
Gas turbine engines are complex and highly nonlinear dynamical systems. Deriving their physics-based models can be challenging because it requires performance characteristics that are not always available, often leading to many simplifying…
In this paper we consider an optimal control problem in large time horizon and solve it numerically. More precisely, we are interested in an aerial vehicle guidance problem: launched from a ground platform, the vehicle aims at reaching a…
A general problem in optimal control consists of finding a terminal reward that makes the value function independent of the horizon. Such a terminal reward can be interpreted as a max-plus eigenvector of the associated Lax-Oleinik…
In this paper, we present a framework for solving continuous optimal control problems when the true system dynamics are approximated through an imperfect model. We derive a control strategy by applying Pontryagin's Minimum Principle to the…
Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronisation of a Li\'enard system to its limit cycle using a bounded external force. To tackle…
This paper presents an inverse optimal control methodology and its application to training a predictive model of human motor control from a manipulation task. It introduces a convex formulation for learning both objective function and…