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We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear…
This paper is concerned with the design of a linear control law for linear systems with stationary additive disturbances. The objective is to find a state feedback gain that minimizes a quadratic stage cost function, while observing chance…
The Linear Quadratic Regulator (LQR) framework considers the problem of regulating a linear dynamical system perturbed by environmental noise. We compute the policy regret between three distinct control policies: i) the optimal online…
Learning-based control methods for industrial processes leverage the repetitive nature of the underlying process to learn optimal inputs for the system. While many works focus on linear systems, real-world problems involve nonlinear…
Algebraically speaking, linear time-invariant (LTI) systems can be considered as modules. In this framework, controllability is translated as the freeness of the system module. Optimal control mainly relies on quadratic Lagrangians and the…
In this paper, we propose a new Robust Nonlinear Quadratic Gaussian (RNQG) controller based on State-Dependent Riccati Equation (SDRE) scheme for continuous-time nonlinear systems. Existing controllers do not account for combined noise and…
Linear-Quadratic optimal controls are computed for a class of boundary controlled, boundary observed hyperbolic infinite-dimensional systems, which may be viewed as networks of waves. The main results of this manuscript consist in…
We develop an adaptive control architecture to achieve stabilization and command following of uncertain dynamical systems with improved transient performance. Our framework consists of a new reference system and an adaptive controller. The…
The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of the turnpike is the linear quadratic regulator problem and the…
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,…
In this paper we study the linear quadratic regulation (LQR) problem for dynamical systems coupled over large-scale networks and obtain locally computable low-complexity solutions. The underlying large or even infinite networks are…
We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an…
We formulate a general mathematical framework for self-tuning network control architecture design. This problem involves jointly adapting the locations of active sensors and actuators in the network and the feedback control policy to all…
In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…
We discuss the use of Dirac structures to obtain a better understanding of the geometry of a class of optimal control problems and their reduction by symmetries. In particular we will show how to extend the reduction of Dirac structures…
We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following the perspective taken in our previous research work on…
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are…
Reinforcement learning based adaptive/approximate dynamic programming (ADP) is a powerful technique to determine an approximate optimal controller for a dynamical system. These methods bypass the need to analytically solve the nonlinear…
In this work we present a nonlinear adaptive suboptimal control strategy for uncertain nonlinear systems. Stochastic parametric uncertainty is dealt with by employing spectral decomposition of the random variables by means of the…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…