Related papers: Linear structures in nonlinear optimal control
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as an optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic…
In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…
Model-based reinforcement learning is an effective approach for controlling an unknown system. It is based on a longstanding pipeline familiar to the control community in which one performs experiments on the environment to collect a…
Sufficient and necessary conditions are established for controllability of affine control systems where the control is constrained to a set whose convex hull contains the origin but is not necessarily, in contrast with previously known…
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
In this paper we consider a broad class of infinite horizon discrete-time optimal control models that involve a nonnegative cost function and an affine mapping in their dynamic programming equation. They include as special cases classical…
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…
In this paper we study the optimal control of a class of semilinear elliptic partial differential equations which have nonlinear constituents that are only accessible by data and are approximated by nonsmooth ReLU neural networks. The…
We propose an optimal control approach in order to identify the nonlinearity in the monodomain model, from given data. This data-driven approach gives an answer to the problem of selecting the model when studying phenomena related to…
We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the…
We study tracking-type optimal control problems that involve a non-affine, weak-to-weak continuous control-to-state mapping, a desired state $y_d$, and a desired control $u_d$. It is proved that such problems are always nonuniquely solvable…
This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…
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…
This paper explores the controllability and state tracking of ensembles from the perspective of optimal transport theory. Ensembles, characterized as collections of systems evolving under the same dynamics but with varying initial…
Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…
In this letter, we discuss the problem of optimal control for affine systems in the context of data-driven linear programming. First, we introduce a unified framework for the fixed point characterization of the value function, Q-function…
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…
This paper presents a controller design and optimization framework for nonlinear dynamic systems to track a given reference signal in the presence of disturbances when the task is repeated over a finite-time interval. This novel framework…