Related papers: Probabilistic ODE Solvers for Integration Error-Aw…
We employ optimal control theory to study the problem of estimating the probability density function from a data set originating from an unknown probability distribution. The original variational problem is reformulated as a multi-stage…
We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite…
In this paper, we study a data-enabled predictive control (DeePC) algorithm applied to unknown stochastic linear time-invariant systems. The algorithm uses noise-corrupted input/output data to predict future trajectories and compute optimal…
Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
Stochastic Optimal Control Problems (SOCPs) plays a major role in the sequential decision-making challenges. There exist various iterative algorithms, under framework of stochastic maximum principle, that sequentially find the optimal…
Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…
We address the problem of Bayesian inference for parameters in ordinary differential equation (ODE) models based on observational data. Conventional approaches in this setting typically rely on numerical solvers such as the Euler or…
We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By…
The combinatorial integral approximation (CIA) is a solution technique for integer optimal control problems. In order to regularize the solutions produced by CIA, one can minimize switching costs in one of its algorithmic steps. This leads…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
Robust Model Predictive Control (MPC) for nonlinear systems is a problem that poses significant challenges as highlighted by the diversity of approaches proposed in the last decades. Often compromises with respect to computational load,…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
In some of the complicated control problems we have to use the controllers that apply nonlocal operators to the error signal to generate the control. Currently, the most famous controller with nonlocal operators is the fractional-order PID…
This paper addresses the problem of solving a class of nonlinear optimal control problems (OCP) with infinite-dimensional linear state constraints involving Riesz-spectral operators. Each instance within this class has time/control…
We consider the optimal control of a PDE with random source term subject to probabilistic or almost sure state constraints. In the main theoretical result, we provide an exact formula for the Clarke subdifferential of the probability…
This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The robot has fourth-order dynamics that change instantaneously at any pick-up or…
This paper is concerned with the numerical integration of stochastic differential equations (SDEs) which govern diffusion processes driven by a standard Wiener process. With the latter being replaced by a sequence of increments at discrete…
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…