Related papers: Optimality of broken extremals
We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task…
We present a novel extremum seeking method for affine connection mechanical control systems. The proposed control law involves periodic perturbation signals with sufficiently large amplitudes and frequencies. A suitable averaging analysis…
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled…
We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose…
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for…
Semilinear parabolic systems with bi-linear nonlinearities cover a lot of applications and their optimal control leads to relatively simple optimality conditions. An example is the incompressible Navier-Stokes system for homogeneous fluids,…
The numerical analysis of a family of distributed mixed optimal control problems governed by elliptic variational inequalities (with parameter $\alpha >0$) is obtained through the finite element method when its parameter $h\rightarrow 0$.…
We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been recently introduced by…
In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum principle when the admissible control set is compact, the…
In this paper, a new method for solving the problem of optimal control of semi-Markov processes with finitely many states is considered. A new form of the assertion on an extremum of a liner-fractional integral functional given on a set of…
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…
A graph is reducible if it is the lexicographic product of two smaller non-trivial graphs. It is well-known a 1-planar graph with $n ~(\ge3)$ vertices has at most $4n-8$ edges, and a graph $G$ with $n$ vertices is optimal if $G$ has exactly…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
We investigate several control strategies for the transport of an excitation along a spin chain. We demonstrate that fast, high fidelity transport can be achieved using protocols designed with differentiable programming. Building on this,…
We study a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter $\delta$, which…
In this work, we study an optimal control problem for a multi-agent system modeled by an undirected formation graph with nodes describing the kinematics of each agent, given by a left-invariant control system on a Lie group. The agents…
We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin…
A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints.…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…