Related papers: Parabolic optimal control problems with combinator…
We consider the problem of determining a sequence of payments among a set of entities that clear (if possible) the liabilities among them. We formulate this as an optimal control problem, which is convex when the objective function is, and…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators,…
In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…
In this paper we study the optimality condition for the Venttsel boundary control of a parabolic equation, that is, the state of the dynamic system is governed by a parabolic equation together with an initial condition while the control is…
Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions…
In this paper, we study a class of finite-time control problems for discrete-time positive linear systems with time-varying state parameters. Although several interesting control problems appearing in population biology, economics, and…
Most modern control systems are switched, meaning they have continuous as well as discrete decision variables. Switched systems often have constraints called dwell-time constraints (e.g., cycling constraints in a heat pump) on the switching…
This two-part paper is concerned with the problem of minimizing a linear objective function subject to a bilinear matrix inequality (BMI) constraint. In this part, we first consider a family of convex relaxations which transform BMI…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this…
We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary…
An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…
In this paper we consider a constrained parabolic optimal control problem. The cost functional is quadratic and it combines the distance of the trajectory of the system from the desired evolution profile together with the cost of a control.…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
This paper proposes a novel method for designing finite-horizon discrete-valued switching signals in linear switched systems based on discreteness-promoting regularization. The inherent combinatorial optimization problem is reformulated as…
This paper studies the time optimal control problem for systems of heat equations coupled by a pair of constant matrices. The control constraint is of the ball-type, while the target is the origin of the state space. We obtain an upper…
We prove weak duality between two recent convex relaxation methods for bounding the optimal value of a constrained variational problem in which the objective is an integral functional. The first approach, proposed by Valmorbida et al. (IEEE…
Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phe-nomena, by relaxing controls as Young measures. These semi-definite…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…