Related papers: Sequential Linear Integer Programming for Integer …
It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…
In this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
The second part of our study is devoted to an analysis of the exactness of penalty functions for optimal control problems with terminal and pointwise state constraints. We demonstrate that with the use of the exact penalty function method…
This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order…
It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper,…
This paper develops a method to obtain the optimal value for the regularization coefficient in a general mixed-integer problem (MIP). This approach eliminates the cross-validation performed in the existing penalty techniques to obtain a…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…
Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of…
In this paper we address the stable numerical solution of nonlinear ill-posed systems by a trust-region method. We show that an appropriate choice of the trust-region radius gives rise to a procedure that has the potential to approach a…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
The Receding Horizon Control (RHC) strategy consists in replacing an infinite-horizon stabilization problem by a sequence of finite-horizon optimal control problems, which are numerically more tractable. The dynamic programming principle…
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
We reformulate a class of non-linear stochastic optimal control problems introduced by Todorov (2007) as a Kullback-Leibler (KL) minimization problem. As a result, the optimal control computation reduces to an inference computation and…
This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…