A large number of practical algorithms for Optimal Control Problems (OCP) relies on a so-called condensing procedure to exploit the given structure in the quadratic programming (QP) subproblems. While the established structure-exploiting condensing algorithm is of cubic complexity in the horizon length, in this technical note we propose a novel algorithm that is only of … Read more
In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded L 1 -costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing a priori a global variable s heuristically, we show that there exist optimal policies for the infinite horizon … Read more
A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of functions describing the algorithmic steps. The optimization variables are the parameters – within this family of algorithms- that encode algorithm design: … Read more
We study the convergence rate of moment-sum-of-squares hierarchies of semidefinite programs for optimal control problems with polynomial data. It is known that these hierarchies generate polynomial under-approximations to the value function of the optimal control problem and that these under-approximations converge in the $L^1$ norm to the value function as their degree $d$ tends to … Read more
We consider the problem of minimization of the energy consumed by an electrical vehicle performing quite long travels with slopes. The model we address here, takes into account the electrical and mechanical differential equations of the vehicle. This yields a mixed-integer optimal control problem that can be approximated, using a methodology based on some decomposition … Read more
Quadratic programs (QP) with an indefinite Hessian matrix arise naturally in some direct optimal control methods, e.g. as subproblems in a sequential quadratic programming (SQP) scheme. Typically, the Hessian is approximated with a positive definite matrix to ensure having a unique solution; such a procedure is called \emph{regularization}. We present a novel regularization method tailored … Read more
Direct optimal control algorithms first discretize the continuous-time optimal control problem and then solve the resulting finite dimensional optimization problem. If Newton type optimization algorithms are used for solving the discretized problem, accurate first as well as second order sensitivity information needs to be computed. This article develops a novel approach for computing Hessian matrices … Read more
We propose to solve global optimal control problems with a new algorithm that is based on Bock’s direct multiple shooting method. We provide conditions and numerical evidence for a significant overall runtime reduction compared to the standard single shooting approach. CitationOptimal Control Applications and Methods, Vol. 39 (2), pp. 449–470, 2017 DOI 10.1002/oca.2324 Article online … Read more
In this paper we obtained an approach to the optimal switching control problem with unknown switching points which it is described in reference [1, 2]. In reference [1], the authors studied the Decomposition of Linear-Quadratic Optimal Control Problems for Two-Steps Systems. In [1], the authors assumed the switching point t1 is xed in the interval … Read more
Optimal control problems (OCP) containing both integrality and partial differential equation (PDE) constraints are very challenging in practice. The most wide-spread solution approach is to first discretize the problem, it results in huge and typically nonconvex mixed-integer optimization problems that can be solved to proven optimality only in very small dimensions. In this paper, we … Read more