Related papers: Mesh Refinement Method for Solving Bang-Bang Optim…
A study is conducted to evaluate four derivative estimation methods when solving a large sparse nonlinear programming problem that arises from the approximation of an optimal control problem using a direct collocation method. In particular,…
The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal…
This paper is devoted to the analysis of periodic solutions of nonlinear control-affine systems with bang-bang controls. Such problems naturally arise in periodic optimal control with constrained inputs, which have, in particular, important…
This paper presents an optimization framework for sequential reconfiguration using an assortment of switching devices and repair process in distribution system restoration. Compared to existing studies, this paper considers types,…
In this paper, we present a novel solution for real-time, Non-Linear Model Predictive Control (NMPC) exploiting a time-mesh refinement strategy. The proposed controller formulates the Optimal Control Problem (OCP) in terms of flat outputs…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition…
Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained…
A computational method is developed for desensitized optimal guidance using adaptive Gaussian quadrature collocation. The method computes a reference trajectory that reduces the sensitivity to uncertainties in the dynamic model by…
In this paper, we investigate solution stability for control problems of partial differential equations with the cost functional not involving the usual quadratic term for the control. We first establish a sufficient optimality condition…
To manipulate the protein population at certain functional state through chemical stabilizers is crucial for protein-related studies. It not only plays a key role in protein structure analysis and protein folding kinetics, but also affects…
In this paper the empirical observability Gramian calculated around the operating region of a power system is used to quantify the degree of observability of the system states under specific phasor measurement unit (PMU) placement. An…
In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic…
Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach addresses this challenge by solving a corresponding relaxed optimal control problem with only…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
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…
A general-purpose C++ software program called $\mathbb{CGPOPS}$ is described for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation. The software employs a Legendre-Gauss-Radau direct orthogonal…
Direct collocation methods are widely used numerical techniques for solving optimal control problems. The discretization of continuous-time optimal control problems transforms them into large-scale nonlinear programming problems, which…