Design of multi-parametric NCO tracking controllers for linear dynamic systems

© 2016 The Authors.A methodology for combining multi-parametric programming and NCO tracking is presented in the case of linear dynamic systems. The resulting parametric controllers consist of (potentially nonlinear) feedback laws for tracking optimality conditions by exploiting the underlying optimal control switching structure. Compared to the classical multi-parametric MPC controller, this approach leads to a reduction in the number of critical regions. It calls for the solution of more difficult parametric optimization problems with linear differential equations embedded, whose critical regions are potentially nonconvex. Examples of constrained linear quadratic optimal control problems with parametric uncertainty are presented to illustrate the approach

The extended symplectic pencil and the finite-horizon LQ problem with two-sided boundary conditions

This note introduces a new analytic approach to the solution of a very general class of finite-horizon optimal control problems formulated for discrete-time systems. This approach provides a parametric expression for the optimal control sequences, as well as the corresponding optimal state trajectories, by exploiting a new decomposition of the so-called extended symplectic pencil. Importantly, the results established in this paper hold under assumptions that are weaker than the ones considered in the literature so far. Indeed, this approach does not require neither the regularity of the symplectic pencil, nor the modulus controllability of the underlying system. In the development of the approach presented in this paper, several ancillary results of independent interest on generalised Riccati equations and on the eigenstructure of the extended symplectic pencil will also be presented

Optimal control for halo orbit missions

This paper addresses the computation of the required trajectory correction maneuvers (TCM) for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combiningdynamical systems theory with optimal control techniques, we produce a portrait of the complex landscape of the trajectory design space. This approach enables parametric studies not available to mission designers a few years ago, such as how the magnitude of the errors and the timingof the first TCM affect the correction ΔV. The impetus for combiningdynamical systems theory and optimal control in this problem arises from design issues for the Genesis Discovery mission being developed for NASA by the Jet Propulsion Laboratory

Swing Contract Pricing: A Parametric Approach with Adjoint Automatic Differentiation and Neural Networks

We propose two parametric approaches to price swing contracts with firm constraints. Our objective is to create approximations for the optimal control, which represents the amounts of energy purchased throughout the contract. The first approach involves explicitly defining a parametric function to model the optimal control, and the parameters using stochastic gradient descent-based algorithms. The second approach builds on the first one, replacing the parameters with neural networks. Our numerical experiments demonstrate that by using Langevin-based algorithms, both parameterizations provide, in a short computation time, better prices compared to state-of-the-art methods (like the one given by Longstaff and Schwartz).Comment: 33 page

Pseudo-spectral method to control three-degree-of-freedom wave energy converters

The invention provides optimal control of a three-degree-of-freedom wave energy converter using a pseudo-spectral control method. The three modes are the heave, pitch and surge. A dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. The invention can use a Fourier series as basis functions to approximate the states and the control. For the parametric excited case, a sequential quadratic programming approach can be implemented to numerically solve for the optimal control. The numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.https://digitalcommons.mtu.edu/patents/1143/thumbnail.jp

On the P-coverage Problem on the Real Line

Abstract: In this paper we consider the p-coverage problem on the real line. We first give a detailed description of an algorithm to solve the coverage problem without the upper bound p on the number of open facilities. Then we analyze how the structure of the optimal solution changes if the setup costs of the facilities are all decreased by the same amount. This result is used to develop a parametric approach to the p-coverage problem which runs in O(pnlogn) time, n being the number of clients. OR/MS subject classification: Analysis of algorithms, computational complexity: parametric application of dynamic programming; Dynamic programming/optimal control, applications: parametric approach to p-coverage problem on the real line; Facilities/equipment planning, location, discrete: p-coverage problem on the real line