Model Reduction of Parabolic PDEs using Multivariate Splines

A new methodology is presented for model reduction of linear parabolic partial differential equations (PDEs) on general geometries using multivariate splines on triangulations. State-space descriptions are derived that can be used for control design. This method uses Galerkin projection with B-splines to derive a finite set of ordinary...

A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines

This paper presents a sparse collocation method for solving the time-dependent Hamilton–Jacobi–Bellman (HJB) equation associated with the continuous-time optimal control problem on a fixed, finite timehorizon with integral cost functional. Through casting the problem in a recursive framework using the value iteration procedure, the value...

An optimal control framework for estimating autopilot safety margins

This paper presents an optimal control framework to determine a collection of open-loop command signals that mathematically guarantees operation of an aircraft within certain prescribed state constraints. The framework is specifically applied to estimate margins for the reference command inputs of aircraft autopilot systems, so that safe...

Nonlinear Multivariate Spline-Based Control Allocation for High-Performance Aircraft

High performance flight control systems based on the nonlinear dynamic inversion (NDI) principle require highly accurate models of aircraft aerodynamics. In general, the accuracy of the internal model determines to what degree the system nonlinearities can be canceled; the more accurate the model, the better the cancellation, and with that, the...

Online Aerodynamic Model Identification using a Recursive Sequential Method for Multivariate Splines

Avoiding high computational loads is essential to online aerodynamic model identi- fication algorithms, which are at the heart of any model-based adaptive flight control system. Multivariate simplex B-spline (MVSB) methods are excellent function approximation tools for modeling the nonlinear aerodynamics of high performance aircraft. However,...

Differential constraints for bounded recursive identification with multivariate splines

The ability to perform online model identification for nonlinear systems with unknown dynamics is essential to any adaptive model-based control system. In this paper, a new differential equality constrained recursive least squares estimator for multivariate simplex splines is presented that is able to perform online model identification and...

A new approach to linear regression with multivariate splines

A new methodology for creating highly accurate, static nonlinear maps from scattered, multivariate data is presented. This new methodology uses the B-form polynomials of multivariate simplex splines in a new linear regression scheme. This allows the use of standard parameter estimation techniques for estimating the B-coefficients of the...