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A class of computational methods for solving a wide variety of optimal control problems is presented; these problems include nonsmooth, nonlinear, switched optimal control problems, as well as standard multiphase problems. Methods are based on pseudospectral approximations of the differential constraints that are assumed to be given in the form of… (More)

- I. Michael Ross, Fariba Fahroo
- Mathematical and Computer Modelling
- 2006

Under appropriate conditions, the dynamics of a control system governed by ordinary differential equations can be formulated several ways: differential inclusion, control parameterization, flatness parameterization, higher-order inclusions and so on. A plethora of techniques have been proposed for each of these formulations but they are typically not… (More)

We consider nonlinear optimal control problems with mixed statecontrol constraints. A discretization of the Bolza problem by a Legendre pseudospectral method is considered. It is shown that the operations of discretization and dualization are not commutative. A set of Closure Conditions are introduced to commute these operations. An immediate consequence of… (More)

Recently, the Legendre pseudospectral (PS) method migrated from theory to flight application onboard the International Space Station for performing a finite-horizon, zeropropellant maneuver. A small technical modification to the Legendre PS method is necessary to manage the limiting conditions at infinity for infinite-horizon optimal control problems.… (More)

Acentral computational issue in solving infinite-horizonnonlinear optimal control problems is the treatment of the horizon. In this paper, we directly address this issue by a domain transformation technique that maps the infinite horizon to a finite horizon. The transformed finite horizon serves as the computational domain for an application of… (More)

- Yutaka Kanayama, Fariba Fahroo
- ICRA
- 1997

In this paper, we investigate the problem of finding an algorithm for the movement of a vehicle under the nonholonomic constraint to track a given directed straight lane without allowing any spinning motion. We propose a new principle of computing the derivative of path curvature as a linear combination of the current vehicle path curvature, vehicle… (More)

- Qi Gong, I. Michael Ross, Wei Kang, Fariba Fahroo
- Comp. Opt. and Appl.
- 2008

- I. Michael Ross, Fariba Fahroo
- IEEE Trans. Automat. Contr.
- 2004

This note presents some preliminary results on combining two new ideas from nonlinear control theory and dynamic optimization. We show that the computational framework facilitated by pseudospectral methods applies quite naturally and easily to Fliess’ implicit state variable representation of dynamical systems. The optimal motion planning problem for… (More)

Recent convergence results with pseudospectral methods are exploited to design a robust, multigrid, spectral algorithm for computing optimal controls. The design of the algorithm is based on using the pseudospectral differentiation matrix to locate switches, kinks, corners, and other discontinuities that are typical when solving practical optimal control… (More)

During the last decade, pseudospectral methods for optimal control, the focus of this tutorial session, have been rapidly developed as a powerful tool to enable new applications that were previously considered impossible due to the complicated nature of these problems. The purpose of this tutorial section is to introduce this advanced technology to a wider… (More)