Nonlinear control systems: an introduction (2nd ed.)
Nonlinear control systems: an introduction (2nd ed.)
Lagrange multipliers and optimality
SIAM Review
Digital logic circuit analysis and design
Digital logic circuit analysis and design
New Necessary Conditions for the Generalized Problem of Bolza
SIAM Journal on Control and Optimization
Generation of Pseudospectral Differentiation Matrices I
SIAM Journal on Numerical Analysis
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
Journal of Optimization Theory and Applications
Rigid-Body Dynamics with Friction and Impact
SIAM Review
Spectral methods in MatLab
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
Convex Optimization
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming
Three-dimensional optimal deployment of a tethered subsatellite with an elastic tether
International Journal of Computer Mathematics - Computer Mathematics in Dynamics and Control
Modeling and optimal control of a nonlinear dynamical system in microbial fed-batch fermentation
Mathematical and Computer Modelling: An International Journal
| Hi-index | 0.98 |
Under appropriate conditions, the dynamics of a control system governed by ordinary differential equations can be formulated in several ways: differential inclusion, control parametrization, flatness parametrization, higher-order inclusions and so on. A plethora of techniques have been proposed for each of these formulations but they are typically not portable across equivalent mathematical formulations. Further complications arise as a result of configuration and control constraints such as those imposed by obstacle avoidance or control saturation. In this paper, we present a unified framework for handling the computation of optimal controls where the description of the governing equations or that of the path constraint is not a limitation. In fact, our method exploits the advantages offered by coordinate transformations and harnesses any inherent smoothness present in the optimal system trajectories. We demonstrate how our computational framework can easily and efficiently handle different cost formulations, control sets and path constraints. We illustrate our ideas by formulating a robotics problem in eight different ways, including a differentially flat formulation subject to control saturation. This example establishes the loss of convexity in the flat formulation as well as its ramifications for computation and optimality. In addition, a numerical comparison of our unified approach to a recent technique tailored for control-affine systems reveals that we get about 30% improvement in the performance index.