6,333 research outputs found
Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control
Variational integrators are well-suited for simulation of mechanical systems
because they preserve mechanical quantities about a system such as momentum, or
its change if external forcing is involved, and holonomic constraints. While
they are not energy-preserving they do exhibit long-time stable energy
behavior. However, variational integrators often simulate mechanical system
dynamics by solving an implicit difference equation at each time step, one that
is moreover expressed purely in terms of configurations at different time
steps. This paper formulates the first- and second-order linearizations of a
variational integrator in a manner that is amenable to control analysis and
synthesis, creating a bridge between existing analysis and optimal control
tools for discrete dynamic systems and variational integrators for mechanical
systems in generalized coordinates with forcing and holonomic constraints. The
forced pendulum is used to illustrate the technique. A second example solves
the discrete LQR problem to find a locally stabilizing controller for a 40 DOF
system with 6 constraints.Comment: 13 page
Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control
Variational integrators are well-suited for simulation of mechanical systems
because they preserve mechanical quantities about a system such as momentum, or
its change if external forcing is involved, and holonomic constraints. While
they are not energy-preserving they do exhibit long-time stable energy
behavior. However, variational integrators often simulate mechanical system
dynamics by solving an implicit difference equation at each time step, one that
is moreover expressed purely in terms of configurations at different time
steps. This paper formulates the first- and second-order linearizations of a
variational integrator in a manner that is amenable to control analysis and
synthesis, creating a bridge between existing analysis and optimal control
tools for discrete dynamic systems and variational integrators for mechanical
systems in generalized coordinates with forcing and holonomic constraints. The
forced pendulum is used to illustrate the technique. A second example solves
the discrete LQR problem to find a locally stabilizing controller for a 40 DOF
system with 6 constraints.Comment: 13 page
On the Benefits of Surrogate Lagrangians in Optimal Control and Planning Algorithms
This paper explores the relationship between numerical integrators and
optimal control algorithms. Specifically, the performance of the differential
dynamical programming (DDP) algorithm is examined when a variational integrator
and a newly proposed surrogate variational integrator are used to propagate and
linearize system dynamics. Surrogate variational integrators, derived from
backward error analysis, achieve higher levels of accuracy while maintaining
the same integration complexity as nominal variational integrators. The
increase in the integration accuracy is shown to have a large effect on the
performance of the DDP algorithm. In particular, significantly more optimized
inputs are computed when the surrogate variational integrator is utilized
Crone control of a nonlinear hydraulic actuator
The CRONE control (fractional robust control) of a hydraulic actuator whose dynamic model is nonlinear is presented. An input-output linearization under diffeomorphism and feedback is first achieved for the nominal plant. The relevance of this linearization when the parameters of the plant vary is then analyzed using the Volterra input-output representation in the frequency domain. CRONE control based on complex fractional differentiation is finally applied to control the velocity of the input-output linearized model when parametric variations occur
Robust nonlinear control of vectored thrust aircraft
An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations
Parameter estimation in softmax decision-making models with linear objective functions
With an eye towards human-centered automation, we contribute to the
development of a systematic means to infer features of human decision-making
from behavioral data. Motivated by the common use of softmax selection in
models of human decision-making, we study the maximum likelihood parameter
estimation problem for softmax decision-making models with linear objective
functions. We present conditions under which the likelihood function is convex.
These allow us to provide sufficient conditions for convergence of the
resulting maximum likelihood estimator and to construct its asymptotic
distribution. In the case of models with nonlinear objective functions, we show
how the estimator can be applied by linearizing about a nominal parameter
value. We apply the estimator to fit the stochastic UCL (Upper Credible Limit)
model of human decision-making to human subject data. We show statistically
significant differences in behavior across related, but distinct, tasks.Comment: In pres
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