10,165 research outputs found
Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems
We show that, near periodic orbits, a class of hybrid models can be reduced
to or approximated by smooth continuous-time dynamical systems. Specifically,
near an exponentially stable periodic orbit undergoing isolated transitions in
a hybrid dynamical system, nearby executions generically contract
superexponentially to a constant-dimensional subsystem. Under a non-degeneracy
condition on the rank deficiency of the associated Poincare map, the
contraction occurs in finite time regardless of the stability properties of the
orbit. Hybrid transitions may be removed from the resulting subsystem via a
topological quotient that admits a smooth structure to yield an equivalent
smooth dynamical system. We demonstrate reduction of a high-dimensional
underactuated mechanical model for terrestrial locomotion, assess structural
stability of deadbeat controllers for rhythmic locomotion and manipulation, and
derive a normal form for the stability basin of a hybrid oscillator. These
applications illustrate the utility of our theoretical results for synthesis
and analysis of feedback control laws for rhythmic hybrid behavior
Learning an Approximate Model Predictive Controller with Guarantees
A supervised learning framework is proposed to approximate a model predictive
controller (MPC) with reduced computational complexity and guarantees on
stability and constraint satisfaction. The framework can be used for a wide
class of nonlinear systems. Any standard supervised learning technique (e.g.
neural networks) can be employed to approximate the MPC from samples. In order
to obtain closed-loop guarantees for the learned MPC, a robust MPC design is
combined with statistical learning bounds. The MPC design ensures robustness to
inaccurate inputs within given bounds, and Hoeffding's Inequality is used to
validate that the learned MPC satisfies these bounds with high confidence. The
result is a closed-loop statistical guarantee on stability and constraint
satisfaction for the learned MPC. The proposed learning-based MPC framework is
illustrated on a nonlinear benchmark problem, for which we learn a neural
network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter
3 sampled-data control of nonlinear systems
This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring the basic parts of the new developments within the comfortable grasp of graduate students. Instead of presenting the more general results that are available in the literature, we opted to present their less general versions that are easier to understand and whose proofs are easier to follow. We note that some of the proofs we present have not appeared in the literature in this simplified form. Hence, we believe that this chapter will serve as an important reference for students and researchers that are willing to learn about this area of research
Data-driven control design for neuroprotheses: a virtual reference feedback tuning (VRFT) approach
This paper deals with design of feedback controllers for knee joint movement of paraplegics using functional electrical stimulation (FES) of the paralyzed quadriceps muscle group. The controller design approach, virtual reference feedback tuning (VRFT), is directly based on open loop measured data and fits the controller in such a way that the closed-loop meets a model reference objective. The use of this strategy, avoiding the modeling step, significantly reduces the time required for controller design and considerably simplifies the rehabilitation protocols. Linear and nonlinear controllers have been designed and experimentally tested, preliminarily on a healthy subject and finally on a paraplegic patient. Linear controller is effective when applied on small range of knee joint angle. The design of a nonlinear controller allows better performances. It is also shown that the control design is effective in tracking assigned knee angle trajectories and rejecting disturbances
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