1,067 research outputs found
Analysis of Theoretical and Numerical Properties of Sequential Convex Programming for Continuous-Time Optimal Control
Sequential Convex Programming (SCP) has recently gained significant
popularity as an effective method for solving optimal control problems and has
been successfully applied in several different domains. However, the
theoretical analysis of SCP has received comparatively limited attention, and
it is often restricted to discrete-time formulations. In this paper, we present
a unifying theoretical analysis of a fairly general class of SCP procedures for
continuous-time optimal control problems. In addition to the derivation of
convergence guarantees in a continuous-time setting, our analysis reveals two
new numerical and practical insights. First, we show how one can more easily
account for manifold-type constraints, which are a defining feature of optimal
control of mechanical systems. Second, we show how our theoretical analysis can
be leveraged to accelerate SCP-based optimal control methods by infusing
techniques from indirect optimal control
Earlier Identification of Medications Needing Prior Authorization Can Reduce Delays in Hospital Discharge
Based on our experience, there are no studies that evaluate delays due to discharge medications needing to undergo the PA process. Thus, in our pilot study, we both aim to define the scope of this problem by surveying resident physicians as well as provide an intervention to identify earlier medications that will need to undergo a PA process. Pharmacy-led interventions in processing PAs have resulted in a statistically significant benefit in improving time to PA approval, fill, and pickup.5 Therefore, in our intervention, we utilize a specialized \u27transitions of care\u27 (TOC) pharmacist to analyze the medications of patients who are predicted to be discharged and alert the medical team of potential medications that may need PA approval, with the intended effect that this process will start long before a patient is actually discharged
Exact Characterization of the Convex Hulls of Reachable Sets
We study the convex hulls of reachable sets of nonlinear systems with bounded
disturbances. Reachable sets play a critical role in control, but remain
notoriously challenging to compute, and existing over-approximation tools tend
to be conservative or computationally expensive. In this work, we exactly
characterize the convex hulls of reachable sets as the convex hulls of
solutions of an ordinary differential equation from all possible initial values
of the disturbances. This finite-dimensional characterization unlocks a tight
estimation algorithm to over-approximate reachable sets that is significantly
faster and more accurate than existing methods. We present applications to
neural feedback loop analysis and robust model predictive control
Risk-Averse Trajectory Optimization via Sample Average Approximation
Trajectory optimization under uncertainty underpins a wide range of
applications in robotics. However, existing methods are limited in terms of
reasoning about sources of epistemic and aleatoric uncertainty, space and time
correlations, nonlinear dynamics, and non-convex constraints. In this work, we
first introduce a continuous-time planning formulation with an
average-value-at-risk constraint over the entire planning horizon. Then, we
propose a sample-based approximation that unlocks an efficient,
general-purpose, and time-consistent algorithm for risk-averse trajectory
optimization. We prove that the method is asymptotically optimal and derive
finite-sample error bounds. Simulations demonstrate the high speed and
reliability of the approach on problems with stochasticity in nonlinear
dynamics, obstacle fields, interactions, and terrain parameters
Sequential Convex Programming For Non-Linear Stochastic Optimal Control
This work introduces a sequential convex programming framework to solve
general non-linear, finite-dimensional stochastic optimal control problems,
where uncertainties are modeled by a multidimensional Wiener process. We
provide sufficient conditions for the convergence of the method. Moreover, we
prove that when convergence is achieved, sequential convex programming finds a
candidate locally-optimal solution for the original problem in the sense of the
stochastic Pontryagin Maximum Principle. We then leverage these properties to
design a practical numerical method for solving non-linear stochastic optimal
control problems based on a deterministic transcription of stochastic
sequential convex programming.Comment: Free-final-time problems with stochastic controls are now discussed
in a separate sectio
Estimating the Convex Hull of the Image of a Set with Smooth Boundary: Error Bounds and Applications
We study the problem of estimating the convex hull of the image
of a compact set with smooth
boundary through a smooth function . Assuming
that is a submersion, we derive a new bound on the Hausdorff distance
between the convex hull of and the convex hull of the images of
sampled inputs on the boundary of . When applied to the problem of
geometric inference from a random sample, our results give tighter and more
general error bounds than the state of the art. We present applications to the
problems of robust optimization, of reachability analysis of dynamical systems,
and of robust trajectory optimization under bounded uncertainty.Comment: The error bound in Theorem 1.1 is tighter in this revisio
A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis
In this work, we analyze an efficient sampling-based algorithm for
general-purpose reachability analysis, which remains a notoriously challenging
problem with applications ranging from neural network verification to safety
analysis of dynamical systems. By sampling inputs, evaluating their images in
the true reachable set, and taking their -padded convex hull as a set
estimator, this algorithm applies to general problem settings and is simple to
implement. Our main contribution is the derivation of asymptotic and
finite-sample accuracy guarantees using random set theory. This analysis
informs algorithmic design to obtain an -close reachable set
approximation with high probability, provides insights into which reachability
problems are most challenging, and motivates safety-critical applications of
the technique. On a neural network verification task, we show that this
approach is more accurate and significantly faster than prior work. Informed by
our analysis, we also design a robust model predictive controller that we
demonstrate in hardware experiments
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