3 research outputs found
Voronoi Partition-based Scenario Reduction for Fast Sampling-based Stochastic Reachability Computation of LTI Systems
In this paper, we address the stochastic reach-avoid problem for linear
systems with additive stochastic uncertainty. We seek to compute the maximum
probability that the states remain in a safe set over a finite time horizon and
reach a target set at the final time. We employ sampling-based methods and
provide a lower bound on the number of scenarios required to guarantee that our
estimate provides an underapproximation. Due to the probabilistic nature of the
sampling-based methods, our underapproximation guarantee is probabilistic, and
the proposed lower bound can be used to satisfy a prescribed probabilistic
confidence level. To decrease the computational complexity, we propose a
Voronoi partition-based to check the reach-avoid constraints at representative
partitions (cells), instead of the original scenarios. The state constraints
arising from the safe and target sets are tightened appropriately so that the
solution provides an underapproximation for the original sampling-based method.
We propose a systematic approach for selecting these representative cells and
provide the flexibility to trade-off the number of cells needed for accuracy
with the computational cost.Comment: Under review at American Control Conference, 201
Sample Truncation for Scenario Approach to Closed-loop Chance Constrained Trajectory Optimization for Linear Systems
This paper studies closed-loop chance constrained control problems with
disturbance feedback (equivalently state feedback) where state and input
vectors must remain in a prescribed polytopic safe region with a predefined
confidence level. We propose to use a scenario approach where the uncertainty
is replaced with a set of random samples (scenarios). Though a standard form of
scenario approach is applicable in principle, it typically requires a large
number of samples to ensure the required confidence levels. To resolve this
drawback, we propose a method to reduce the computational complexity by
eliminating the redundant samples and, more importantly, by truncating the less
informative samples. Unlike the prior methods that start from the full sample
set and remove the less informative samples at each step, we sort the samples
in a descending order by first finding the most dominant ones. In this process
the importance of each sample is measured via a proper mapping. Then the most
dominant samples can be selected based on the allowable computational
complexity and the rest of the samples are truncated offline. The truncation
error is later compensated for by adjusting the safe regions via properly
designed buffers, whose sizes are functions of the feedback gain and the
truncation error.Comment: 8 pages, 3 figure
Contingency Model Predictive Control for Linear Time-Varying Systems
We present Contingency Model Predictive Control (CMPC), a motion planning and
control framework that optimizes performance objectives while simultaneously
maintaining a contingency plan -- an alternate trajectory that avoids a
potential hazard. By preserving the existence of a feasible avoidance
trajectory, CMPC anticipates emergency and keeps the controlled system in a
safe state that is selectively robust to the identified hazard. We accomplish
this by adding an additional prediction horizon in parallel to the typical
Model Predictive Control (MPC) horizon. This extra horizon is constrained to
guarantee safety from the contingent threat and is coupled to the nominal
horizon at its first command. Thus, the two horizons negotiate to compute
commands that are both optimized for performance and robust to the contingent
event. This article presents a linear formulation for CMPC, illustrates its key
features on a toy problem, and then demonstrates its efficacy experimentally on
a full-size automated road vehicle that encounters a realistic pop-out
obstacle. Contingency MPC approaches potential emergencies with safe,
intuitive, and interpretable behavior that balances conservatism with incentive
for high performance operation.Comment: Preprint of manuscript submitted for peer review to Transactions on
Control Systems Technology. 12 pages, 14 figures, 1 tabl