60 research outputs found
On the Sample Size of Random Convex Programs with Structured Dependence on the Uncertainty (Extended Version)
The "scenario approach" provides an intuitive method to address chance
constrained problems arising in control design for uncertain systems. It
addresses these problems by replacing the chance constraint with a finite
number of sampled constraints (scenarios). The sample size critically depends
on Helly's dimension, a quantity always upper bounded by the number of decision
variables. However, this standard bound can lead to computationally expensive
programs whose solutions are conservative in terms of cost and violation
probability. We derive improved bounds of Helly's dimension for problems where
the chance constraint has certain structural properties. The improved bounds
lower the number of scenarios required for these problems, leading both to
improved objective value and reduced computational complexity. Our results are
generally applicable to Randomized Model Predictive Control of chance
constrained linear systems with additive uncertainty and affine disturbance
feedback. The efficacy of the proposed bound is demonstrated on an inventory
management example.Comment: Accepted for publication at Automatic
Optimization under Uncertainty with Applications to Multi-Agent Coordination
In this thesis several approaches for optimization and decision-making under uncertainty with a strong focus on applications in multi-agent systems are considered. These approaches are chance constrained optimization, random convex programs, and partially observable Markov decision processes
Stochastic receding horizon control with output feedback and bounded controls
International audienceWe study the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and incomplete state information. Given a suitable choice of causal control policies, we first present a slight extension of the Kalman filter to estimate the state optimally in mean-square sense. We then show how to augment the underlying optimization problem with a negative drift-like constraint, yielding a second-order cone program to be solved periodically online. We prove that the receding horizon implementation of the resulting control policies renders the state of the overall system mean-square bounded under mild assumptions. We also discuss how some quantities required by the finite-horizon optimization problem can be computed off-line, thus reducing the on-line computation
Reliable autonomous vehicle control - a chance constrained stochastic MPC approach
In recent years, there is a growing interest in the development of systems capable of performing
tasks with a high level of autonomy without human supervision. This kind of systems are known as
autonomous systems and have been studied in many industrial applications such as automotive,
aerospace and industries. Autonomous vehicle have gained a lot of interest in recent years and have
been considered as a viable solution to minimize the number of road accidents. Due to the
complexity of dynamic calculation and the physical restrictions in autonomous vehicle, for example,
deterministic model predictive control is an attractive control technique to solve the problem of
path planning and obstacle avoidance. However, an autonomous vehicle should be capable of driving
adaptively facing deterministic and stochastic events on the road. Therefore, control design for
the safe, reliable and autonomous driving should consider vehicle model uncertainty as well
uncertain external influences. The stochastic model predictive control scheme provides the
most convenient scheme for the control of autonomous vehicles on moving horizons, where chance
constraints are to be used to guarantee the reliable fulfillment of trajectory constraints and
safety against static and random obstacles. To solve this kind of problems is known as chance
constrained model predictive control. Thus, requires the solution of a chance constrained
optimization on moving horizon. According to the literature, the major challenge for solving chance
constrained optimization is to calculate the value of probability. As a result, approximation
methods have been proposed for solving this task.
In the present thesis, the chance constrained optimization for the autonomous vehicle is solved
through approximation method, where the probability constraint is approximated by using a smooth
parametric function. This methodology presents two approaches that allow the solution of chance
constrained optimization problems in inner approximation and outer approximation. The aim of this
approximation methods is to reformulate the chance constrained optimizations problems as a sequence
of nonlinear programs. Finally, three case studies of autonomous vehicle for tracking and obstacle
avoidance are presented in this work, in which three levels probability of reliability are
considered
for the optimal solution.Tesi
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