An official website of the United States government
This paper introduces a method of identifying a maximal set of safe strategies from data for stochastic systems with unknown dynamics using barrier certificates. The first step is learning the dynamics of the system via Gaussian Process (GP) regression and obtaining probabilistic errors for this estimate. Then, we develop an algorithm for constructing piecewise stochastic barrier functions to find a maximal permissible strategy set using the learned GP model, which is based on sequentially pruning the worst controls until a maximal set is identified. The permissible strategies are guaranteed to maintain probabilistic safety for the true system. This is especially important for learned systems, because a rich strategy space enables additional data collection and complex behaviors while remaining safe. Case studies on linear and nonlinear systems demonstrate that increasing the size of the dataset for learning grows the permissible strategy set.
more »
« less
Backup Plan Constrained Model Predictive Control with Guaranteed Stability
Safe control designs for robotic systems remain challenging because of the difficulties of explicitly solving optimal control with nonlinear dynamics perturbed by stochastic noise. However, recent technological advances in computing devices enable online optimization or sampling-based methods to solve control problems. For example, Control Barrier Functions (CBFs) have been proposed to numerically solve convex optimization problems that ensure the control input to stay in the safe set. Model Predictive Path Integral (MPPI) control uses forward sampling of stochastic differential equations to solve optimal control problems online. Both control algorithms are widely used for nonlinear systems because they avoid calculating the derivatives of the nonlinear dynamic functions. In this paper, we use Stochastic Control Barrier Functions (SCBFs) constraints to limit sample regions in the samplingbased algorithm, ensuring safety in a probabilistic sense and improving sample efficiency with a stochastic differential equation. We also show that our algorithm needs fewer samples than the original MPPI algorithm does by providing a sampling complexity analysis.
more »
« less
- Award ID(s):
- 1932529
- PAR ID:
- 10482834
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- Journal of Guidance, Control, and Dynamics
- ISSN:
- 0731-5090
- Page Range / eLocation ID:
- 1 to 14
- Subject(s) / Keyword(s):
- Path Integral Methods, Stochastic Control, Barrier Functions
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstarct This work presents a theoretical framework for the safety‐critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay‐free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced, to attain formal safety guarantees by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.more » « less
-
Control barrier functions are mathematical constructs used to guarantee safety for robotic systems. When integrated as constraints in a quadratic programming optimization problem, instantaneous control synthesis with real-time performance demands can be achieved for robotics applications. Prevailing use has assumed full knowledge of the safety barrier functions, however there are cases where the safe regions must be estimated online from sensor measurements. In these cases, the corresponding barrier function must be synthesized online. This paper describes a learning framework for estimating control barrier functions from sensor data. Doing so affords system operation in unknown state space regions without compromising safety. Here, a support vector machine classifier provides the barrier function specification as determined by sets of safe and unsafe states obtained from sensor measurements. Theoretical safety guarantees are provided. Experimental ROS-based simulation results for an omnidirectional robot equipped with LiDAR demonstrate safe operation.more » « less
-
Soner, Mete (Ed.)We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then apply this algorithm to a variety of energy scheduling problems, including novel high-dimensional energy production problems. Our experimental results demonstrate that the algorithm performs with accuracy and experiences linear to sub-linear slowdowns as dimension increases, demonstrating the value of the algorithm for solving high-dimensional switching problem. Keywords. Deep neural networks, forward-backward systems of stochastic differential equations, optimal switching, Monte Carlo algorithm, optimal investment in power generation, planning problemsmore » « less
-
Abstract Practical engineering designs typically involve many load cases. For topology optimization with many deterministic load cases, a large number of linear systems of equations must be solved at each optimization step, leading to an enormous computational cost. To address this challenge, we propose a mirror descent stochastic approximation (MD-SA) framework with various step size strategies to solve topology optimization problems with many load cases. We reformulate the deterministic objective function and gradient into stochastic ones through randomization, derive the MD-SA update, and develop algorithmic strategies. The proposed MD-SA algorithm requires only low accuracy in the stochastic gradient and thus uses only a single sample per optimization step (i.e., the sample size is always one). As a result, we reduce the number of linear systems to solve per step from hundreds to one, which drastically reduces the total computational cost, while maintaining a similar design quality. For example, for one of the design problems, the total number of linear systems to solve and wall clock time are reduced by factors of 223 and 22, respectively.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.2514/1.G007627
