Belangrijkste concepten
Developing computationally efficient solutions for covariance control with chance constraints using output feedback.
Samenvatting
This paper explores the development of efficient solutions for steering state distribution between Gaussian distributions with chance constraints. It introduces a method using Kalman filters and DC constraints, showcasing its effectiveness on a double integrator example. Chance-constrained covariance steering problems are discussed, along with practical applications and data-driven control methods.
I. Introduction
- Covariance control aims to steer system states' distribution.
- Historical context from the 1980s to recent years.
- Practical applications involve constraints on state and control.
II. Problem Statement
- Notation conventions for vectors, matrices, and random variables.
- Formulation of the stochastic linear system dynamics and measurement model.
III. Kalman Filter
- Optimal observer for linear dynamics with a measurement model.
- State estimation updates using Kalman filter equations.
IV. Filtered State Control Design
- Affine filtered state feedback control design formulation.
- Separable cost function into mean and covariance costs.
V. Chance Constraints
- Imposing probabilistic constraints on state and input domains.
- Decomposition of joint chance constraints into individual ones.
VI. Numerical Example
- Illustration of OFCS algorithm on a double integrator system.
- Enforcement of state chance constraints with polytope definitions.
VII. Conclusion
- Extension of efficient CC-CS approach to partial state information cases.
- Introduction of DC constraints handling for chance constraints.
Statistieken
The proposed method is illustrated on a double integrator example with varying time horizons compared to other methods.
Citaten
"The efficiency of the proposed method is illustrated on a double integrator example."
"The proposed method introduces a novel approach to make the state and control chance constraints tractable."