Predictive Vehicle Control Under Chance Constraints
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Solution Overview
Problem
Stochastic nonlinear predictive control for systems with uncertainty faces high computational costs and memory requirements due to the need for exact linearization-based optimization, which is inefficient in real-time applications with limited resources.
Innovation Solution
An inexact derivative-based optimization algorithm that reduces computational complexity and memory requirements by using approximate linearization-based covariance propagation, eliminating covariance matrices, and employing adjoint gradient computations, allowing for efficient solution of inequality constrained nonlinear dynamic optimization problems with probabilistic chance constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exact linearization-based optimization is used for stochastic predictive control, then control accuracy and constraint satisfaction are improved, but computational complexity and memory requirements increase significantly
Solution Approach 1:
The patent replaces expensive exact linearization computations with cheaper approximate methods. Specifically, it uses pre-computed covariance matrices and simplified gradient calculations instead of performing full linearization at each optimization iteration, making the computational process more affordable for real-time embedded systems
Solution Approach 2:
The patent performs preliminary computations of covariance matrices and their inverses before the main optimization process. By pre-computing these quantities and storing them for reuse, the method avoids redundant calculations during real-time control, significantly reducing online computational burden while maintaining control accuracy
2Manufacturing precision
If exact linearization-based optimization is used for stochastic predictive control, then optimality of control solution is improved, but memory requirements increase significantly
Solution Approach 1:
The patent extracts and eliminates the covariance matrices from the optimization problem formulation. By using alternative representations and computational approaches that do not require storing these large matrices during optimization, the method significantly reduces memory requirements while preserving the ability to compute optimal control solutions
Solution Approach 2:
The patent uses simplified approximations and surrogate models instead of exact representations. By copying only the essential statistical properties needed for control rather than storing complete covariance information, the method reduces memory usage while maintaining sufficient accuracy for stochastic predictive control
3Reliability
If sampling techniques are used to characterize stochastic system dynamics, then probabilistic constraint formulation is improved, but computational cost increases due to large number of samples required
Solution Approach 1:
The patent changes the parameter representation from individual sample trajectories to aggregated statistical moments (covariance matrices). By working with second-order statistical properties rather than individual samples, the method captures probabilistic behavior with far fewer computational resources while maintaining the ability to formulate and satisfy probabilistic constraints
Data Source
AI summary
A predictive controller controls a system under uncertainty subject to constraints on state and control variables of the system. At each control step, the predictive controller solves an inequality constrained nonlinear dynamic optimization problem including probabilistic chance constraints representing the uncertainty to produce a control command, and controls an operation of the system using the control command. The predictive controller solves the dynamic optimization problem based on a two-level optimization that alternates, until a termination condition is met, propagation of covariance matrices of the probabilistic chance constraints within the prediction horizon for fixed values of the state and control variables with optimization of the state and control variables within the prediction horizon for fixed values of the covariance matrices.