Deterministic Optimization Control for Fast Dynamic Systems
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Solution Overview
Problem
Optimization-based control (OBC) systems for complex dynamic control systems are computationally demanding, making them inefficient for real-time control due to the complexity of solving constrained optimization problems like quadratic programming, which can take seconds or minutes, and are not well-suited for systems with fast dynamics.
Innovation Solution
A deterministic optimization-based control method that includes determining a linear approximation of a non-linear process model, convexifying constraints, and using a stabilization function to find a feasible control trajectory within a predetermined time window, employing a deterministic solver like a primal active set method to efficiently manage complex constraints and reduce computational load.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If general optimization solvers are used to solve constrained optimization problems, then optimal control performance is achieved, but computation time becomes too long (seconds or minutes)
Solution Approach 1:
The patent pre-calculates and stores the null space basis matrices and other decomposition results offline before real-time control. This preliminary action transforms the complex online optimization into a simpler problem that only requires solving linear equations with pre-computed matrices, dramatically reducing real-time computation time while maintaining optimality.
Solution Approach 2:
The patent segments the optimization problem into offline preprocessing (computing null space basis, system decomposition) and online execution (solving simplified linear equations). This segmentation allows computationally intensive operations to be performed once offline, while real-time control only requires lightweight calculations.
2Speed
If deterministic control time is enforced for fast dynamic systems, then real-time control capability is achieved, but the optimization problem becomes more constrained and harder to solve
Solution Approach 1:
The patent changes the parameters of the optimization problem by transforming it into a specific form where the Hessian matrix has a particular structure (combining quadratic cost and linear constraints). This parameter transformation enables the use of efficient deterministic algorithms like active set methods that can guarantee solutions within predetermined time for fast dynamic systems.
Solution Approach 2:
The patent replaces general-purpose optimization solvers with a specialized deterministic solver tailored for the specific control problem structure. This substitution uses mathematical properties of the control problem (null space projection, active set methods) to create a more efficient solution mechanism that guarantees real-time performance.
3Reliability
If complex constrained optimization is solved in real-time, then optimal control is achieved, but computational burden becomes too high for embedded systems
Solution Approach 1:
The patent performs computationally intensive operations (matrix decompositions, null space calculations) as preliminary actions during offline setup. This shifts the computational burden from real-time execution to offline preprocessing, enabling embedded systems with limited processing power to run the control algorithm efficiently in real-time.
Solution Approach 2:
The patent extracts and removes the computationally intensive parts of the optimization problem (Hessian matrix inversion, constraint qualification checks) from the real-time execution loop. These operations are pre-computed and stored, leaving only simple linear equation solutions for real-time implementation on embedded systems.
Data Source
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AI summary
The embodiments described herein include one embodiment that provides a control method including determining a linear approximation of a pre-determined non-linear model of a process to be controlled, determining a convex approximation of the nonlinear constraint set, determining an initial stabilizing feasible control trajectory for a plurality of sample periods of a control trajectory, executing an optimization-based control algorithm to improve the initial stabilizing feasible control trajectory for a plurality of sample periods of a control trajectory, and controlling the controlled process by application.