Extremum-Seeking Control with Stochastic Gradient Estimation
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Solution Overview
Problem
Existing extremum-seeking control systems face challenges in efficiently estimating the gradient of an unknown cost function for systems with multiple actuators, leading to computationally burdensome and sometimes impractical excitation of all setpoints, especially when some setpoints are fixed or constrained, making real-time optimization of energy consumption difficult.
Innovation Solution
A stochastic gradient descent algorithm is employed to estimate the full gradient of the cost function based on partial gradients from subsets of setpoints, allowing for dynamic optimization of multiple actuators while accounting for non-controllable or constrained setpoints, thereby optimizing energy consumption in systems like HVAC and solar thermal power plants.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all setpoints are excited to estimate the full gradient of the cost function, then the optimization accuracy is improved, but the computational burden increases significantly
Solution Approach 1:
The patent segments the setpoints into multiple subsets and assigns different excitations to each subset. Instead of exciting all setpoints simultaneously, the gradient estimation is divided into multiple smaller tasks, each handling a subset of setpoints. This segmentation reduces the computational burden of each individual estimation while collectively achieving full gradient estimation through aggregation of subset gradients.
Solution Approach 2:
The patent applies partial action by exciting only a subset of setpoints at each time step rather than all setpoints. The stochastic gradient estimation method uses partial gradient information from selected subsets to approximate the full gradient, reducing the immediate computational load while maintaining optimization effectiveness through iterative updates.
2Loss of information
If all setpoints are excited in real-time, then the complete gradient information is obtained, but the real-time computational efficiency deteriorates
Solution Approach 1:
The gradient estimation process is segmented across multiple time steps and subset combinations. Each time step processes a manageable subset of excitations, and the results are aggregated over time to build complete gradient information. This approach maintains real-time efficiency by limiting per-step computation while ensuring information completeness through temporal accumulation.
Solution Approach 2:
The patent employs periodic excitation patterns where different subsets of setpoints are excited in a cyclic or scheduled manner. This periodic action ensures that all setpoints are eventually excited and gradient information is collected comprehensively, while maintaining real-time efficiency by distributing the computational load across multiple periodic cycles rather than requiring simultaneous processing of all setpoints.
3Productivity
If the ESC optimizes multiple actuators collectively, then the system performance is improved, but the number of setpoints to be excited increases making the process impractical
Solution Approach 1:
The patent segments the actuator control into multiple subsets, where each subset is optimized with its own excitation signals. This segmentation makes the control process more manageable and practical to implement, as each subset can be handled independently with reduced computational resources, while collectively all actuators are optimized for improved system performance.
Solution Approach 2:
The patent applies partial action by optimizing a subset of actuators at each time step rather than all actuators simultaneously. This approach makes the optimization process practically implementable by reducing the immediate operational complexity, while still achieving collective optimization of all actuators through iterative sequential updates.
Data Source
AI summary
A control system for controlling a set of actuators of a system. The control system comprising a switcher configured to select a subset of setpoints from a set of setpoints that control the corresponding set of actuators. An extremum-seeking controller (ESC) configured to perturb a subset of setpoints at each iteration based on a probabilistic distribution of partial gradients of a cost function relating values of the subset of setpoints to a cost of operation of the system. A stochastic gradient estimator is configured to estimate a full gradient of the cost function and update the estimation of the full gradient based on the probabilistic distribution of the partial gradients generated at each ESC iteration. A feedback controller is configured to drive a state of the subset of actuators of the system towards the corresponding perturbed subset of setpoints.