Stochastic Predictive Control With Online Uncertainty Estimation
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Solution Overview
Problem
Current stochastic model predictive control (SMPC) systems assume predetermined offline uncertainty, which is restrictive as uncertainties often change with time and depend on system states, necessitating real-time updates and accurate uncertainty estimation for effective control.
Innovation Solution
The SMPC system incorporates an estimator that recursively determines uncertainty distributions online, allowing for state-dependent and state-independent uncertainty modeling, using Gaussian processes and weighted basis functions to update uncertainty estimates efficiently and accurately.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If SMPC uses predetermined offline uncertainty, then the control problem formulation is simpler, but the controller cannot adapt to time-varying uncertainties
Solution Approach 1:
The patent implements dynamic uncertainty estimation by using recursive algorithms that update uncertainty parameters online based on current system state and measurements. The uncertainty model transitions from static predetermined values to dynamic time-varying estimates that adapt to changing system conditions, resolving the contradiction between adaptability and complexity.
Solution Approach 2:
The patent incorporates feedback mechanisms where system measurements and state estimates are continuously fed back to update the uncertainty parameters. This closed-loop uncertainty estimation allows the controller to adapt to time-varying uncertainties while maintaining computational tractability through efficient recursive updates.
2Reliability
If SMPC incorporates probabilistic description of uncertainties, then control performance near constraint boundaries is improved, but computational tractability is reduced
Solution Approach 1:
The patent transforms the computationally intractable chance constraints into tractable forms by parameterizing the probability distributions of uncertainties and using moment-matching techniques. This allows the SMPC to incorporate probabilistic descriptions while maintaining computational feasibility through efficient parameter-based formulations.
Solution Approach 2:
The patent uses approximate formulations of chance constraints that are computationally efficient, sacrificing some precision for tractability. These approximate constraints provide sufficient reliability for practical applications while keeping the computational burden manageable.
3Reliability
If robust MPC uses worst-case scenarios, then safety-critical constraints are guaranteed, but control performance becomes conservative
Solution Approach 1:
The patent applies partial probabilistic constraints rather than requiring satisfaction with probability one. By allowing small violation probabilities for non-critical constraints while maintaining strict guarantees for safety-critical ones, the controller achieves better performance without compromising essential safety requirements.
Solution Approach 2:
The patent differentiates between safety-critical constraints and performance constraints, applying different levels of probabilistic guarantee to each. Safety-critical constraints receive strict guarantees while performance constraints use softer probabilistic formulations, achieving local optimization of both reliability and productivity.
Data Source
AI summary
A stochastic model predictive controller (SMPC) estimates a current state of the system and a probability distribution of uncertainty of a parameter of dynamics of the system based on measurements of outputs of the system, and updates a control model of the system including a function of dynamics of the system modeling the uncertainty of the parameter with first and second order moments of the estimated probability distribution of uncertainty of the parameter. The SMPC determines a control input to control the system by optimizing the updated control model of the system at the current state over a prediction horizon and controls the system based on the control input to change the state of the system.