State Space Model Estimation for Controllable ODE-Based Systems
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Solution Overview
Problem
In modeling a target system with a discrete time state space model, existing methods fail to ensure controllability, which is crucial for controlling the system, as controllability is often overlooked and can result in models that are not usable for control purposes.
Innovation Solution
A model estimation system that constructs and estimates a discrete time state space model using matrices with only some elements as unknown, allowing for the estimation of these unknowns using input data and past states, ensuring the model has controllability by representing the system with ordinary differential equations and observable states.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing methods are used to model a target system with a discrete time state space model, then the modeling process is simple and follows conventional approaches, but the resulting model lacks controllability and cannot be used for control purposes
Solution Approach 1:
The patent transforms the continuous-time system parameters (matrices A, B, C, D) into discrete-time parameters (matrices Φ, Γ, H, J) through mathematical transformation. This parameter change enables the model to achieve controllability in discrete time while maintaining the underlying system dynamics, resolving the contradiction between model reliability and modeling complexity
Solution Approach 2:
The patent segments the modeling process into distinct stages: (1) obtaining continuous-time system parameters from measurement data, (2) transforming these parameters to discrete-time parameters using mathematical relationships, and (3) constructing the discrete-time state space model. This segmentation makes the complex controllability assurance process manageable and systematic
2Reliability
If measurement data is obtained from a physical system to create a state space model, then the model can be constructed from real system behavior, but the model may still lack controllability if conventional estimation methods are used
Solution Approach 1:
The patent uses measurement data from the physical system as feedback to estimate the continuous-time system parameters, which are then transformed into discrete-time parameters. This feedback mechanism ensures the model accurately represents the actual system behavior while maintaining controllability through the structured parameter transformation approach
Solution Approach 2:
By changing the parameter representation from continuous-time to discrete-time through mathematical transformation, the patent ensures that the model maintains both accuracy (faithfulness to measured system behavior) and controllability (ability to be used for control purposes)
Data Source
AI summary
A model estimation system estimates a model of a system represented by an ordinary differential equation with all coefficients being non-zero, and with which input data and a state at each time can be obtained. When an order of the ordinary differential equation and input data and a state at multiple past times in the system are inputted, a model expression construction unit constructs an expression representing a model by using a first matrix that is a matrix according to the order and has only some elements as unknown elements and a second matrix that is a matrix according to the order and has only some one element as an unknown element. A model estimation unit uses input data and a state at multiple past times, to estimate the model by learning unknown elements of the first matrix and the unknown element of the second matrix.