From model-based control to data-driven control, Survey, classification and perspective
#AdaptiveControl #DataDrivenControl
This paper is a survey of Data-driven Control.
[! summary] Summary The paper starts with model-based controllers (MBC) and points out their need for an accurate or at least a good-enough model and proceeds to draw attention to the difficulty of deriving such a model. Four classes of systems are defined based on the accuracy of their model and data-driven control is then suggested as the solution to the most difficult classes to deal with. Different DDC (data-driven control) methods are categorized into 3 main catogories:
- Online data-based DDC Several famous DDC methods in this category are mentioned:
SPSA Simultaneous perturbation stochastic approximation (SPSA) works like this: The controller serves as a function approximator whose structure is fixed. Its parameters are then tuned using system’s I/O data. The inputs of the controller are \(y(k),y(k-1),...,y(k-M+1),u(k-1),u(k-2),...,u(k-n),y_d(k+1)\) and $u(k)$ is its output. The aim of controller design is to minimize \(J-k(\theta_k)=E{(y(\theta_k,k+1)-y_d(k+1))^2}\) where $y_d(k+1)$ is the desired output at the next sample. $\theta_k$ is updated using \(\hat{\theta}_k=\hat{\theta_{k-1}}-a_k \hat{g_k (\hat{\theta-{k-1}})}\) where $\hat{g_k (\hat{\theta-{k-1}})}$ is the estimation of simultaneous perturbation which is explained in this survey.
MFAC A general SISO nonlinear system is considered as: \(y(k+1)=f(y(k),...,y(k-n_y),u(k),...,u(k-n_u))\) A constant $L$ under the name control input length constant of linearization has been introduced. Under two very simple assumptions (one of them being that the system has to be Lipschitz), an equivalent PFDL description is introduced: \(\Delta y(k+1) = \Phi^T(k) \Delta U(k)\) This equivalent system is then identified iteratively using a time-varying parameter estimation method. For example, using a modified projection algorithm, we can write: \(\hat{\phi}(k)=\hat{\phi}(k-1)+\frac{\eta_k \Delta u(k-1)}{\mu + \Delta^2 u(k-1)}(\Delta y(k)-\hat{\phi}(k-1)\Delta u(k-1))\) It is important to reset the estimator when $\hat{\phi} < \epsilon$ or $\Delta u(k-1) < \epsilon$. The control law is then defined, usually by minimizing a cost function like \(J(u(k))=|y^\ast (k+1)-\hat{y}(k+1)|^2+\lambda|\Delta^2 U(k)|^2\)
UC Unfalsified control (UC) is a control method that recursively falsifies control parameter sets that fail to satisfy the performance specification. The main elements of UC are as follows: an invertible controller candidate set, cost-detectable performance specifications, and the switching mechanism. Using I/O data of the system, a fictitious reference signal for each controller is computed and then each controller is evaluated using a control performance measure.
a
- c
- c
a