A data‐driven approximate solution to the model‐free HJB equation

Summary A recent river environmental restoration problem is approached from a standpoint of stochastic control of hybrid regime‐switching diffusion processes with discrete and costly observations. This setting harmonizes with real problems because continuously obtaining environmental and ecological information is difficult, and is often costly. The main problem is to decide when and how much of the sediment should be supplied into a river environment to effectively suppress bloom of benthic algae. The interventions are allowed only at observation times. Finding the optimal river restoration policy ultimately reduces to solving an optimality equation in an unconventional form due to the observation cost and discrete observations. We show its unique solvability and present a connection with degenerate parabolic partial differential equations, with which we can construct an effective algorithm for its approximation. An uncertainty‐averse optimization problem is also considered as an advanced problem. Coefficients and parameter values are identified from experimental and observation results to numerically compute the optimal restoration policy of an existing river environment with and without uncertainty.

Section: Discussionmentioning

confidence: 99%

A hybrid stochastic river environmental restoration modeling with discrete and costly observations

Yoshioka

Tsujimura

Hamagami

et al. 2020

“…In this section, compared with the KECA method, 25 the TKPLS method, 11 the TPCR method, 4 and the PLS method, 12 the feasibility of the proposed algorithm is illustrated under two selected scenarios (IDV(1) and IDV( 4)). For these two scenarios, the input matrix U is composed of XMEAS and XMV (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11), and then the KPI variable Y is set as XMEAS(35). The parameters are given as A = 17, c = 10 3 , 𝛼 = 0.95, and 𝜉 = 6.…”

Section: Simulation Experimentsmentioning

confidence: 99%

“…With the advances in storing hardware, data-driven methods are exploited largely in industrial systems and engineering. [1][2][3][4][5] The multivariable statistics (MS) approach, as the common data-driven method, reduces the high-dimensional data into a lower-dimensional representation to avoid the "curse of dimensionality.". [6][7][8] Many successful extensions of the MS method have been generated via the principal component analysis (PCA) method and the partial least squares (PLS) method into the fault detection and diagnosis field.…”

Section: Introductionmentioning

confidence: 99%

A key performance indicator‐relevant approach based on kernel entropy component regression model for industrial system

Sun

Kang

et al. 2021

Key performance indicator (KPI)‐relevant fault detection method has been raised for decades to hugely increase the economic interest of modern industries. However, the typical data‐driven approaches like the kernel principal component analysis (KPCA) and the kernel entropy analysis (KECA) are inefficient to consider the influence taken by the fault factor on the KPI. Thus, in this work, an algorithm called the kernel entropy regression (KECR) is proposed to enhance the interpretability between the fault and the KPI. The proposed algorithm captures the information relevant to the KPI state in the subspace and rewords the decomposition of the KECA method. The angular structure of the KECR method achieves an accurate partition for process variables to hugely decrease false detection results. In the end, an industrial case is utilized to demonstrate the effectiveness of the KECR method.

“…In Reference 6, a data‐based Hamilton–Jacobi–Bellman function is proposed, and a data‐based model‐free approximate solution of the HJB equation is realized. In Reference 7, the dynamic linearization method is proposed to transform the strong nonlinear system into a linear data model. Then the model‐free adaptive control (MFAC) method is proposed by using the optimization method, which is an effective data‐based method.…”

Section: Introductionmentioning

confidence: 99%

Quantized data‐based iterative learning control under denial‐of‐service attacks

Zhou

Che

2021

This article mainly studies the quantized data‐based iterative learning tracking control (QDBILTC) problem of nonlinear networked control systems in the presence of signals quantization and denial‐of‐service (DoS) attacks. The quantizer considered here is static with the logarithmic form. First, an estimate output attack compensation mechanism is designed to compensate for the effect of DoS attacks based on the extended dynamic linearization method. Then, a QDBILTC algorithm is developed to guarantee the system tracking performance and the bounded input and bounded output stability in mean‐square sense. The process of designing the QDBILTC algorithm only uses the input and output data of the system, and the proof of which uses the compression mapping principle and the mathematical induction. The effectiveness of the proposed QDBILTC algorithm is illustrated by a digital simulation.