Xiaoqing Li, Kaibo Shi, Jun Cheng, Zhinan Peng, Liang Han
{"title":"A Semi-Markovian Model Approach to Resilient Fault-Tolerant Control of Interval Type-2 Fuzzy Systems With Stochastic Actuator Failures and Its Applications","authors":"Xiaoqing Li, Kaibo Shi, Jun Cheng, Zhinan Peng, Liang Han","doi":"10.1002/rnc.7805","DOIUrl":"https://doi.org/10.1002/rnc.7805","url":null,"abstract":"<div>\u0000 \u0000 <p>This article mainly presents a fresh systematic framework to tackle the resilient fault-tolerant sampled-data control (SDC) synthesis problem for networked interval type-2 fuzzy systems (IT-2FSs) suffering with semi-Markovian-type jump actuator failures (SMJAFs) and mismatched membership functions (MMFs), which portrays more features than some prior developments. The principally target of the addressed problem under this systematic investigation is to precisely architect a faulty mode-dependent sampled-data controller such that the resultant IT-2FSs are asymptotically stable with a prescribed <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {H}_{infty } $$</annotation>\u0000 </semantics></math> attenuation level simultaneously. Firstly, in a departure from conventional control approaches, to better depict the stochastic actuator failures (SAFs) and cater to the engineering practice more accurately, a neoteric control input model that incorporated with semi-Markovian jump-type faulty coefficients with stochastically occurring bias terms is reconstructed for IT-2FSs in specifically. Secondly, the occurrence of controller gain fluctuations is randomly, which is regulated by a Bernoulli random binary distribution with a pre-known probability distribution. Thirdly, in comparison with majority of the existing SDC strategies, the intrinsic lag signal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ϱ</mi>\u0000 </mrow>\u0000 <annotation>$$ varrho $$</annotation>\u0000 </semantics></math> is intensionally introduced in the control loop, which exploited initially to handle the IT-2 fuzzy control synthesis issue. In doing so, a novelty looped-type semi-Markovian Lyapunov functional alleged dual-sided looped semi-Markovian Lyapunov functional that adequate acquisition the characteristic information of whole sampling intervals from <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ xleft({t}_kright) $$</annotation>\u0000 </semantics></math> to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ x","PeriodicalId":50291,"journal":{"name":"International Journal of Robust and Nonlinear Control","volume":"35 6","pages":"2399-2424"},"PeriodicalIF":3.2,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shih-Chi Liao, A. Leonid Heide, Maziar S. Hemati, Peter J. Seiler
{"title":"A Convex Optimization Approach to Compute Trapping Regions for Lossless Quadratic Systems","authors":"Shih-Chi Liao, A. Leonid Heide, Maziar S. Hemati, Peter J. Seiler","doi":"10.1002/rnc.7807","DOIUrl":"https://doi.org/10.1002/rnc.7807","url":null,"abstract":"<p>Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a bounded set. Conditions for the existence and characterization of trapping regions have been established in prior work for boundedness analysis. However, prior solutions have used non-convex optimization methods, resulting in conservative estimates. In this paper, we build on this prior work and provide a convex semidefinite programming condition for the existence of a trapping region. The condition allows for precise verification or falsification of the existence of a trapping region. If a trapping region exists, then we provide a second semidefinite program to compute the least conservative radius of the spherical trapping region. Two low-dimensional systems are provided as examples to illustrate the results. A third high-dimensional example is also included to demonstrate that the computation required for the analysis can be scaled to systems of up to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>∼</mo>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <mn>100</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ sim O(100) $$</annotation>\u0000 </semantics></math> states. The proposed method provides a precise and computationally efficient numerical approach for computing trapping regions. We anticipate this work will benefit future studies on modeling and control of lossless quadratic dynamical systems.</p>","PeriodicalId":50291,"journal":{"name":"International Journal of Robust and Nonlinear Control","volume":"35 6","pages":"2425-2436"},"PeriodicalIF":3.2,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.7807","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Somers, C. Roos, J.-M. Biannic, F. Sanfedino, V. Preda, S. Bennani, H. Evain
{"title":"Delay Margin Analysis of Uncertain Linear Control Systems Using Probabilistic \u0000 \u0000 \u0000 μ\u0000 \u0000 $$ mu $$","authors":"F. Somers, C. Roos, J.-M. Biannic, F. Sanfedino, V. Preda, S. Bennani, H. Evain","doi":"10.1002/rnc.7780","DOIUrl":"https://doi.org/10.1002/rnc.7780","url":null,"abstract":"<div>\u0000 \u0000 <p>Monte Carlo simulations have long been a widely used method in the industry for control system validation. They provide an accurate probability measure for sufficiently frequent phenomena but are often time-consuming and may fail to detect very rare events. Conversely, deterministic techniques such as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 <annotation>$$ mu $$</annotation>\u0000 </semantics></math> or IQC-based analysis allow fast calculation of worst-case stability margins and performance levels, but in the absence of a probabilistic framework, a control system may be invalidated on the basis of extremely rare events. Probabilistic <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 <annotation>$$ mu $$</annotation>\u0000 </semantics></math>-analysis has therefore been studied since the 1990s to bridge this analysis gap by focusing on rare but nonetheless possible situations that may threaten system integrity. The solution adopted in this paper implements a branch-and-bound algorithm to explore the whole uncertainty domain by dividing it into smaller and smaller subsets. At each step, sufficient conditions involving <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 <annotation>$$ mu $$</annotation>\u0000 </semantics></math> upper bound computations are used to check whether a given requirement–related to the delay margin in the present case–is satisfied or violated on the whole considered subset. Guaranteed bounds on the exact probability of delay margin satisfaction or violation are then obtained, based on the probability distributions of the uncertain parameters. The difficulty here arises from the exponential term <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mi>τ</mi>\u0000 <mi>s</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {e}^{-tau s} $$</annotation>\u0000 </semantics></math> classically used to represent a delay <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>$$ tau $$</annotation>\u0000 </semantics></math>, which cannot be directly translated into the Linear Fractional Representation (LFR) framework imposed by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 <annotation>$$ mu $$</annotation>\u0000 </semantics></math>-analysis. Two differen","PeriodicalId":50291,"journal":{"name":"International Journal of Robust and Nonlinear Control","volume":"35 6","pages":"2101-2118"},"PeriodicalIF":3.2,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143582080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}