Polytopic [formula omitted] filter design and relaxation for nonlinear systems via tensor product technique

International audience

An optimization-based multilayer operability framework is introduced for the process design of nonlinear energy systems that are challenged by complexity and highly constrained environments. In the first layer of this framework, a mixed-integer linear programming (MILP)-based iterative algorithm considers the minimization of the footprint and the achievement of process intensification targets. Then, in the second layer, an operability analysis is performed to incorporate into the approach key features for optimality and feasibility, accounting for the system operation with changeable input conditions. The outcome of the framework consists of a set of modular designs, considering the aspects of both size and process operability. For this study, the nonlinear system is represented by multiple linearized models, resulting in low computational expense and efficient quantification of operability regions. The developed framework is applied to a membrane reactor for direct methane aromatization conversion to hyd...

Practical stability analysis and synthesis for nonlinear singular systems .- 3 Strongly absolute stability analysis for Lur'e singular .- 4 Input-to-state stability analysis and design for Lur'e singular systems .- 5 Observer design for nonlinear singular systems .- 6 Absolute stability of Lur'e singularly perturbed systems .- 7 Multi-objective control for T-S fuzzy singularly perturbed systems. 4 Input-to-state stability analysis and design for Lur'e singular systems .- 5 Observer design for nonlinear singular systems .- 6 Absolute stability of Lur'e singularly perturbed systems .- 7 Multi-objective control for T-S fuzzy singularly perturbed systems.

This study introduces a new approach using supervised learning deep neural networks (DNNs) to develop an AI-driven filter for nonlinear stochastic signal systems with external disturbance and measurement noise. The filter aims to achieve a balanced design between and norm of the state estimation error to achieve both optimal and robust filtering design of nonlinear signal system simultaneously while considering environmental disturbance and measurement noise. Traditionally, this nonlinear filter design involves solving complex two-coupled Hamilton-Jacobi-Issac Equations (HJIEs). To simplify this complicated design process, a novel two-coupled HJIEs-supervised Adam learning algorithm is proposed for DNN-based AI-driven filter. This algorithm trains a DNN-based AI-driven filter offline using worst-case scenarios of environmental disturbance and measurement noise. This training phase generates state estimation errors that teach the DNN-based AI-driven filter how to coordinate nonlinear system model with worst-case external disturbance and measurement noise, Luenberger-type filter, estimation error dynamic model and two-coupled HJIEs-supervised deep Adam learning algorithm to achieve the mixed filtering strategy effectively. The study demonstrates theoretically that this approach will achieve the desired mixed filtering strategy once the Adam learning algorithm converges. Finally, the effectiveness of the proposed DNN-based AI-driven filter design method is validated through simulations, specifically involving trajectory estimation and prediction of an incoming ballistic missile detected by a radar system.

Designing minimum variance controllers (MVC) for nonlinear systems is confronted with many difficulties. The methods which are able to identify MIMO nonlinear systems are scarce, and linear models are not accurate in modeling nonlinear systems. In this paper, Vector ARX (VARX) models are proposed for designing MVC and generalized minimum variance controller (GMVC) for linear and nonlinear systems, and the accuracy of these models in approximating the nonlinear MIMO system is studied. However, the VARX is a linear model. It is shown that this model can identify some kinds of nonlinear systems with any desired accuracy. Therefore, the controller designed by the VARX is accurate, even for these nonlinear systems. The proposed controller is tested on a both linear system and a nonlinear four-tank benchmark process. In spite of the simplicity of designing GMVCs for the VARX models, the results show that the proposed method is accurate and implementable.

Event-triggered fault detection filter design for nonlinear networked systems via fuzzy Lyapunov functions

Vibration actuators are widely used in handheld devices to provide vibrotactile feedback or silent notification to the users. In most cases, miniature DC motors with eccentric rotors or the so‐called coin‐type shaftless vibration motors are utilized. The common disadvantage of the single rotor designs is that the frequency and the intensity of the generated vibration cannot be adjusted separately. The construction composed of two independently driven coaxial eccentric rotors – which makes a strongly coupled nonlinear system – allows for the separate control of the frequency and amplitude by the adjustment of the angular speed and the total eccentricity. This paper presents a complete control design approach based on quasi‐linear parameter varying (qLPV) modelling and linear matrix inequality (LMI)‐based synthesis utilizing the tensor product (TP) model transformation to determine the convex polytopic representation of the parameter dependent nonlinear system. The design approach is demonstrated via a concrete numerical example using the parameters of a real dual‐excenter prototype device. The control performance is validated through numerical simulations. This case study goes through a complete nonlinear control problem from the modelling phase to the implementation‐ready controller, while drawing generalizable conclusions for qLPV modelling.

This article investigates the problem of secure memory adaptive event‐triggered filter design for nonlinear network systems under hybrid network attacks. First, the introduction of memory adaptive event‐triggered mechanism and numerical quantization is employed to enhance system performance, optimize network channel utilization, and prevent network congestion. Second, we consider the impact of deceptive attacks and DoS attacks occurring in the network channel on data transmission, which form the hybrid network attacks studied in this article. Subsequently, based on the established error model, we derive sufficient conditions for the mean‐square exponential stability of the system under a given performance index using Lyapunov–Krasovskii function and linear matrix inequality (LMI) techniques. Furthermore, the filter parameters are determined using the LMI method. Finally, we illustrate the feasibility and generality of the conclusions through numerical simulation examples and a tunnel diode circuit system.

This paper proposes an H ∞ polytopic filter design for a nonlinear system. Based on the polytopic approximation of the nonlinear system, the polytopic filter design is converted into a group of linear matrix inequalities (LMIs) so that the polytopic filter parameters can be effectively acquired by numerical convex optimization algorithms. At this stage, the tensor product (TP) model transformation is utilized to compute the polytopic approximation of the nonlinear system. Particularly, a new rectification procedure is further developed to obtain a specific polytopic approximation with all the vertex systems being stable, which premises the solvability of the LMIs. The method is much easier to be implemented than traditional approaches such as the Hamilton-Jacobi inequality (HJI)-based methods. Simulation demonstrates the method is much less conservative than the existing method and has good estimation performance.

This paper presents the central finite‐dimensionalH∞filter for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the originalH∞filtering problem to the corresponding optimalH2filtering problem, using the technique proposed in (IEEE Trans. Automat. Control1989;34:831–847). The paper presents the central suboptimalH∞filter for the general case of nonlinear polynomial systems based on the optimalH2filter given in (Int. J. Robust Nonlinear Control2006;16:287–298). The central suboptimalH∞filter is also derived in a closed finite‐dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimalH∞filter available for the corresponding linearized system. Copyright © 2008 John Wiley & Sons, Ltd.

In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS) was proposed by Okubo (1985). In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k))║≤α + β║v (k)║^γ , where α≥0, β≥0, 0≤γ≤1. When 0≤γ<1. It is easy to extend the method to discrete time systems. But in the case γ = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.

One of the approaches to sampled-data controller design for nonlinear continuous-time systems consists of obtaining an appropriate model and then proceeding to design a controller for the model. Then, it is important to derive a good approximate sampled-data model because the exact sampled- data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin have proposed an accurate sampled-data model which includes extra zero dynamics, so-called the sampling zero dynamics, corresponding to the relative degree of the continuous-time nonlinear system. This paper shows that a more accurate sampled-data model is required for a controlled Van der Pol system with the relative degree two. The reason is that the closed-loop system becomes unstable when a controller design method based on cancellation of the zero dynamics is applied, and the phenomenon seems related to the instability of the sampling zero dynamics of the more accurate sampled-data model. Further, this paper derives a more accurate model than that of Yuz and Goodwin for continuous-time nonlinear systems with the relative degree two, and presents a condition which assures the stability of the sampling zero dynamics of the obtained model.

The theory and design of linear adaptive filters based on FIR filter structures is well developed and widely applied in practice. However, the same is not true for more general classes of adaptive systems such as linear infinite impulse response adaptive filters (MR) and nonlinear adaptive systems. This situation results because both linear IIR structures and nonlinear structures tend to produce multi-modal error surfaces for which stochastic gradient optimization strategies may fail to reach the global minimum. After briefly discussing the state of the art in linear adaptive filtering, the attention of this paper is turned to MR and nonlinear adaptive systems for potential use in echo cancellation, channel equalization, acoustic channel modeling, nonlinear prediction, and nonlinear system identification. Structured stochastic optimization algorithms that are effective on multimodal error surfaces are then introduced, with particular attention to the particle swarm optimization (PSO) technique. The PSO algorithm is demonstrated on some representative IIR and nonlinear filter structures, and both performance and computational complexity are analyzed for these types of nonlinear systems.

The work deals finite frequency H&lt;sub&gt;∞&lt;/sub&gt; control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H&lt;sub&gt;∞&lt;/sub&gt; lower can be by our method obtained developed where further comparison.

Stability domain estimation and design for nonlinear systems with bounded control inputs