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The separation principle has been extensively used in the literature to tackle the observer-based control problem for integer-order linear and Lipschitz nonlinear systems. However, less interest has been given by researchers to treat the same problem, in the fractional-order framework. In this context, this paper introduces and investigates a separation principle tailored for two advantageous classes of nonlinear fractional-order fuzzy systems. These two classes can be regarded as generalizations of the classical nonlinear Lipshchitz systems. The research explores both asymptotic stability and practical Mittag-Leffler stability, unveiling a novel approach to handling intricate fractional-order systems with fuzzy characteristics. Through rigorous theoretical analysis and simulation studies, the paper demonstrates the efficacy and applicability of the separation principle, for both considered classes of fractional fuzzy systems.

This paper mainly studies the issue of fractional parameter identification of generalized bilinear-in-parameter system(GBIP) with colored noise. Hierarchical fractional least mean square algorithm based on the key term separation principle(K-HFLMS) and multi-innovation hierarchical fractional least mean square algorithm based on the key term separation principle (K-MHFLMS) are presented for the effective parameter estimation of GBIP system. The K-MHFLMS expands the scalar innovation into the vector innovation by making full use of the system input and output data information at each recursive step. The detailed performance analyses of the K-MHFLMS strategy are compared with the K-HFLMS algorithm for GBIP identification model based on the Fitness metrics, the mean square error metrics and the average predicted output error. The effectiveness and reliability of K-HFLMS and K-MHFLMS algorithms are further verified through the simulation experimentation under different noise variances, fractional orders and innovation lengths, and the K-MHFLMS yields faster convergence speed than the K-HFLMS by increasing the innovation length.

In this contribution, a fault-tolerant control strategy for the longitudinal dynamics of an autonomous vehicle is presented. The aim is to be able to detect potential failures of the vehicle’s speed sensor and then to keep the vehicle in a safe state. For this purpose, the separation principle, composed of a static output feedback controller and fault estimation observers, is designed. Indeed, two observer techniques were proposed: the proportional and integral observer and the descriptor observer. The effectiveness of the proposed scheme is validated by means of the experimental demonstrator of the VEDECOM (Véhicle Décarboné et Communinicant) Institut.

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.

The accurate measurement and modeling of ferromagnetic material losses are vital issues during the design and analysis of electrical machines. Higher loss values can describe the manufactured rotor and stator machine plates better than the catalog data obtained by standardized measurements using the Epstein frame. In this paper, different temperature-dependent models based on the loss-separation principle are introduced and compared with the measurements. The model parameters are computed from customized laboratory and standardized measurements. The customized measurements based on the stator part of an induction machine in the range of the automotive industry standard, i.e., in [−40 °C, ⋯, 180 °C]. The proposed model and measurement process can be used in the post-processing stage of numerical field analysis to obtain electromagnetic losses according to the agreement between measured and simulated results. During a numerically expensive optimization process, this model can be used to consider the temperature dependence of the losses more accurately. The study shows that more than 50% of loss increase can be measured, compared with the catalog data, if we use the manufactured, stator-based, customized measurements based on the estimation of the iron loss parameters.

The paper deals with a new application of the key term separation principle in identification of nonlinear dynamic systems. A multiplicative form of this operator decomposition technique is proposed and applied to the Wiener model. The resulting mathematical model is linear in both the linear and the nonlinear block parameters. Illustrative examples are included.

Robust positive sampled-data observer-based output-feedback energy-to-peak disturbance attenuation is challenging problem because of the following reasons. (i) The typical Luenberger observer has a limited structure for guaranteeing closed-loop positivity. (ii) The conventional sampled-data control framework has no lever to manage closed-loop positivity during sampling intervals and at sampling instants. (iii) A separation principle is to be established for this problem. In this paper, we propose an affirmative methodology to solve this problem.

This paper presents two estimation algorithms for Hammerstein controlled autoregressive autoregressive systems. The key-term separation principle is used to solve the problem that the identification model contains the products of the parameters of the nonlinear part and the linear part, which causes large amount of computation. To improve the parameter estimation accuracy of the stochastic gradient algorithm, we derive a forgetting factor multi-innovation generalized stochastic gradient algorithm expanding the innovation length. To improve the convergence rate, we derive a filtering-based forgetting factor multi-innovation stochastic gradient algorithm using the filtering technique. The simulation results show that the proposed algorithms are effective.

In this paper, we investigate a linear-quadratic (LQ) optimal control problem for partially observed forward-backward stochastic systems with random jumps, where the observation’s drift term is linear with respect to the state x and control variable v . In our model, the observation process is no longer a Brownian motion but a controlled stochastic process driven by Brownian motions and Poisson random measures, which also have correlated noises with the state equation. Applying a backward separation approach to decompose the state and observation, we overcome the problem of cyclic dependence of control and observation. Then, the necessary and sufficient conditions for optimal control are derived. We also obtain the feedback representation of optimal control and provide two special cases to illustrate the significance of our results. Moreover, we also provide a financial application to demonstrate the practical significance of our results.

The control problem of the linear output of an autonomous nonlinear stochastic differential system is considered. The infinite horizon and the quadratic functional make it possible to interpret the control goal as stabilization of the output near the position determined by the state, which is described by a nonlinear stochastic differential equation. The solution is obtained for two variants of the model: with accurate measurements and under the assumption that the linear output represents indirect observations of the state. In the case of indirect observations, a continuous Markov chain is used as a state model, which makes it possible to separate the control and filtering tasks and apply the Wonham filter. In both variants, sufficient conditions for the existence of the optimal solution consist of typical requirements for linear systems that ensure the existence of a limiting solution of the Riccati equation. The ergodicity of the nonlinear dynamics and the existence of a limit in the Feynman–Kac formula for the coefficients of the nonlinear part of the control are additional requirements due to the nonlinear elements. The results of the numerical experiment are presented and analyzed.