The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Ito differential equations

This paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state- and control-dependent noise in singularly perturbed stochastic systems. First, an asymptotic structure along with a stabilizing solution for the stochastic algebraic Riccati equation (ARE) are newly established. It is shown that the dominant part of this solution can be obtained by solving a parameter-independent system of coupled Riccati-type equations. Moreover, sufficient conditions for the existence of the stabilizing solution to the problem are given. A new sequential numerical algorithm for solving the reduced-order AREs is also described. Based on the asymptotic behavior of the ARE, a class of O(√ε) approximate controller that stabilizes the system is obtained. Unlike the existing results in singularly perturbed deterministic systems, it is noteworthy that the resulting controller achieves an O(ε) approximation to the optimal cost of the original LQ optimal control problem. As a result, the proposed control methodology can be applied to practical applications even if the value of the small parameter ε is not precisely known. © 2012 Society for Industrial and Applied Mathematics.Vasile Dragan, Hiroaki Mukaidani and Peng Sh

A novel robust H1 fuzzy state-feedback control design on nonlinear Markovian jump systems with time-varyin delay

This paper considers the problem of designing a robust H∞ fuzzy state-feedback controller for a class of nonlinear Markovian jump systems with time-varying delay. A novel design methodology has been proposed for designing a controller that guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value. Solutions to the problem are provided in terms of linear matrix inequalities. To illustrate the effectiveness of the design developed in this paper, a numerical example is also provided

H∞ Takagi-Sugeno Fuzzy State-Derivative Feedback Control Design for Nonlinear Dynamic Systems

This paper considers an H∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H∞ TS fuzzy state-derivative feedback control law which guarantees L2-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller

Robust H∞ control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach

Examination is made of the problems of designing robust H infin state-feedback and output feedback controllers for a class of uncertain Markovian jump nonlinear singularly perturbed systems described by a Takagi-Sugeno fuzzy model with Markovian jumps. Based on the linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear singularly perturbed systems to have an Hinfin performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problems are given in terms of linear matrix inequalities that are independent of the singular perturbation epsiv, when epsiv is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear singularly perturbed systems. A numerical example is provided to illustrate the design developed in this paper

H∞ output feedback control design for uncertain fuzzy singularly perturbed systems: an LMI approach

This paper examines the problem of designing a robust H∞ output feedback controller for a class of singularly perturbed systems described by a Takagi–Sugeno fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain singularly perturbed nonlinear systems to have an H∞ performance are derived. To eliminate the ill-conditioning caused by the interaction of slow and fast dynamic modes, solutions to the problem are presented in terms of LMIs which are independent of the singular perturbation . The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design developed in this paper

Modelling Dependencies and Couplings in the Design Space of Meshing Gear Sets

This work presents a design methodology based on the combination of a set of compatibility equations for determining nominal tooth and cutter geometry and a set of tooth contact analysis equations for determining modified tooth surfaces and motion transmission laws. Both have been shown separately to lead to various optimisations, and some parametric subspaces of the designed gears are shown to be so weakly coupled that optimisations found individually may be superimposed, as shown in the case of the gear pair stiffness function, dynamical load factor, bending fatigue strength and pitting/ scoring resistance optimisation. This is in contrast to traditional strengthening methods, such as profile shifting, which invariably produce much stronger couplings and thereby trade-offs