An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

LMI_based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.

Nonlinear symbolic LFT model for UAV

A nonlinear modeling framework is presented for an oceanographic unmanned aerial vehicle （UAV） by using symbolic modeling and linear fractional transformation （LFT） techniques . Consequently, an exact nonlinear symbolic LFT model of the UAV is derived in a standard M-A form where M represents the nominal, known, part of the system and A contains the time-varying, uncertain and nonlinear components. The advantages of the proposed modeling approach are that： it not only provides an ideal starting point to obtain various final design-oriented models through subse- quent assumptions and simplifications, but also it facilitates the control system analysis with models of different levels of fidelity/complexity. Furthermore, a linearized symbolic LFT model of the UAV is proposed based on the LFT differentiation, which is amenable directly to a sophisticated linear ro- bust control strategy such as μ synthesis/analysis. Both of the derived LFT models are validated with the original nonlinear model in time domain. Simulation results show the effectiveness of the pro- posed algorithm.

Mathematical Aspects of SU (2) and SO(3,R) Derived from Two-Mode Realization in Coordinate-Invariant Form

Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.

Robustness assessment for flight control system of an oceanographic unmanned aerial vehicle

A post-design robustness assessment for the longitudinal flight control system of an oceanographic unmanned aerial vehicle （UAV） is presented in this paper. Two novel systematic approaches of generating the linear fractional transformation （LFT） model directly from nonlinear equations are proposed for this particular robustness analysis problem. The closed-loop system combined with each controller is used to determine combinations of aerodynamic parameters that result in worst-case performance. Classical simultaneous gain and phase margin stability metrics currently used in the aerospace industry are introduced for the certification of robustness of this uncertain multivariable system. The results show that the control system remains stable and achieves desired performance for all possible parameter variations over a specified range in both frequency domain and time domain.