Design of Retarded Fractional Delay Differential Systems Using the Method of Inequalities

Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems （RFDDSs） by the method of inequalities, in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian＇s original formulation, which was first proposed in connection with rational systems, is extended to the case of RFDDSs. In making the use of this formulation possible for RFDDSs, the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors. During the design process, the time responses are obtained by a known method for the numerical inversion of Laplace transforms. Two numerical examples are given, where fractional controllers are designed for a time-delay and a heat-conduction plants.

Method of Inequalities-based Multiobjective Genetic Algorithm for Optimizing a Cart-double-pendulum System

This article presents a multiobjective approach to the design of the controller for the swing-up and handstand control of a general cart-double-pendulum system （CDPS）. The designed controller, which is based on the human-simulated intelligent control （HSIC） method, builds up different control modes to monitor and control the CDPS during four kinetic phases consisting of an initial oscillation phase, a swing-up phase, a posture adjustment phase, and a balance control phase. For the approach, the original method of inequalities-based （MoI） multiobjective genetic algorithm （MMGA） is extended and applied to the case study which uses a set of performance indices that includes the cart displacement over the rail boundary, the number of swings, the settling time, the overshoot of the total energy, and the control effort. The simulation results show good responses of the CDPS with the controllers obtained by the proposed approach.

Design of Poiseuille Flow Controllers Using the Method of Inequalities

This paper investigates the use of the method of inequalities （MoI） to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flows, the dynamics of streamwise vortices in plane Poiseuille flow are very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger nonlinearities and lead to turbulence even though such perturbations would, in a linear flow model, eventually decay. Such a system can be described as a conditionally linear system. The sensitivity is measured using the maximum transient energy growth, which is widely used in the fluid dynamics community. The paper considers two approaches. In the first approach, the MoI is used to design low-order proportional and proportional-integral （PI） controllers. In the second one, the MoI is combined with McFarlane and Glover＇s H∞ loop-shaping design procedure in a mixed-optimization approach.

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional（LKF）, sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities（LMIs）. The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.

UNCONSTRAINED METHODS F0R GENERALIZED NONLINEAR COMPLEMENTARITY AND VARIATIONAL INEQUALITY PROBLEMS

In this papert we construct unconstrained methods for the generalized nonlinearcomplementarity problem and variational inequalities. Properties of the correspon-dent unconstrained optimization problem are studied. We apply these methods tothe subproblems in trust region method, and study their interrelationships. Nu-merical results are also presented.

Two-Level Defect-CorrectionMethod for Steady Navier-Stokes Problem with Friction Boundary Conditions

In this paper,we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions,which results in a variational inequality problem of the second kind.Based on Taylor-Hood element,we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh.The error estimates for the velocity in the H1 norm and the pressure in the L^(2) norm are derived.Finally,the numerical results are provided to confirm our theoretical analysis.

Design of Non-rational MIMO Feedback Systems with Inputs and Outputs Satisfying Certain Bounding Conditions by Using Rational Approximants

When a feedback system has components described by non-rational transfer functions, a standard practice in designing such a system is to replace the non-rational functions with rational approximants and then carry out the design with the approximants by means of a method that copes with rational systems. In order to ensure that the design carried out with the approximants still provides satisfactory results for the original system, a criterion of approximation should be explicitly taken into account in the design formulation. This paper derives such a criterion for multi-input multi-output（MIMO） feedback systems whose design objective is to ensure that the absolute values of every error and every controller output components always stay within prescribed bounds whenever the inputs satisfy certain bounding conditions. The obtained criterion generalizes a known result which was derived for single-input single-output（SISO） systems; furthermore, for a given rational approximant matrix, it is expressed as a set of inequalities that can be solved in practice. Finally, a controller for a binary distillation column is designed by using the criterion in conjunction with the method of inequalities. The numerical results clearly demonstrate that the usefulness of the criterion in obtaining a design solution for the original system.