Yasushi Kami

Iterative method for designing an observer-based mixed H2/D-stability controller

This paper treats the output feedback H2 control with regional pole placement condition. In general, this problem is a BMI problem which is difficult to be solved theoretically. The purpose of this paper is to propose an iterative method for obtaining a sub-optimal solution of the H2 control problem with regional pole placement condition. The key idea of this paper is to employ a full-order observer-based controller. The proposed method produces a sequence of controllers which approaches to the unconstrained globally optimal H2 controller while it satisfies the D-stability constraint. A numerical example shows the effectiveness of our method

A Gradient Method for the Static Output Feedback Mixed H2/H∞ Control

This paper is concerned with the mixed H2/H∞ control problem via static output feedback control. The main purpose of this paper is to give an iterative method for finding a sub-optimal static output-feedback controller for the mixed H2/H∞ control problem. The contribution of this paper is to derive a gradient of the H2 cost function. Using this gradient, we propose a gradient method for H2 and mixed H2/H∞ control problems. Numerical examples show the efficiency of our methods.

An Iterative Approach to the Fixed-Order Robust H∞ Control Problem Using a Sequence of Infeasible Controllers

It is well known that the robust disturbance attenuation against uncertainties can be achieved by the robust H controllers and some practical situations make us use the fixedorder controllers. These facts imply that the fixed-order robust H controllers are important for practical control problems. However it is difficult to design such robust controllers, because the robust H control problems include an infinite number of matrix inequality constraints, in other words, they are described by Robust Semi-Definite Programming (RSDP) problems. For obtaining a feasible solution of the RSDP problems coming from the robust control problems with state feedback controllers or full-order controllers, many numerical methods have been proposed. Classically, the quadratic stability theory, i.e. a common constant Lyapunov function for the entire uncertain set is used for reducing the infinite constraints to the finite ones at the expense of conservatism (Boyd et al. 1994). Recently, parameter dependent Lyapunov functions are used to improve the conservatism (Chesi et al. 2005) (Ichihara et al. 2003), (Kami et al. 2009) (Shaked 2001), (Xie 2008) and some one-shot type approaches using extended LMI conditions, which allows to use the affine parameter dependent Lyapunov functions, have been proposed (Pipeleers et al. 2009), (Shaked 2001), (Xie 2008). However these methods can not always produce the robust controller, because common additional variables are required and these methods can not be used for designing fixed-order controllers. In this sense, an iterative type approach may be useful to the problems such that these one-shot type approaches can not be applied. In the field of the numerical optimization, there are two types of iterative approaches for finding feasible or locally optimal solutions of the optimization problems: one is an interiorpoint approach which needs an initial feasible solution to be carried out and the other is an exterior-point approach which does not need it. From these facts, exterior-point approach can be efficient for obtaining the solutions of the problems such that feasible solutions are difficult to be found. However, there are no exterior-point approaches except those in (Iwasaki & Skelton 1995), (Kami & Nobuyama 2004), (Kami et al. 2009), (Vanbierviet 2009) for control problems to our knowledge.

An exterior-point approach to the robust D-stability control problem

This paper treats the robust D-stability control against a parameter dependent uncertainty. It is well known that such robust control problems are difficult to be solved, because they become non-convex problems described by parameter dependent bilinear matrix inequalities (PDBMIs). In this paper, we propose an exterior-point approach to the PDBMI problems such that a non-stabilizing controller can be used as an initial point. The feature of our approach is to produce a controller sequence from an infeasible region to a feasible one. Numerical example shows the efficiency of our approach.

A Sum of Squares Optimization Approach to Robust Control of Bilinear Systems

Robust control problems for nonlinear systems are usually formulated as L2-induced norm minimization problems and those problems are reduced to the solvability of the so-called “Hamilton-Jacobi equation” (see, for example, van der Schaft (1996) and references therein). However, in the case of bilinear systems the usual L2-induced norm minimization problem leads to an obvious solution (the zero input is optimal!). To avoid the obvious solution Shimizu et al. (1997) introduced nonlinear weights on the evaluated signal and proposed a design method using linearization of the state-dependent matrix Riccati inequality derived from the Hamilton-Jacobi equation. In contrast to this, the purpose of this paper is to propose a new design method using SOS (Sum-of-Squares) optimization without linearization. It is known that the Hamilton-Jacobi equality coming from the L2-induced normminimization problem is reduced to the solvability of an inequality condition of quadratic form, i.e.,

An iterative method for output feedback mixed H 2 /H ∞ control problem

This paper treats the output feedback H2 control with H∞ norm constraint (mixed H2/H∞ control problem). In general, this problem is a BMI problem which is difficult to be solved theoretically. The purpose of this paper is to propose an iterative method for obtaining a sub-optimal solution of the mixed H2/H∞ control problem. The key idea of this paper is to employ a full-order observer-based controller. The proposed method produces a sequence of controllers which approaches to the unconstrained globally optimal H2 controller while it satisfies the H∞ norm constraint. A numerical example shows the effectiveness of our method.

An exterior-point approach to the fixed-order mixed H ∞ /D-stability controller design

This paper deals with the mixed H∞/D-stability control problem with a fixed-order output feedback controller. It is well known that this control problem is described as a combined bilinear matrix inequality (BMI) problem whose feasible solution is difficult to be found. In this paper, we propose a new exterior-point approach for finding a feasible solution of this problem. The advantage of our approach is to be able to use a non-stabilizing controller as an initial point. Numerical examples show the efficiency of our approach.

An exterior-point approach to the mixed H2=H∞ control problem

The purpose of this paper is to propose an exterior-point approach to the mixed H2/H∞ control problems using a partial derivative of the H2 cost function. The main contribution of this paper is to give an iterative method for obtaining a feasible solution of the problem, which produces a sequence of controller variables from the infeasible region to the feasible one. This approach has the property such that any stabilizing controller can be used as an initial point. The efficiency of our approach is shown by a numerical example which cannot be solved with the common Lyapunov variable method.

An iterative approach to the robust H ∞ synthesis problem with a sequence of infeasible controllers

This paper aims to design a robust H∞ control system against time invariant polytopic uncertainties. In general, such robust control problems are described by parameter dependent bilinear matrix inequality (PDBMI) problems which are not tractable numerically and there are few efficient methods for solving them. In this paper, we propose an iterative approach to the robust H∞ controller synthesis problems, which constructs a sequence of infeasible controllers. The feature of our approach is to be able to use any controller variables which may not be a robust stabilizing controller as an initial point. The efficiency of our approach is shown by a numerical example.

A New Exterior-point Approach to a Fixed-order Output Feedback Controller Design*

Abstract This paper deals with fixed-order controller design problems with output-feedback. It is well known that the control problems are difficult to be solved, because they become non-convex problems described by bilinear matrix inequality(BMI). In this paper, a new exterior-point approach to such BMI problems is proposed. This approach produces a controller sequence from a infeasible region to a feasible one. The advantage of this approach is that non-stabilizing controllers can be used as an initial controller. Numerical examples show the efficiency of our method.