Ben M. Chen

A reduced order observer based controller design for H/sub /spl infin//-optimization

In this note the H/sub /spl infin// control problem with measurement feedback is investigated. It is well-known that for this problem, in general, we need controllers of the same dynamic order as the given system. However, in the case that some entries of the measurement vector are not noise-corrupted, we show that one can find dynamic compensators of a lower dynamical order. Note that this implies that the standard assumptions on the direct feedthrough matrices, as made in most papers on H/sub /spl infin// control, are not satisfied. Our result can be derived by using reduced order observer based controllers. >

Construction and parameterization of all static and dynamic H/sub 2/-optimal state feedback solutions, optimal fixed modes and fixed decoupling zeros

A problem of H/sub 2/ optimization via state feedback is considered. The problems dealt with are of the general singular type, with a left invertible transfer matrix function from the control input to the controlled output. All the static and dynamic H/sub 2/ optimal state feedback solutions are constructed and parameterized, and all the eigenvalues of an optimal closed-loop system are characterized. All optimal closed-loop systems share a set of eigenvalues which are termed the optimal fixed modes, which must be assigned among the closed-loop eigenvalues. This set includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and location of pole-zero cancellations present in any H/sub 2/ optimal design. It is shown that both the sets of optimal fixed modes and optimal fixed decoupling zeros do not vary. >

The discrete-time H/sub /spl infin// control problem with strictly proper measurement feedback

This paper is concerned with the discrete-time H/sub /spl infin// control problem with strictly proper measurement feedback. We derive necessary and sufficient conditions for the existence of a strictly proper compensator which achieves a given H/sub /spl infin// norm bound. Note that contrary to the continuous time, in discrete time there might exist a suitable proper compensator but no suitable strictly proper compensator. Finally, we give an explicit formula for one controller which achieves this bound. >

Necessary and sufficient conditions under which an H 2 optimal control problem has a unique solution

A set of necessary and sufficient conditions under which a general H 2-optimal control problem has a unique solution is derived. It is shown that the solution for an H 2-optimal control problem, if it exists, is unique if and only if (i) the transfer function from the control input to the controlled output is left invertible, and (ii) the transfer function from the disturbance to the measurement output is right invertible.

Simultaneous H/sub 2//H/sub /spl infin// optimal control for discrete-time systems: the state feedback case

This paper presents a simultaneous H/sub 2//H/sub /spl infin// optimal control problem for discrete-time systems in the state-feedback case. By the use of dynamic state feedback controllers, the design seeks to minimize the H/sub 2/ norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H/sub /spl infin// norm bound on some other closed-loop transfer matrix. The class of problems addressed here is relatively general and consists of systems which have left invertible transfer function matrix from the control input to the controlled output. Necessary and sufficient conditions are established so that the posed simultaneous H/sub 2//H/sub /spl infin// problem is solvable with state feedback controllers.

Simultaneous H2/H-infinity optimal control - The state feedback case

A simultaneous H2/H-infinity control problem is considered. This problem seeks to minimize the H2 norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H-infinity norm bound on some other closed-loop transfer matrix by utilizing dynamic state feedback controllers. Such a problem was formulated earlier by Rotea and Khargonekar (1991) who considered only so called regular problems. Here, for a class of singular problems, necessary and sufficient conditions are established so that the posed simultaneous H2/H-infinity problem is solvable by using state feedback controllers. The class of singular problems considered have a left invertible transfer function matrix from the control input to the controlled output which is used for the H2 norm performance measure. This class of problems subsumes the class of regular problems.

An exact algebraic solution of the infimum in H-infinity optimization with output feedback

This paper presents a simple and noniterative procedure for the computation of the exact value of the infimum in the standard H-infinity-optimal control with output feedback. The problem formulation is general and does not place any restrictions on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. The method is applicable to systems that satisfy (1) the transfer function from the control input to the controlled output is right-invertible and has no invariant zeros on the j(w) axis and, (2) the transfer function from the disturbance to the measurement output is left-invertible and has no invariant zeros on the j(w) axis. A set of necessary and sufficient conditions for the solvability of H-infinity-almost disturbance decoupling problem via measurement feedback with internal stability is also given.