The problem of state estimation for uncertain systems has attracted a recurring interest in the past decade. In this paper, we shall give an overview on some of the recent development in the area by focusing on the ro...The problem of state estimation for uncertain systems has attracted a recurring interest in the past decade. In this paper, we shall give an overview on some of the recent development in the area by focusing on the robust H2 (Kaiman) filtering of uncertain discrete-time systems. The robust H2 estimation is concerned with the design of a fixed estimator for a family of plants under consideration such that the estimation error covariance is of a minimal upper bound. The uncertainty under consideration includes norm-bounded uncertainty and polytopic uncertainty. In the finite horizon case, we shall discuss a parameterized difference Riccati equation approach for systems with normbounded uncertainty and pinpoint the difference of state estimation between systems without uncertainty and those with uncertainty. In the infinite horizon case, we shall deal with both the norm-bounded and polytopic uncertainties using a linear matrix inequality (LMI) approach. In particular, we shall demonstrate how the conservatism of design can be improved using a slack variable technique. We also propose an iterative algorithm to refine a designed estimator. An example will be given to compare estimators designed using various techniques.展开更多
This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncerta...This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities (LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared to the existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.展开更多
文摘The problem of state estimation for uncertain systems has attracted a recurring interest in the past decade. In this paper, we shall give an overview on some of the recent development in the area by focusing on the robust H2 (Kaiman) filtering of uncertain discrete-time systems. The robust H2 estimation is concerned with the design of a fixed estimator for a family of plants under consideration such that the estimation error covariance is of a minimal upper bound. The uncertainty under consideration includes norm-bounded uncertainty and polytopic uncertainty. In the finite horizon case, we shall discuss a parameterized difference Riccati equation approach for systems with normbounded uncertainty and pinpoint the difference of state estimation between systems without uncertainty and those with uncertainty. In the infinite horizon case, we shall deal with both the norm-bounded and polytopic uncertainties using a linear matrix inequality (LMI) approach. In particular, we shall demonstrate how the conservatism of design can be improved using a slack variable technique. We also propose an iterative algorithm to refine a designed estimator. An example will be given to compare estimators designed using various techniques.
文摘This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities (LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared to the existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.
