Abstract
The discrete coupled algebraic Riccati equation (DCARE) has wide applications in robust control, optimal control, and so on. In this paper, we present two iterative algorithms for solving the DCARE. The two iterative algorithms contain both the iterative solution in the last iterative step and the iterative solution in the current iterative step. And, for different initial value, the iterative sequences are increasing and bounded in one algorithm and decreasing and bounded in another. They are all monotonous and convergent. Numerical examples demonstrate the convergence effect of the presented algorithms.
Highlights
Introduction and Preliminaries e discrete coupled Riccati equation is usually encountered in optimal control and filter design problems in control theory [1,2,3,4,5,6,7,8,9], in the jump-linear quadratic optimal control problem [10]
Where Ai ∈ Rn×n is a constant matrix, Bi ∈ Rn×m, Qi ∈ Rn×n is a symmetric positive definite matrix, i ∈ S, Fi Pi + j≠ieijPj is the coupled term, eij are real nonnegative constants defined as eij ≡ (eij/eii) with the properties eij ∈ [0, 1], eii > 0, and j∈Seij 1, and Pi ∈ Rn×n denotes the symmetric positive definite solution of the discrete coupled algebraic Riccati equation (DCARE)
We find less work has been done to discuss the numerical solution of the DCARE
Summary
E discrete coupled algebraic Riccati equation (DCARE) has wide applications in robust control, optimal control, and so on. We present two iterative algorithms for solving the DCARE. For different initial value, the iterative sequences are increasing and bounded in one algorithm and decreasing and bounded in another. Numerical examples demonstrate the convergence effect of the presented algorithms. K is the time index, rk is the form process taking values in the finite set. Minimizing the cost criterion of system (1) reduces to solving coupled algebraic Riccati-like equations. The coupled algebraic Riccati-like equations turn the following discrete coupled algebraic Riccati equation (DCARE)
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