Algorithmic Differentiation of the MWGS-Based Arrays for Computing the Information Matrix Sensitivity Equations within the Problem of Parameter Identification

The paper considers the problem of algorithmic differentiation of information matrix difference equations for calculating the information matrix derivatives in the information Kalman filter. The equations are presented in the form of a matrix MWGS (modified weighted Gram–Schmidt) transformation. The solution is based on the usage of special methods for the algorithmic differentiation of matrix MWGS transformation of two types: forward (MWGS-LD) and backward (MWGS-UD). The main result of the work is a new MWGS-based array algorithm for computing the information matrix sensitivity equations. The algorithm is robust to machine round-off errors due to the application of the MWGS orthogonalization procedure at each step. The obtained results are applied to solve the problem of parameter identification for state-space models of discrete-time linear stochastic systems. Numerical experiments confirm the efficiency of the proposed solution.

General Lyapunov-Based Iterative Algorithm for Linear Quadratic Regulator Problem of Stochastic Systems with Markovian Jump

This paper investigates the linear quadratic regulator(LQR) problem of linear stochastic systems with Markovian jump. Firstly, two iterative algorithms are proposed for solving the corresponding coupled algebraic Riccati equa- tions (CAREs) based on the general-type Lyapunov equation derived from linear stochastic systems. It is verified that the second algorithm adding an adjustable factor converges faster than the first one without it. Secondly, a monotonic convergence theorem is established for the proposed iterative algorithms under certain initial conditions. In the end, a numerical example is given to verify the efficiency of the proposed algorithms.

General Lyapunov-Based Iterative Algorithm for Linear Quadratic Regulator Problem of Stochastic Systems with Markovian Jump

This paper investigates the linear quadratic regulator(LQR) problem of linear stochastic systems with Markovian jump. Firstly, two iterative algorithms are proposed for solving the corresponding coupled algebraic Riccati equa- tions (CAREs) based on the general-type Lyapunov equation derived from linear stochastic systems. It is verified that the second algorithm adding an adjustable factor converges faster than the first one without it. Secondly, a monotonic convergence theorem is established for the proposed iterative algorithms under certain initial conditions. In the end, a numerical example is given to verify the efficiency of the proposed algorithms.