Rodolfo Martinez-Zuniga

Optimal control for linear systems with time delay in control input

This paper presents the optimal regulator for a linear system with time delay in control input and a quadratic cost function. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with time delay in observations, and then proved using the maximum principle. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included.

Optimal filtering for linear state delay systems

In this note, the optimal filtering problem for linear systems with state delay over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the optimal estimate equation similar to the traditional Kalman-Bucy one is derived; however, it is impossible to obtain a system of the filtering equations, that is closed with respect to the only two variables, the optimal estimate and the error variance, as in the Kalman-Bucy filter. The resulting system of equations for determining the error variance consists of a set of equations, whose number is specified by the ratio between the current filtering horizon and the delay value in the state equation and increases as the filtering horizon tends to infinity. In the example, performance of the designed optimal filter for linear systems with state delay is verified against the best Kalman-Bucy filter available for linear systems without delays and two versions of the extended Kalman-Bucy filter for time-delay systems.

Alternative optimal filter for linear systems with multiple state and observation delays

In this paper, the optimal filtering problem for linear systems with multiple state and observation delays is treated using the optimal estimate of the state transition matrix. As a result, the alternative optimal filter is derived in the form similar to the traditional Kalman-Bucy one, i.e., consists of only two equations, for the optimal estimate and the estimation error variance. This presents a significant advantage in comparison to the previously obtained optimal filter [1], which includes infinite or variable number of covariance equations, unboundedly growing as the filtering horizon tends to infinity. Performances of the two optimal filters are compared in example; the obtained results are discussed.

Optimal control for linear systems with time delay in control input based on the duality principle

This paper presents the optimal regulator for a linear system with time delay in control input and a quadratic criterion. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with time delay in observations. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included.

Optimal linear filtering over observations with multiple delays

In this paper, the optimal filtering problem for a linear system over observations with multiple delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and its variance. As a result, the optimal filtering equations similar to the traditional Kalman-Bucy ones are obtained in the form dual to the Smith predictor, commonly used for robust control design in time delay systems. In the example, the obtained optimal filter over observations with multiple delays is verified for a sample system and compared with the best Kalman-Bucy filter available for delayed measurements.

Optimal filtering for linear systems with multiple delays in observations

Abstract In this paper, the optimal filtering problem for a linear system over observations with multiple delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and its variance. As a result, the optimal filtering equations similar to the traditional Kalman-Bucy ones are obtained in the form dual to the Smith predictor, commonly used for robust control design in time delay systems. In the example, the obtained optimal filter over observations with multiple delays is verified for a sample system and compared with the best Kalman-Bucy filter available for delayed measurements.

Optimal Filtering for Linear Systems with Multiple State and Observation Delays

In this paper, the optimal filtering problem for linear systems with multiple state and observation delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate, error variance, and various error covariances. The resulting system of equations for determining the filter gain matrix consists, in the general case, of an infinite set of equations. It is however demonstrated that a finite set of the filtering equations can be obtained in the particular case of equal or commensurable (tauj =qjh, qj are natural) delays in the observation and state equations. In the example, performance of the designed optimal filter for linear systems with state and observation delays is verified against the best Kalman-Bucy filter available for linear systems without delays

Alternative Optimal Filter for Linear State Delay Systems

In this paper, the optimal filtering problem for linear systems with state delay over linear observations is treated using the optimal estimate of the state transition matrix. As a result, the alternative optimal filter is derived in the form similar to the traditional Kalman-Bucy one, i.e., consists of only two equations, for the optimal estimate and the estimation error variance. This presents a significant advantage in comparison to the previously obtained optimal filter by Basin MV, et al (2005), which includes a variable number of covariance equations, unboundedly growing as the filtering horizon tends to infinity. Performances of the two optimal filters are compared in example; the obtained results are discussed

Optimal Filtering for Nonlinear Polynomial Systems Over Linear Observations With Time Delay

Abstract In this paper, the optimal filtering problem for nonlinear systems over linear observations with time delay is treated proceeding from the general expression for the stochastic !to differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for a polynomial state over linear observations with delay is then established, which yields the explicit closed form of the filtering equations in the particular case of a bilinear system state. In the example, performance of the designed optimal filter for bilinear states over linear observations with delay is verified against the best filter available for bilinear states over linear observations without delays and the conventional extended Kalman-Bucy filter.