Pablo Cesar Rodriguez-Ramirez

Sliding Mode Controller Design for Stochastic Polynomial Systems With Unmeasured States

This paper addresses the optimal controller problem for a polynomial system over linear observations with respect to different Bolza-Meyer criteria, where: 1) the integral control and state energy terms are quadratic and the nonintegral term is of the first degree or 2) the control energy term is quadratic and the state energy terms are of the first degree. The optimal solutions are obtained as sliding mode controllers, each consisting of a sliding mode filter and a sliding mode regulator, whereas the conventional feedback polynomial-quadratic controller fails to provide a causal solution. Performance of the obtained optimal controllers is verified in the illustrative example against the conventional LQG controller that is optimal for the quadratic Bolza-Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode controllers.

Sliding mode filter design for nonlinear polynomial systems with unmeasured states

This paper addresses the mean-square and mean-module filtering problems for a nonlinear polynomial stochastic system with Gaussian white noises. The obtained solutions contain a sliding mode term, signum of the innovations process. It is shown that the designed sliding mode mean-square filter generates the mean-square estimate, which has the same minimum estimation error variance as the estimate given by the conventional mean-square polynomial filter Basin et al. (2008) [8], although the gain matrices of both filters are different. The designed sliding mode mean-module filter generates the mean-module estimate, which yields a better value of the mean-module criterion in comparison to the conventional mean-square polynomial filter. The theoretical result is complemented with an illustrative example verifying performance of the designed filters. It is demonstrated that the estimates produced by the designed sliding mode mean-square filter and the conventional mean-square polynomial filter yield the same estimation error variance, and there is an advantage in favor of the designed sliding mode mean-module filter.

Sliding-Mode Filter Design for Linear Systems With Unmeasured States

This paper addresses the mean-square and mean-module filtering problems for a linear system with Gaussian white noises. The obtained solutions contain a sliding-mode term, signum of the innovation process. It is shown that the designed sliding-mode mean-square filter generates the mean-square estimate, which has the same minimum estimation-error variance as the best estimate given by the classical Kalman-Bucy filter, although the gain matrices of both filters are different. The designed sliding-mode mean-module filter generates the mean-module estimate, which yields a better value of the mean-module criterion in comparison with the mean-square Kalman-Bucy filter. The theoretical result is complemented with an illustrative example verifying the performance of the designed filters. It is demonstrated that the estimates produced by the designed sliding-mode mean-square filter and the Kalman-Bucy filter yield the same estimation-error variance, and there is an advantage in favor of the designed sliding-mode mean-module filter.

Sliding mode mean-module filter design for polynomial systems

This paper addresses the mean-module filtering problem for a stochastic polynomial system with Gaussian white noises. The obtained solution contains a sliding mode term, signum of the innovations process. It is shown that the designed sliding mode filter generates the mean-module estimate, which yields a better value of the mean-module criterion in comparison to the mean-square polynomial filter. The theoretical result is complemented with an illustrative example verifying performance of the designed filter, which is compared to the mean-square polynomial filter. The simulation results confirm an advantage in favor of the designed sliding mode filter.

A nonhomogeneous super-twisting algorithm for systems of relative degree more than one

Abstract This paper presents a nonhomogeneous continuous super-twisting algorithm for systems of relative degree more than one. The conditions of finite-time convergence to the origin are obtained and the robustness of the designed algorithm is discussed. The paper concludes with numerical simulations illustrating performance of the designed algorithms.

Sliding mode controller design for linear systems with unmeasured states

This paper addresses the optimal controller problem for a linear system over linear observations with respect to different Bolza-Meyer criteria, where 1) the integral control and state energy terms are quadratic and the non-integral term is of the first degree or 2) the control energy term is quadratic and the state energy terms are of the first degree. The optimal solutions are obtained as sliding mode controllers, each consisting of a sliding mode filter and a sliding mode regulator, whereas the conventional feedback LQG controller fails to provide a causal solution. Performance of the obtained optimal controllers is verified in the illustrative example against the conventional LQG controller that is optimal for the quadratic Bolza-Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode controllers.

Sliding mode mean-module filtering for linear stochastic systems

This paper addresses the mean-module filtering problem for a linear system with Gaussian white noises. The obtained solution contains a sliding mode term, signum of the innovations process. It is shown that the designed sliding mode filter generates the mean-module estimate, which yields a better value of the mean-module criterion in comparison to the mean-square Kalman-Bucy filter. To the best of our knowledge, this is the first designed sliding mode filter that is optimal with respect to the mean-module criterion. The theoretical result is complemented with an illustrative example verifying performance of the designed filter, which is compared to the conventional Kalman-Bucy filter. The simulation results confirm an advantage in favor of the designed sliding mode filter.

Sliding mode filtering for stochastic systems with polynomial state and observation equations

Abstract In this paper, the mean-square and mean-module filtering problems for polynomial system states over polynomial observations are studied proceeding from the general expression for the stochastic Ito differentials of the estimate and the error variance. The paper deals with the general case of nonlinear polynomial states and observations. As a result, the Ito differentials for the estimates and error variances corresponding to the stated filtering problems are first derived. The procedure for obtaining an approximate closed-form finite-dimensional system of the sliding mode filtering equations for any polynomial state over observations with any polynomial drift is then established. In the examples, the obtained sliding mode filters are applied to solve the third-order sensor filtering problems for a quadratic state, assuming a conditionally Gaussian initial condition for the extended second-order state vector. The simulation results show that the designed sliding mode filters yield reliable and rapidly converging estimates.

A super-twisting control algorithm for systems of relative degree more than one

This paper presents a homogeneous continuous super-twisting algorithm for systems with relative degree more than one. The conditions of finite-time convergence to an equilibrium are obtained demonstrating that the equilibrium can be moved as close to the origin as necessary, increasing a value of the control gain. The paper concludes with numerical simulations illustrating performance of the designed algorithms.

Sliding mode controller design for linear stochastic systems with unknown parameters

Abstract This paper presents the sliding mode mean-square and mean-module controllers for linear stochastic systems with unknown parameters. In both cases, the controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. Performance of the obtained controllers is verified in the illustrative example against the sliding mode mean-square and sliding mode controllers that are optimal for linear systems with known parameters. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.