Tracking control design for nonlinear polynomial systems via augmented error system approach and block pulse functions technique

Abstract

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Combining Augmented Error Modeling Technique and Block-Pulse Functions Method for Tracking Control Design of Nonlinear Polynomial Systems with Multiple Time-Delayed States Subject to Nonsymmetric Input Saturation

“…Using the vectorization operator vec (see Appendix B in [34]) allows us to develop the last relation (75) in the following form:…”

“…Due to the necessity of bringing remedy to the drawbacks of the exiting control methods based on the Lyapunov theory, increasing interests are showed up as of late toward the improvement of numerical approximation methods based on the modeling concept of nonlinear polynomial systems. Some works are devoted to the tracking control problem for such undelayed system in the case of a step input [31] as well as in the case of a time-varying set point input [34]. For the subclass of the nonlinear polynomial system under the presence of a single time-delayed state, whose value is supposed to be constant and known, the tracking control problem has been addressed in [35] using block-pulse functions as a tool of approximation.…”

“…Proceeding from the above idea, a new algebraic scheme for the development of a memory polynomial state feedback controller with an integral-action-based compensator for continuous-time nonlinear polynomial system affected by multiple time delays in the states and under nonsymmetric input saturation is presented in the current study. Right off the bat, the modeling technique of augmented error is performed to determine an equivalent augmented form for the closed-loop controlled system, which permits to achieve high trajectory tracking performance [34,36]. +en, the block-pulse functions basis as an approximation tool as well as their operational matrices are exploited to transform the augmented state-space model of controlled saturated process into an equivalent constrained linear model of algebraic equations, which depends only on the controller gains.…”

Combined Constrained Robust Least Squares Approach and Block-Pulse Functions Technique for Tracking Control Synthesis of Uncertain Bilinear Systems with Multiple Time-Delayed States under Bounded Input Control

“…e whole development uses block-pulse functions as a tool of approximation as well as their operational matrices. Among all other piecewise constant basis functions, the block-pulse functions set proved to be the most fundamental, which has the advantage of reducing computational complexities and execution time [30][31][32][33][34].…”

“…XYZ) � Z T ⊗ X vec(Y).Property 2.Let the matrices A � [a ij ] ∈ R m×n and B ∈ R p×q ; we have[34] vec(A ⊗ B) � vec B ⋮ . .…”