Abstract
The present study tackles the tracking control problem for unstructured uncertain bilinear systems with multiple time-delayed states subject to control input constraints. First, a new method is introduced to design memory state feedback controllers with compensator gain based on the use of operational properties of block-pulse functions basis. The proposed technique permits transformation of the posed control problem into a constrained and robust optimization problem. The constrained robust least squares approach is then used for determination of the control gains. Second, new sufficient conditions are proposed for the practical stability analysis of the closed-loop system, where a domain of attraction is estimated. A real-world example, the headbox control of a paper machine, demonstrates the efficiency of the proposed method.
Highlights
Many physical systems existing in real life exhibit nonlinear behavior
In order to provide the suitable choice of the number of block-pulse functions, we compare the exact solution xr(t) with approximate solution, given by xr(t) XrNSN(t)
E implementation of the proposed tracking control approach leads to the following control gains: 0.250 0.347
Summary
Many physical systems existing in real life exhibit nonlinear behavior. For system analysis and control, an approximate model is practically used for the purposes of simplicity because an exact system model is too difficult to obtain or too complicated to handle. e class of bilinear systems, representing the particular nonlinear systems whose dynamics are jointly linear in state and input variables, was introduced in the control theory due to its simple structure and applicability in the 1960s. There are a few works in which the stabilization control problem of saturated bilinear systems without uncertainties and/or time delays has been studied [22,23,24] All of these works have addressed only the case of discrete systems in which the nonlinear function is absorbed in a linear differential inclusion. AT represents the transpose of the matrix A. e adopted vector norm is the Euclidean norm and the matrix norm is the corresponding induced norm
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