Article

On the stability of output feedback predictive control for systems with input nonlinearity

Institute of Automation, Hebei University of Technology, Tianjin, 300130, P.R. China.
Asian Journal of Control (Impact Factor: 1.56). 08/2004; 6(3):388 - 397. DOI: 10.1111/j.1934-6093.2004.tb00214.x

ABSTRACT

For input saturated Hammerstein systems, a two-step output feedback predictive control (TSOFPC) scheme is adopted. A receding horizon state observer is chosen, the gain matrix of which has a form similar to the linear control law. Through application of Lyapunov's stability theory, the closed-loop stability for this kind of system is analyzed. The intermediate variable may or may not be available in real applications, and these two cases are considered separately in this paper. Furthermore, the domain of attraction for this kind of system is discussed, and we prove that it can be tuned to be arbitrarily large if the system matrix is semi-stable. The stability results are validated by means of an example simulation.

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    • "Model predictive control (MPC) is an effective control algorithm for handling constrained control problems, and various MPC algorithms have been proposed for control of Hammerstein systems with constraints4567891011. Making use of the geometry structure of Hammerstein model,456789developed two-step MPC schemes for Hammerstein systems with input constraints, where the intermediate variable was firstly obtained by linear MPC and then the actual control was calculated by solving nonlinear algebraic equations, desaturation, and so forth. Although two-step MPC algorithms possess more light computational burden than that where the nonlinearities were incorporated into optimal control problems directly[10,11], solving nonlinear algebraic equations will inevitably have error and the restricted control is generally different from the desired one for constrained Hammerstein systems[6]. "
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    ABSTRACT: A two-step predictive controller is studied for the input saturated uncertain Hammerstein model. The first step utilizes an unconstrained linear predictive controller that calculates a desired intermediate variable. The second step deals with nonlinearities by solving nonlinear algebraic equation (group) and desaturation. The polytopic description is applied to explore the exponential stability of the closed-loop system and the domain of attraction is further discussed. The effectiveness of the stability results is validated via a simulation example.
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