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


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: This paper presents a new nonlinear model predictive control (MPC) algorithm for Hammerstein systems subject to constraints on the state, input, and intermediate variable. Taking no account of constraints, a desired linear controller of the intermediate variable is obtained by applying pole placement to the linear subsystem. Then, actual control actions are determined in consideration of constraints by online solving a finite horizon optimal control problem, where only the first control is calculated and others are approximated to reduce the computational demand. Moreover, the asymptotic stability can be guaranteed in certain condition. Finally, the simulation example of the grade transition control of industrial polypropylene plants is used to demonstrate the effectiveness of the results proposed here.
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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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    ABSTRACT: For input saturated Hammerstein systems, the two-step predictive control strategy is adopted. The first step calculates the desired intermediate variable applying unconstrained linear model and predictive control. The second step obtains the real-time control action by solving algebraic equation and desaturation. The case of immeasurable state is considered where the observer gain matrix is solved by Sylvester equation. The sufficient closed-loop stability condition is given and the designing and tuning algorithm for the domain of attraction is proposed. The theoretical results are validated by an example.
    No preview · Article · Mar 2006 · Journal of Systems Engineering and Electronics
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