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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    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.
    Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on; 09/2005
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    ABSTRACT: This paper addresses synthesis approaches to output feedback model predictive control (OFMPC) for systems with Hammerstein-Wiener nonlinearity and bounded disturbance/noise. The Hammerstein nonlinearity is removed (or partially removed) by constructing its inverse (or pseudo-inverse). The remaining nonlinearities in the model are incorporated by polytopic descriptions. At each sampling time, OFMPC finds a feedback gain and an estimator, such that the state of the closed-loop system asymptotically converges to a neighbourhood of the origin. A numerical example is given to illustrate the effectiveness of the controller.
    IET Control Theory and Applications 10/2007; 1(5-1):1302 - 1310. DOI:10.1049/iet-cta:20060420 · 2.05 Impact Factor
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    ABSTRACT: In the process industry, there exist many systems which can be approximated by a Hammerstein model. Moreover, these systems are usually subjected to input magnitude constraints. In this paper, a multi-channel identification algorithm (MCIA) is proposed, in which the coefficient parameters are identified by least squares estimation (LSE) together with a singular value decomposition (SVD) technique. Compared with traditional single-channel identification algorithms, the present method can enhance the approximation accuracy remarkably, and provide consistent estimates even in the presence of coloured output noises under relatively weak assumptions on the persistent excitation (PE) condition of the inputs. Then, to facilitate the following controller design, this MCIA is converted into a two stage single-channel identification algorithm (TS-SCIA), which preserves most of the advantages of MCIA. With this TS-SCIA as the inner model, a dual-mode non-linear model predictive control (NMPC) algorithm is developed. In detail, over a finite horizon, an optimal input profile found by solving a open-loop optimal control problem drives the non-linear system state into the terminal invariant set; afterwards a linear output-feedback controller steers the state to the origin asymptotically. In contrast to the traditional algorithms, the present method has a maximal stable region, a better steady-state performance and a lower computational complexity. Finally, simulation results on a heat exchanger are presented to show the efficiency of both the identification and the control algorithms.
    International Journal of Control 10/2008; 81(10). DOI:10.1080/00207170701885453 · 1.65 Impact Factor
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