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Stable output feedback model predictive control design: LMI approach

Vesely V., Bars R.

Archives of Control Sciences

2008

Vol. 18, no. 3

385-394

The paper addresses two design problems dealing with a quadratic stable output/state feedback model predictive control for linear systems without constraints. For the first approach the model predictive control is designed for a N2 state ahead prediction using the Lyapunov function approach with cost function. In the second approach, the one step ahead prediction control is designed using classical LQR state feedback controller approach. By Diophantine matrix equation, the classical state feedback is recalculated to output one step ahead model predictive control. Three examples are given to demonstrate the effectiveness of proposed methods.

Sub-Optimal Nonlinear Predictive and Adaptive Control Based on the Parametric Volterra Model

Haber R., Bars R., Lengyel O.

International Journal of Applied Mathematics and Computer Science

1999

Vol. 9, no 1

161-173

Predictive control algorithms have been worked out mainly to control linear plants. There is a great demand to apply different control ideas to nonlinear systems. Using predictive control algorithms for nonlinear systems is a promising technique. Extended horizon one-step-ahead and long-range optimal predictive control algorithms are given here for the parametric Volterra model (which includes also the generalized Hammerstein model). A quadratic cost function is minimized which considers the quadratic deviations of the reference signal and the output signal at a future point (or points) beyond the dead time and also penalizes large control signal increments. For prediction of the output signal, a predictive model is applied which uses information about the input and output signals up to the current time. A predictive transformation of the nonlinear dynamic model is given. The incremental model is advantageous since the cost function contains the control increment and not the control signal itself. An incremental transformation of the predictive forms is also described. Sub-optimal solutions to the optimal control algorithms are discussed with different assumptions for the control signal during the control horizon. The effect of the different strategies and the effect of the tuning parameters is investigated through simulation examples.