Owing to their ubiquitous presence, control designs have to deal with the presence of constraints and nonlinearity. Lyapunov-Based Model Predictive Control (LMPC) is one control method that enables achieving stability from a well characterized region [1, 2]. LMPC method like other MPC methods utilizes a model of the plant. In several scenarios, a good first principles model is unavailable, however, sufficient historical data exists to possibly build a data driven model for the purpose of utilization within LMPC based approaches.
The subspace identification methods (SIM) approach uses a set of input and output data, to estimate linear time-invariant models in a state space form. These methods are exploit concepts such as geometrical projections and numerical linear algebra. Numerical robustness, fewer user parameters, MIMO systems identification, model order reduction make SIMs a good choice for industrial applications [3]. SIMs are usually non-iterative methods, which makes their application, computationally affordable, and, this simplicity would make the model update, affordable.
Motivated by the above, in this work we develop a framework to integrate LMPC with the model identified by SIMs. To this end, a data driven model is first identified and utilized within offset-free LMPC approaches. Simulation results demonstrate the effectiveness of the proposed method.
[1] Mahmood, M. and Mhaskar, P. (2012). Lyapunov-based model predictive control of stochastic nonlinear systems. Automatica, 48(9), 2271-2276.
[2] Mahmood, M. and P. Mhaskar, Constrained Control Lyapunov Function Based Model Predictive Control Design, Int. J. Rob. & Nonl. Contr., 24, 374–388, 2014.
[3] Trnka, P. (2007). Subspace identification methods. PhD thesis, Ph. D. Thesis, Czech Technical University in Prague.
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