![]() ![]() Usually for this type of problem, when the output feedback MPC approach is adopted, the overall optimization problem adopts both the state estimator gain and state feedback gain as the on-line decision variables (Famularo & Franzè, 2011). In this paper, we consider linear systems with norm-bounded model parametric uncertainty and disturbance. The resulting optimization problem is bilinear, so it has to be solved by iterations. ![]() In Famularo and Franzè (2011), the system with norm-bounded model parametric uncertainty and disturbance is considered, where the estimation error bound is pre-fixed as a constraint of the optimization problem which may bring some conservativeness. (2008), by pre-specifying the feedback gain, an output feedback MPC approach for systems with unstructured model uncertainty is developed. In Ding, 2011a, Ding, 2011b, the dynamic output feedback robust MPC approach is proposed, where the ellipsoid estimation error bound is properly refreshed at each sampling instant, so that the closed-loop system is proven as quadratically bounded. Hence, the refreshment of this estimation error bound is crucial for guaranteeing the recursive feasibility of the optimization problem (Ding, 2011a). Since the estimation error is unknown, it is advisable to replace it by its outer bound. When the state is unmeasurable, the system output is utilized to estimate the state. For this reason, output feedback MPC studies have gained many attentions due to its ability to tolerate state estimation errors (Ding, 2011a, Ding, 2011b, Hu and Ding, 2019, Li et al., 2013, Løvaas et al., 2008, Mayne et al., 2006, Park et al., 2011, Sato and Peaucelle, 2013). Indeed, in many applications, all states are not measurable. The assumption that the state is measurable is not generally practical. (2012), a bounded disturbance is considered, and a so-called uncertainty-based dynamic control policy is used to reduce computational burden. In Garone and Casavola (2012), the nonlinear parameter-dependent Lyapunov functions are adopted to reduce the conservativeness. (1996) which utilizes a single quadratic Lyapunov function, several quadratic Lyapunov functions, each corresponding to a vertex of the polytope, are utilized to extend the result. The state feedback gain is designed off-line, and the performance cost is a quadratic term on the perturbations. In Imsland et al., 2005, Kouvaritakis et al., 2000, the control move is defined as state feedback plus perturbation. Since the seminal work (Kothare, Balakrishnan, & Morari, 1996), Linear Matrix Inequality (LMI) based MPC has become one of the most efficient approaches to handle system with uncertainties and achieve satisfactory control performance (Cuzzola et al., 2002, Garone and Casavola, 2012, Gautam et al., 2012, Imsland et al., 2005, Kouvaritakis et al., 2000). ![]() For this reason, different approaches to model system uncertainties have been proposed, e.g., polytopic (represented by Linear Parameter-Varying (LPV) model (Bumroongsri and Kheawhom, 2012, Calafiore and Fagiano, 2013, Gautam et al., 2012, He et al., 2014, Zheng et al., 2013)) and norm-bounded (Casavola et al., 2004, Famularo and Franzè, 2011, Løvaas et al., 2008). However, in real industrial processes, there always exist various uncertainties and nonlinearities, so the theoretical analysis based on the nominal linear model may be impractical. An explicit linear model is typically utilized in MPC because the on-line optimization problem would reduce to a linear or quadratic programming problem (Kouvaritakis et al., 2002, Shead et al., 2010) (sometimes even linear operations (Ghaemi, Sun, & Kolmanovsky, 2012)). It is a model-based control technique that solves an optimal control problem at each sampling instant, based on an explicit model of the system. Model predictive control (MPC), also known as receding horizon control, has gained notably attentions in both academia and industry due to its ability to optimally control nonlinear systems subject to physical constraints (Mayne et al., 2000, Morari and Lee, 1999). ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |