Some of these recent development are further detailed: In fact, these methods have recently been shown to outrank (or perform equivalently as) fast NMPC solvers, such as ACADO. As previously evidenced, these qLPV methods are able to use the scheduling proxy ρ(k) = f( x( k), u( k)) to compute the process predictions rapidly. Instead of using a moving-window linearization strategy to yield fast NMPCs with time-varying models, or of using approximated solutions of the NP iterations, this paper follows the lines of the qLPV embedding framework, which allows for an exact description of the nonlinear system and, thereby, no time-consuming linearization or Jacobian computation needs to take place.
![mpc 2 norm state feedback solution mpc 2 norm state feedback solution](https://i1.rgstatic.net/publication/224627267_Application_of_MPC_to_an_active_structure_using_sampling_rates_up_to_25kHz/links/00463517eed7d1e93f000000/largepreview.png)
The basic requirement of these methods is that the nonlinearities must respect the Linear Differential Inclusion (LDI) property, in such a way that they can be embedded into a qLPV realisation, appropriately “hidden” in scheduling parameters ρ. A recent survey details the vast possibilities of issuing NMPC through LPV structures.
![mpc 2 norm state feedback solution mpc 2 norm state feedback solution](https://i1.rgstatic.net/publication/228358774_Explicit_Model_Predictive_Control_for_Large-Scale_Systems_via_Model_Reduction/links/00b7d5211f29f4864b000000/largepreview.png)
Since LPV models retain linearity properties through the input/output channels, the optimization can be reduced to the complexity of a QP. Parallel to these approximated methods, another research route is now expanding to address the complexity drawback of “full-blown” NMPC strategies: using quasi-/Linear Parameter Varying (qLPV/LPV) model structures to embed the nonlinear dynamics, as in, and thus facilitate the online optimization. Some of these faster NMPC algorithms run within the range of a few milliseconds, resorting to solver-based solutions (as in ACADO or GRAMPC algorithms) or GPU-based schemes. Originally, NMPC algorithms were hardly able to run in real-time, but recent research effort has focused to a great extent on ways to simplify or approximate, usually through Gauss-Newton, Lagrangian or multiple-shooting discretization approaches, the online Nonlinear Programming Problem (NP) in order to make it viable for fast, time-critical processes. Nevertheless, the majority of system is indeed nonlinear and, thus, literature has devoted special attention to feasible NMPC design since the 00’s. Nonlinear MPC (NMPC) algorithms yield complex optimization procedure, with exponential growth of the numerical burden. This was mainly due to the fact that the inherent optimization procedures were excessively costly (numerical-wise) and became impractical for real-time systems. ) should be -class upper bounded and Lyapunov-decreasing (it must decay along the horizon).įor many years, MPC was mostly seen in the process industry, regulating usually slower applications (with longer sampling periods).Essentially, the terminal set must be robust positively invariant for the controlled system, the stage cost must be -class lower bounded and the terminal cost V( ) and to a terminal constraint X f are verified.
![mpc 2 norm state feedback solution mpc 2 norm state feedback solution](https://i1.rgstatic.net/publication/350855852_High-Frequency_Nonlinear_Model_Predictive_Control_of_a_Manipulator/links/60f53368fb568a7098bd8f56/largepreview.png)
These properties are enabled when some conditions with respect to a terminal stage cost V( For the case of processes represented by Linear Time-Invariant (LTI) models, MPC is translated as a constrained Quadratic Programming Problem (QP), which can be evaluated in real-time by the majority of standard solvers.Įxtra attention should be payed to the fact that the theoretical establishment MPC was especially consolidated after the proposition of “terminal ingredients”, which served to demonstrate robust stability and recursive feasibility properties.
![mpc 2 norm state feedback solution mpc 2 norm state feedback solution](https://www.mathworks.com/help/examples/mpc/win64/ReviewModelPredictiveControllerForStabilityAndRobustnessExample_02.png)
The core idea of MPC is simple enough: a process model is used to predict the future output response of the process then, at each instant, the control law is found through the solution of an online optimization problem, which is written in terms of the model, the process constraints and the performance goals. Model Predictive Control (MPC) is a very powerful control method, with widespread industrial application.