Contact information: Juraj Oravec
Brief introduction of the Institute of Information Engineering, Automation and Mathematics (IAM) [link]. Introduced the possibilities to study at IAM by ERASMUS+ Program [link].
Robust MPC is an advanced control strategy to optimize control performance subject to the constraints of the system inputs/outputs and in the presence of bounded disturbance. Several alternative approaches of online robust MPC design based on LMI formulation are formulated. The proposed alternative approaches are based on existing approaches. Suitable properties of these approaches are adopted to reduce the conservativeness of the quadratic stability condition, to reduce the conservativeness of control inputs constraints evaluation, and to minimize a computational effort. Therefore, these alternative robust MPC methods may be considered as a tool for overcoming some of the robust MPC design obstacles. Simulation case studies are proposed to demonstrate the effectiveness of the proposed strategies.
Software MUP represents an efficient and user-friendly MATLAB-based toolbox for online robust MPC design in LMI-framework. The toolbox enables designing robust MPC using an all-in-one MATLAB/Simulink block. The advanced users may benefit from designing robust MPC using MATLAB Command-Line-Interface. One of the most valuable features is an advanced feasibility check, i.e., when the optimization problem is found infeasible, then we suggest to the user how to modify the robust MPC design problem to make it feasible. The MUP is dependent on the YALMIP toolbox that reformulates the optimization problem and delegates it to an external SDP solver, e.g., MOSEK or SeDuMi. An illustrative case study of robust MPC design for a real process is proposed to demonstrate the effectiveness of the MUP toolbox.
The LMI-based robust MPC design exercises are oriented on the implementation of simple robust MPC for the uncertain system with input and state constraints. Two approaches are considered, i.e., manual implementation and implementation using the MUP toolbox. The manual implementation aims to point out the key ideas of robust MPC design. On the other hand, MUP-based implementation demonstrates the efficacy of the software and enables the user to focus the attention on the robust MPC tuning to improve the closed-loop control performance. This task includes also some hints on how to solve the considered robust MPC design problem.
The LMI-based robust MPC design exercises are evaluated using MATLAB/Simulink environment. Although there were not observed obstacles by using older releases of MATLAB, the recommended release is R2014b or later.
We strongly recommend to use tbxmanager for MATLAB whenever possible. The install instructions can be found on its homepage. Then, you can download the required toolboxes YALMIP, SEDUMI, and MUP, using tbxmanager via MATLAB Command Window by typing:
tbxmanager install yalmip sedumi mup
To keep the releases up-to-date you should run the commands:
tbxmanager update yalmip sedumi mup
Obviously, there should be a much more extensive list of references focused on LMI-based robust MPC design. Here are mentioned just several publications closely related to the considered topic. The following works (listed subject to the time of publishing) are crucial to cover the necessary theoretical backgrounds, considered software implementation, and selected applications.
Chapters 2 and 3 discussed wide classes of process control problems that can be formulated using linear matrix inequalities. Chapter 7 considered State-Feedback Synthesis for the systems in the continuous-time domain.
Principles of formulating and solving SDP problems.
Pioneer work of LMI-based robust MPC design. Based on former American Control Conference (1995) paper.
Robust positive invariant sets are crucial to guarantee the closed-loop system stability.
Extensive survey on robust MPC.
Reference to well-known and freely available MATLAB-based toolbox to solve the SDP problems.
The conservativeness of the quadratic stability condition was reduced by introducing the parameter-dependent Lyapunov function. Note, that robust MPC design did not consider the time-varying uncertainties. This issue was fixed in the paper Mao (2003).
Fixed the issue of PDLF-based robust MPC design subject to the time-varying uncertainties.
System states have to converge into the origin in each control step. This paper considered the robust MPC design subject to the required value of states convergence just for the nominal system, i.e., system vertices were forced to converge without preset value.
Chapter 11 discussed in detail the theoretical backgrounds of Interior-point methods.
Basic reference to an advanced MATLAB-based toolbox YALMIP that serves to formulate the complex optimization problems in user-friendly and tractable form. YALMIP was introduced already in 2003 by the author's PhD-thesis and originally was developed to solve especially LMI-based optimization problems.
Conservativeness of constraints on the control inputs was reduced using advanced additional control input saturation.
PDLF-based robust MPC design subject to the nominal system optimization.
The drawback of the infinity prediction horizon is that the single controller is considered to control an uncertain system forever. Although the state-feedback controller is redesigned in each control step, the results may be conservative. The conservativeness was reduced by designing two controllers, one for the current control step, and the second for the next control steps.
Extension of Cao et al. (2005). The robust MPC design tuning parameter was introduced to set the weight of the constrained and non-constrained control action. It enabled to compute more aggressive control action when the control input is not constrained.
Chapter 2 of the book provides excellent insight into Semidefinite Optimization.
LMI-based robust MPC design considering a set of linear control laws for a finite control horizon.
Conservativeness of robust MPC design subject to the constrained control inputs is reduced by saturation-dependent Lyapunov functions.
Speed up of LMI-based robust MPC design by the advanced fixing of the control inputs in the next control step. The approach leads to the suboptimal solution.
Basic reference to MATLAB-based toolbox MUP for on-line LMI-based robust MPC design. Case study of robust MPC implementation for real process.
Current survey on MPC, issues of robust MPC were briefly discussed.
Various alternative robust MPC design procedures were proposed. These approaches were derived considering the suitable properties of exiting strategies.
Introduction to MATLAB-based toolbox MUP for on-line LMI-based robust MPC design.
Control performance analysis of alternative robust MPC design implemented for real process.
Fouling of the heat exchanger network modelled using the parametric uncertainty and the control performance analysis of alternative robust MPC design.
Novel convex-lifting-based robust control strategy and its implementation to laboratory plants.
Experimental analysis of the energy-efficient control of plate heat exchanger by implementing soft-constraints.
Extensive experimental analysis of the multivariable control of a chemical reactor using a performance tuning.
Last Update: 2021-07-08