Model predictive control (MPC) has been applied and studied extensively in the literature. It remains challenging to maintain stability under various conditions as well as perform the underling optimization in real-time. These challenges are amplified when the physical system is described by a large set of equations with inherent complexity. Distributed parameter systems (DPS) is a class of large scale physical systems that are described by infinite-dimensional state-space models. The direct use of such models may be difficult, and simplifications are applied based on the nature of the physical system and/or knowledge that is acquired through data analysis. The research detailed in this Thesis is divided into two directions: (i) stability analysis of MPC under unstructured uncertainty and (ii) optimization algorithms for complex large scale systems. Different stability conditions are constructed, using the theory of robust control. This is a classic approach that has been developed in the last two decades for both continuous and discrete time systems. Integral quadratic constraints (IQCs) and their associated multipliers are employed to handle the nonlinear structure of the input-output map of MPC. A special class of MPC that is considered in this thesis is the barrier-based MPC where a self-concordant function replaces the constraints in the objective function. The use of this has been reported to produce smoother control actions than those of the nominal MPC. This property is mathematically formulated, showing that the use of barriers can increase the stability region. Conditions for the robust stability of multi-model MPC are also developed. The use of linear models can be very restrictive in practice due to the complex nature of the (nonlinear) physical system. As a result, multiple linear models can be used to facilitate better performance. Similar to the barrier-based MPC, IQCs are developed to incorporate multi-model MPC in stability analysis. Dissipativity, in conjunction with IQCs, is explored to construct the stability conditions for this class of controllers. The combination of the above methodologies results in a systematic framework for the stability conditions of large-scale systems when model reduction is applied. The optimization of large scale systems is not trivial especially in the case of dynamic optimization or nonlinear MPC. The equations of the DPS may be complex nonlinear or unknown. As a result, the optimization technique that is applied should effectively use an available simulator. Two different approaches are formulated: The first one aims to develop an optimization algorithm that uses a black-box simulator directly while the second approach does that indirectly. The optimization algorithm exploits the simulator in an equation-free fashion in a 2-step projection scheme, firstly onto the dominant modes and secondly onto the degrees of freedom. A distinctively different approach is also considered. The previous algorithm utilizes a black-box simulator efficiently, however for systems where fast control actions are needed the direct use of the simulator is not preferable. To overcome this limitation, data-driven nonlinear multiparametric (mp) optimization is proposed. First a set of data are used to train deep recurrent neural networks for the reduced space and then a data-driven methodology is formulated to construct an approximate mp-nonlinear MPC.
- Robust MPC
- Stability Analysis
- Dynamic Optimization
- Multiparametric Programming
Intelligent Methodologies for Optimization and Model Predictive Control of Complex Nonlinear Systems
Petsagkourakis, P. (Author). 31 Dec 2019
Student thesis: Phd