Control of Unknown Nonlinear Systems with Linear Time-Varying MPC

We present a Model Predictive Control (MPC) strategy for unknown input-affine nonlinear dynamical systems. A non-parametric method is used to estimate the nonlinear dynamics from observed data. The estimated nonlinear dynamics are then linearized over time-varying regions of the state space to construct an Affine Time-Varying (ATV) model. Error bounds arising from the estimation and linearization procedure are computed by using sampling techniques. The ATV model and the uncertainty sets are used to design a robust Model Predictive Controller (MPC) which guarantees safety for the unknown system with high probability. A simple nonlinear example demonstrates the effectiveness of the approach where commonly used estimation and linearization methods fail

Data-driven Nonlinear Predictive Control for Feedback Linearizable Systems

We present a data-driven nonlinear predictive control approach for the class of discrete-time multi-input multi-output feedback linearizable nonlinear systems. The scheme uses a non-parametric predictive model based only on input and noisy output data along with a set of basis functions that approximate the unknown nonlinearities. Despite the noisy output data as well as the mismatch caused by the use of basis functions, we show that the proposed multistep robust data-driven nonlinear predictive control scheme is recursively feasible and renders the closed-loop system practically exponentially stable. We illustrate our results on a model of a fully-actuated double inverted pendulum.Comment: accepted to IFAC World Congress 2023. arXiv admin note: substantial text overlap with arXiv:2204.0114

Manufacturing systems considered as time domain control systems : receding horizon control and observers

This thesis considers manufacturing systems and model-based controller design, as well as their combinations. The objective of a manufacturing system is to create products from a selected group of raw materials and semifinished goods. In the field of manufacturing systems control is an important issue appearing at various operation levels. At the level of fabrication, for example, control is necessary in order to assure properly working production processes such that products are being fabricated in the desired way. At a higher level in the hierarchy of manufacturing system control, the product streams through the system are controlled in order to satisfy, for example, customer demands in an optimal way. Here, the definition of optimal can be interpreted in various ways, such as "with the least possible costs in terms of money" or "in the shortest possible time". In this research, the attention is focussed on this higher hierarchy level of manufacturing system control. In the literature, many heuristic methods have been developed for the control of a manufacturing system. Nowadays, some heuristicmethods are still being used in combination with operator experience for management of resources and planning of production. However, as the complexity of the manufacturing systems increases rapidly, the (simple) heuristic methods and operator experience will at some point become incapable of finding an optimal control strategy. In this dissertation the potential of consideringmanufacturing system control from a control systems point of view is investigated. The ultimate goal of the research is to eventually obtain a more constructive way to address controller design for manufacturing systems. One control strategy from control systems theory, on which is in particularly focused in this research, is a model-based receding horizon control strategy, known in literature as Model Predictive Control (MPC). Since in manufacturing systems a lot of physical system constraints are involved, like for example finite machine process capacities, finite product storage capacities, finite product arrival rates, etc., the capability for a manufacturing control strategy to handle those constraints is a necessity. One of the key features of model predictive control is the capability of handling constraints in the controller design. This is one of the major motivations to investigate the model predictive control principle as a control strategy for manufacturing systems. Other issues that are important and that the model predictive control design methodology can handle is to enforce optimality, to introduce feedback, and the capability of allowing for mixed continuous and discrete model structures. The later are typically encountered when models of manufacturing systems are derived. The main results that are obtained in this dissertation and that are relevant in the context of manufacturing systems control, but are certainly also relevant beyond this field are: • One has developed an robust computationally friendly nonlinear model predictive control algorithm that can handle model structures with mixed continuous and discrete dynamics. The algorithm can be designed for additive disturbance rejection purposes; • Robustness (with respect to measurement noise) results that are in particulary of interest in the field of nonlinear model predictive control are obtained; • An asymptotically stabilizing output based nonlinear model predictive control scheme for a class of nonlinear discrete-time systems is developed. Results that are relevant in the context of manufacturing systems control are: • It is illustrated howthe aforementioned developed robust computationally friendly nonlinear model predictive control algorithm can be employed to solve a large scale manufacturing control problem in an efficient decentralized manner; • The relation between the so-called event domain modeling approaches for a class of discrete-eventmanufacturing systems to time domainmodels is derived. This results enables one to solve seemingly untractable time domain formulated optimal control problems for a class of manufacturing systems in a tractable manner; • An observer theory for a class of discrete-event manufacturing systems is developed

Robust predictive feedback control for constrained systems

A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model

Stability Properties of the Adaptive Horizon Multi-Stage MPC

This paper presents an adaptive horizon multi-stage model-predictive control (MPC) algorithm. It establishes appropriate criteria for recursive feasibility and robust stability using the theory of input-to-state practical stability (ISpS). The proposed algorithm employs parametric nonlinear programming (NLP) sensitivity and terminal ingredients to determine the minimum stabilizing prediction horizon for all the scenarios considered in the subsequent iterations of the multi-stage MPC. This technique notably decreases the computational cost in nonlinear model-predictive control systems with uncertainty, as they involve solving large and complex optimization problems. The efficacy of the controller is illustrated using three numerical examples that illustrate a reduction in computational delay in multi-stage MPC.Comment: Accepted for publication in Elsevier's Journal of Process Contro

Incremental State-Space Model Predictive Control of a Fresnel Solar Collector Field

Model predictive control has been demonstrated to be one of the most efficient control techniques for solar power systems. An incremental offset-free state-space Model Predictive Controller (MPC) is developed for the Fresnel collector field located at the solar cooling plant installed on the roof of the Engineering School of Sevilla. A robust Luenberger observer is used for estimating the states of the plant which cannot be measured. The proposed strategy is tested on a nonlinear distributed parameter model of the Fresnel collector field. Its performance is compared to that obtained with a gain-scheduling generalized predictive controller. A real test carried out at the real plant is presented, showing that the proposed strategy achieves a very good performance.Comisión Europea ID 78905

Learning an Approximate Model Predictive Controller with Guarantees

A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter