Direct data-driven control of constrained linear parameter-varying systems: A hierarchical approach

In many nonlinear control problems, the plant can be accurately described by a linear model whose operating point depends on some measurable variables, called scheduling signals. When such a linear parameter-varying (LPV) model of the open-loop plant needs to be derived from a set of data, several issues arise in terms of parameterization, estimation, and validation of the model before designing the controller. Moreover, the way modeling errors affect the closed-loop performance is still largely unknown in the LPV context. In this paper, a direct data-driven control method is proposed to design LPV controllers directly from data without deriving a model of the plant. The main idea of the approach is to use a hierarchical control architecture, where the inner controller is designed to match a simple and a-priori specified closed-loop behavior. Then, an outer model predictive controller is synthesized to handle input/output constraints and to enhance the performance of the inner loop. The effectiveness of the approach is illustrated by means of a simulation and an experimental example. Practical implementation issues are also discussed.Comment: Preliminary version of the paper "Direct data-driven control of constrained systems" published in the IEEE Transactions on Control Systems Technolog

A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems

We derive novel methods that allow to synthesize LPV state-feedback controllers directly from a single sequence of data and guarantee stability and performance of the closed-loop system, without knowing the model of the plant. We show that if the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data. With this representation, we formulate synthesis problems that yield controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\mathcal{L}_2$-gain of the closed-loop system. The controllers are synthesized by solving an SDP with a finite set of LMI constraints. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis that have complete knowledge of the true system model in multiple simulation studies.Comment: Submitted to IEEE Transactions on Automatic Control, extended version, 14 page

Direct data-driven design of LPV controllers with soft performance specifications

If only experimental measurements are available, direct data-driven control design becomes an appealing approach, as control performance is directly optimized based on the collected samples. The direct synthesis of a feedback controller from input-output data typically requires the blind choice of a reference model, that dictates the desired closed-loop behavior. In this paper, we propose a data-driven design scheme for linear parameter-varying (LPV) systems to account for soft performance specifications. Within this framework, the reference model is treated as an additional hyper-parameter to be learned from data, while the user is asked to provide only indicative performance constraints. The effectiveness of the proposed approach is demonstrated on a benchmark simulation case study, showing the improvement achieved by allowing for a flexible reference model.</p

Direct learning ofLPVcontrollers from data

In many control applications, it is attractive to describe nonlinear (NL) and time-varying (TV) plants by linear parametervarying (LPV) models and design controllers based on such representations to regulate the behaviour of the system. The LPV system class offers the representation of NL and TV phenomena as a linear dynamic relationship between input and output signals, which relationship is dependent on some measurable signals, e.g., operating conditions, often called as scheduling variables. For such models, powerful control synthesis tools are available, but the way how to systematically convert available first principles models to LPV descriptions of the plant, to efficiently identify LPV models for control from data and to understand how modeling errors affect the control performance are still subject of undergoing research. Therefore, it is attractive to synthesize the controller directly from data without the need of modeling the plant and addressing the underlying difficulties. Hence, in this paper, a novel data-driven synthesis scheme is proposed in a stochastic framework to provide a practically applicable solution for synthesizing LPV controllers directly from data. Both the cases of fixed order controller tuning and controller structure learning are discussed and two different design approaches are provided. The effectiveness of the proposed methods is also illustrated by means of an academic example and a real application based simulation case study

Machine Learning Integrated with Model Predictive Control for Imitative Optimal Control of Compression Ignition Engines

The high thermal efficiency and reliability of the compression-ignition engine makes it the first choice for many applications. For this to continue, a reduction of the pollutant emissions is needed. One solution is the use of machine learning (ML) and model predictive control (MPC) to minimize emissions and fuel consumption, without adding substantial computational cost to the engine controller. ML is developed in this paper for both modeling engine performance and emissions and for imitating the behaviour of an Linear Parameter Varying (LPV) MPC. Using a support vector machine-based linear parameter varying model of the engine performance and emissions, a model predictive controller is implemented for a 4.5 Cummins diesel engine. This online optimized MPC solution offers advantages in minimizing the \nox~emissions and fuel consumption compared to the baseline feedforward production controller. To reduce the computational cost of this MPC, a deep learning scheme is designed to mimic the behavior of the developed controller. The performance in reducing NOx emissions at a constant load by the imitative controller is similar to that of the online optimized MPC compared to the Cummins production controller. In addition, the imitative controller requires 50 times less computation time compared to that of the online MPC optimization.Comment: Submitted to Advances in Automotive Control - 10th AAC 202

MRAC + H∞ fault tolerant control for linear parameter varying systems

Presentado al SysTol 2010 celebrado en Niza del 6 al 8 de octubre.Two different schemes for Fault Tolerant Control (FTC) based on Adaptive Control, Robust Control and Linear Parameter Varying (LPV) systems are proposed. These schemes include a Model Reference Adaptive Controller for an LPV system (MRAC-LPV) and a Model Reference Adaptive Controller with a H¿ Gain Scheduling Controller for an LPV system (MRAC-H¿ GS-LPV). In order to compare the performance of these schemes, a Coupled-Tank system was used as testbed in which two different types of faults (abrupt and gradual) with different magnitudes and different operating points were simulated. Results showed that the use of a Robust Controller in combination with an Adaptive Controller for an LPV system improves the FTC schemes because this controller was Fault Tolerant against sensor fault and had an accommodation threshold for actuator fault magnitudes from 0 to 6Peer Reviewe