Scheduling Dimension Reduction of LPV Models -- A Deep Neural Network Approach

In this paper, the existing Scheduling Dimension Reduction (SDR) methods for Linear Parameter-Varying (LPV) models are reviewed and a Deep Neural Network (DNN) approach is developed that achieves higher model accuracy under scheduling dimension reduction. The proposed DNN method and existing SDR methods are compared on a two-link robotic manipulator, both in terms of model accuracy and performance of controllers synthesized with the reduced models. The methods compared include SDR for state-space models using Principal Component Analysis (PCA), Kernel PCA (KPCA) and Autoencoders (AE). On the robotic manipulator example, the DNN method achieves improved representation of the matrix variations of the original LPV model in terms of the Frobenius norm compared to the current methods. Moreover, when the resulting model is used to accommodate synthesis, improved closed-loop performance is obtained compared to the current methods.Comment: Accepted to American Control Conference (ACC) 2020, Denve

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

Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.Comment: 6 pages, CDC 2019. Website: https://eleurent.github.io/interval-prediction

Design of parameter-scheduled state-feedback controllers using shifting specifications

In this paper,the problem of designing aparameter-scheduled state-feedback controller is investigated. The paper presents an extension of the classical regional pole placement, H2 control and H1 control problems, so as to satisfy new specifications, that will be referred to as shifting pole placement control, shifting H2 control and shifting H1 control, respectively. By introducing some parameters, or using the existing ones, the controller can be designed in such away that different values of the separameters imply different regions where the closed-loop poles are situated, or different performances in the H2 or H1 sense. The proposed approach is derived within the so-called Lyapunov Shaping Paradigm, where a single quadratic Lyapunov function is used for ensuring stability and desired performances in spite of arbitrary parameter time variation. The problem is analyzed in the continuous-time LPV case, oventhough the developed theory could be applied to LTI systems in cases when it is desired to vary the control system performances online. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.Peer ReviewedPostprint (published version

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

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

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method

Gain scheduling with guardian maps for longitudinal flight control

A new approach to gain scheduling of linear controllers is proposed and applied to a longitudinal flight control pro-blem. Traditionally, gain scheduling is done a posteriori by the interpolation of controller gains designed for several operating points or conditions. The method proposed here is based on guardian maps and does not require as many linear controller syntheses as there are design points. Rather, it extends the performance of an initial single controller carried out on an arbitrary operating point to the entire domain while ensuring generalized stability all along the process. The method, which uses a given fixed architecture controller, is successfully applied on the longitudinal flight control of a business jet aircraft

Flight Testing a Linear Parameter Varying Control Law on a Passenger Aircraft

To improve performance and efficiency of future aircraft generations, multi-objective control design problems considering effects such as over-actuation and lowly damped flexible modes arise from new materials in the wing design. A candidate method, which delivers a solution to this problem for the whole flight envelope is linear parameter varying (LPV) control synthesis. It already incorporates the controller scheduling in the synthesis process, guaranteeing stability and robustness over the entire scheduling envelope, and enables intuitive multi-objective, multiple-input multiple-output (MIMO) controller designs. To prove the concept of LPV controllers in a realistic environment, the flight test campaign results of LPV inner loop control laws on a Cessna Citation II (550) aircraft are presented in this paper. The implemented inner loop controllers are inspired by classical flight controllers used on state-of-the-art fly-by-wire airliners. The longitudinal motion is augmented with load-factor command and the lateral motion controller, which is inherently of MIMO type, features a roll rate command with attitude hold behavior. The control laws are validated in flight by the pilot with respect to functionality, flying and handling qualities. Furthermore, auto generated input signals are used to excite the aircraft without pilot in the loop to allow for a comparability with simulation results