A Comparison of LPV Gain Scheduling and Control Contraction Metrics for Nonlinear Control

Gain-scheduled control based on linear parameter-varying (LPV) models derived from local linearizations is a widespread nonlinear technique for tracking time-varying setpoints. Recently, a nonlinear control scheme based on Control Contraction Metrics (CCMs) has been developed to track arbitrary admissible trajectories. This paper presents a comparison study of these two approaches. We show that the CCM based approach is an extended gain-scheduled control scheme which achieves global reference-independent stability and performance through an exact control realization which integrates a series of local LPV controllers on a particular path between the current and reference states.Comment: IFAC LPVS 201

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

Gain-scheduled H∞ control via parameter-dependent Lyapunov functions

Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques

H∞ and L2–L∞ filtering for two-dimensional linear parameter-varying systems

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Wiley-BlackwellIn this paper, the H∞ and l2–l∞ filtering problem is investigated for two-dimensional (2-D) discrete-time linear parameter-varying (LPV) systems. Based on the well-known Fornasini–Marchesini local state-space (FMLSS) model, the mathematical model of 2-D systems under consideration is established by incorporating the parameter-varying phenomenon. The purpose of the problem addressed is to design full-order H∞ and l2–l∞ filters such that the filtering error dynamics is asymptotic stable and the prescribed noise attenuation levels in H∞ and l2–l∞ senses can be achieved, respectively. Sufficient conditions are derived for existence of such filters in terms of parameterized linear matrix inequalities (PLMIs), and the corresponding filter synthesis problem is then transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is exploited to demonstrate the usefulness and effectiveness of the proposed design method

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

Balanced truncation for linear switched systems

In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this paper, we provide a bound on the approximation error in L2 norm for continuous-time and l2 norm for discrete-time linear switched systems. We provide a system theoretic interpretation of grammians and their singular values. Furthermore, we show that the performance of bal- anced truncation depends only on the input-output map and not on the choice of the state-space representation. For a class of stable discrete-time linear switched systems (so called strongly stable systems), we define nice controllability and nice observability grammians, which are genuinely related to reachability and controllability of switched systems. In addition, we show that quadratic stability and LMI estimates of the L2 and l2 gains depend only on the input-output map.Comment: We have corrected a number of typos and inconsistencies. In addition, we added new results in Theorem