Robust identification/invalidation in an LPV framework

A robust linear parameter varying (LPV) identification/invalidation method is presented. Starting from a given initial model, the proposed method modifies it and produces an LPV model consistent with the assumed uncertainty/noise bounds and the experimental information. This procedure may complement existing nominal LPV identification algorithms, by adding the uncertainty and noise bounds which produces a set of models consistent with the experimental evidence. Unlike standard invalidation results, the proposed method allows the computation of the necessary changes to the initial model in order to place it within the consistency set. Similar to previous LPV identification procedures, the initial parameter dependency is fixed in advance, but here a methodology to modify this dependency is presented. In addition, all calculations are made on state‐space matrices which simplifies further controller design computations. The application of the proposed method to the identification of nonlinear systems is also discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic Output Feedback Robust MPC With one Free Control Move for LPV Model With Bounded Disturbance

For a linear parameter‐varying (LPV) model which is a convex combination of several linear time invariant sub‐models, this paper considers the case when the combining coefficients are unknown (except being nonnegative and their sum being one). For this model with norm‐bounded unknown disturbance, an output feedback robust model predictive control (MPC) is proposed by parameterizing the infinite horizon control moves and estimated states into one free control move, one free estimated state (i.e., one control move and one estimated state as degrees of freedom for optimization) and a dynamic output feedback law. This is the first endeavour to apply the free control move and free estimated state in the output feedback MPC for this model. The algorithm is shown to be recursively feasible and the system state is guaranteed to converge to the neighborhood of the equilibrium point. A numerical example verifies the effectiveness of the proposed algorithm.     

Robust feedforward design in the presence of LTI/LTV uncertainties

A practical method is proposed for the convex design of robust feedforward controllers which ensures H_∞/L₂ performance in the face of LTI and arbitrarily time‐varying model uncertainties. A technique that computes the global minimum of this difficult infinite dimensional optimization problem is proposed, as well as a suboptimal but computationally less involved algorithm. Convergence is proved. An efficient way to analyse the robustness properties of a closed loop with or without feedforward controller is obtained as a subproblem. A missile example illustrates the efficiency of the scheme: a robust feedforward controller is designed either on the continuum of linearized time‐invariant models (corresponding to trim points) or on a quasi‐LPV model representing the non‐linear one. Copyright © 2007 John Wiley & Sons, Ltd.     

A bounded-error approach to piecewise affine system identification

This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.     

Two-Stage Method for Diagonal Recurrent Neural Network Identification of a High-Power Continuous Microwave Heating System

This paper proposes a diagonal recurrent neural network (DRNN) based identification scheme to handle the complexity and nonlinearity of high-power continuous microwave heating system (HPCMHS). The new DRNN design involves a two-stage training process that couples an efficient forward model selection technique with gradient-based optimization. In the first stage, an impact recurrent network structure is obtained by a fast recursive algorithm in a stepwise forward procedure. To ensure stability, update rules are further developed using Lyapunov stability criterion to tune parameters of reduced size model at the second stage. The proposed approach is tested with an experimental regression problem and a practical HPCMHS identification, and the results are compared with four typical network models. The results show that the new design demonstrates improved accuracy and model compactness with reduced computational complexity over the existing methods.

     

Multiple Lyapunov Functions with Blending for Induced L2‐norm Control of Switched LPV Systems and its Application to an F‐16 Aircraft Model

This paper studies the induced L₂‐norm problem for switched linear parameter varying (LPV) systems using a blending method. For a switched LPV system where the parameters are grouped into slow‐varying and fast‐varying parameters, the blending method is used to construct blended Lyapunov functions based on the multiple Lyapunov functions conditions in terms of linear matrix inequalities (LMIs). The proposed method is applied to an F‐16 aircraft longitudinal model and the simulation results demonstrate the effectiveness of the approach.     

A stochastic analysis of robust estimation algorithms in H∞ with rational basis functions

In this paper, a two‐stage nonlinear identification algorithm parameterized in terms of rational basis functions with fixed basis poles is studied when disturbances are subject to mild stochastic assumptions. The two‐stage algorithm is the archetype for robust estimation algorithms in H_∞ and its first stage is linear‐in‐data. Conditions for the consistency of both the stages are derived. It is shown that the two‐stage algorithm enjoys a better stochastic as well as deterministic performance than those of the linear algorithms. Copyright © 2001 John Wiley & Sons, Ltd.     

Identification of dynamic systems using Piecewise-Affine basis function models

Piecewise-Affine (PWA) Basis Function AutoRegressive eXogenous (BPWARX) models are proposed in this paper for nonlinear black-box identification. A BPWARX model is a weighted sum of PWA Basis (BPWA) functions, which are the minimum or maximum of n+1 affine functions in n dimensions. Since the BPWA functions have a universal representation capability for continuous PWA functions, the BPWARX models provide better accuracy than the Hinging Hyperplane ARX (HHARX) models with the same number of parameters, and the same order of computational complexity, when using a modified Gauss-Newton algorithm to build the models from input-output data.     

Gain Scheduled LPV H∞ Control Based on LMI Approach for a Robotic Manipulator

A new approach to the design of a gain scheduled linear parameter‐varying (LPV) H_∞ controller, which places the closed‐loop poles in the region that satisfies the specified dynamic response, for an n‐joint rigid robotic manipulator, is presented. The nonlinear time‐varying robotic manipulator is modeled to be a LPV system with a convex polytopic structure with the use of the LPV convex decomposition technique in a filter introduced. State feedback controllers, which satisfy the H_∞ performance and the closed‐loop pole‐placement requirements, for each vertex of the convex polyhedron parameter space, are designed with the use of the linear matrix inequality (LMI) approach. Based on these designed feedback controllers for each vertex, a LPV controller with a smaller on‐line computation load and a convex polytopic structure is synthesized. Simulation and experiment results verify that the robotic manipulator with the LPV controller always has a good dynamic performance along with the variations of the joint positions. © 2002 Wiley Periodicals, Inc.     

LPV model development and control of a solution copolymerization reactor

In this paper, linear parameter-varying (LPV) control is considered for a solution copolymerization reactor, which takes into account the time-varying nature of the parameters of the process. The nonlinear model of the process is first converted to an exact LPV model representation in the state-space form that has a large number of scheduling variables and hence is not appropriate for control design purposes due to the complexity of the LPV control synthesis problem. To reduce such complexity, two approaches are proposed in this paper. First, an approximate LPV representation with only one scheduling variable is obtained by means of a parameter set mapping (PSM). The second approach is based on reformulating the nonlinear model so that it provides an LPV model with a fewer number of scheduling parameters but preserves the same input–output behavior. Moreover, in the implementation of the LPV controllers synthesized with the derived models, the unmeasurable scheduling variables are estimated by an extended Kalman filter. Simulation results using the nonlinear model of the copolymerization reactor are provided in order to illustrate the performance of the proposed controllers in reducing the convergence time and the control effort.     

Tensor networks for MIMO LPV system identification

ABSTRACT

In this paper, we present a novel multiple input multiple output (MIMO) linear parameter varying (LPV) state-space refinement system identification algorithm that uses tensor networks. Its novelty mainly lies in representing the LPV sub-Markov parameters, data and state-revealing matrix condensely and in exact manner using specific tensor networks. These representations circumvent the ‘curse-of-dimensionality’ as they inherit the properties of tensor trains. The proposed algorithm is ‘curse-of-dimensionality’-free in memory and computation and has conditioning guarantees. Its performance is illustrated using simulation cases and additionally compared with existing methods.     

Robust multiple-model LPV approach to nonlinear process identification using mixture t distributions

In this paper, we propose a robust multiple-model linear parameter varying (LPV) approach to identification of the nonlinear process contaminated with outliers. The identification problem is formulated and solved under the EM framework. Instead of assuming that the measurement noise comes from the Gaussian distribution like conventional LPV approaches, the proposed robust algorithm formulates the LPV solution using mixture t distributions and thus naturally addresses the robust identification problem. By modulating the distribution tails through degrees of freedom, the proposed algorithm can handle various outliers. Two simulated examples and an experiment are studied to verify the effectiveness of the proposed approach.     

H∞ output tracking control for a class of switched LPV systems and its application to an aero‐engine model

This paper aims to investigate the problem of H_∞ output tracking control for a class of switched linear parameter‐varying (LPV) systems. A sufficient condition ensuring the H_∞ output tracking performance for a switched LPV system is firstly presented in the format of linear matrix inequalities. Then, a set of parameter and mode‐dependent switching signals are designed, and a family of switched LPV controllers are developed via multiple parameter‐dependent Lyapunov functions to enhance control design flexibility. Even though the H_∞ output tracking control problem for each subsystem might be unsolvable, the problem for switched LPV systems is still solved by the designed controllers and the designed switching law. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an H_∞ speed adjustment problem of an aero‐engine. Copyright © 2016 John Wiley & Sons, Ltd.     

Prediction error method for identification of LPV models

This paper is concerned with identification of linear parameter varying (LPV) systems in an input-output setting with Box-Jenkins (BJ) model structure. Classical linear time invariant prediction error method (PEM) is extended to the LPV PEM. Under the new LPV framework, identification of two types of input-output LPV models is considered: one is based on parameter interpolation and the other is based on model interpolation. The effectiveness of the proposed solution is validated by comparison with other existing LPV identification approaches through simulation examples and demonstrated by experiment studies.     

Output feedback model predictive control for LPV systems based on quasi-min–max algorithm

This paper proposes a robust output feedback model predictive control (MPC) scheme for linear parameter varying (LPV) systems based on a quasi-min–max algorithm. This approach involves an off-line design of a robust state observer for LPV systems using linear matrix inequality (LMI) and an on-line robust output feedback MPC algorithm using the estimated state. The proposed MPC method for LPV systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems. A numerical example for an LPV system subject to input constraints is given to demonstrate its effectiveness.     

Conservatism reduction for linear parameter‐varying control design facing inexact scheduling parameters illustrated on flight tests

This article addresses the design problem of linear parameter‐varying (LPV) output feedback controllers that depend on inexact scheduling parameters for LPV systems. This problem has already been tackled and several methods have been proposed by overbounding the discrepancies between the actual scheduling parameters and the provided ones in the derivation of controller design condition. However, all methods in literature have conservatism in the overbounding, which is the main issue addressed in this article. We therefore propose a new overbounding for the discrepancies with the reverse use of Elimination lemma, which introduces no conservatism in theory. The new method is formulated in terms of bilinear matrix inequality, which is not tractable compared with linear matrix inequality, thus a practical design procedure composed of line search and iterative algorithm is shown. The effectiveness of our method is illustrated by an application to flight controller design for the lateral‐directional motions of a research airplane MuPAL‐α and the consequently conducted flight tests.     

Missile autopilot design via a multi‐channel LFT/LPV control method

In this paper, the missile pitch‐axis autopilot design is revisited using a new and recently available linear parameter‐varying (LPV) control technique. The missile plant model is characterized by a linear fractional transformation (LFT) representation. The synthesis task is conducted by exploiting new capabilities of the LPV method: firstly, a set of H₂/H_∞ criteria defined channel‐wise is considered; secondly, different Lyapunov and scaling variables are used for each channel/specification which is known to reduce conserva tism; and finally, the controller gain‐scheduling function is constructed as affine matrix‐valued function in the polytopic co‐ordinates of the scheduled parameter. All these features are examined and evaluated in turn for the missile control problem. The method is shown to provide additional flexibility to tradeoff conflicting and demanding performance and robustness specifications for the missile while preserving the practical advantage of previous single‐objective LPV methods. Finally, the method is shown to perform very satisfactorily for the missile autopilot design over a wide range of operating conditions. Copyright © 2001 John Wiley & Sons, Ltd.     

Stability and performance analysis of time‐delay LPV systems with brief instability

Linear parameter‐varying (LPV) systems provide a systematic framework for the study of nonlinear systems by considering a representative family of linear time‐invariant systems parameterized by system parameters residing in a compact set. The brief instability concept in such systems allows the linear system to be unstable for some trajectories of the LPV parameter set, so that instability occurs only for short periods of time. In the present paper, we extend the notion of brief instability to LPV systems with time delay in their dynamics. The results provide tools for the stability and performance analysis of such systems, where performance is evaluated in terms of induced ??₂‐gain (or so‐called ??_∞ norm). The main results of this paper illustrate that stability and performance conditions can be evaluated by examining the feasibility of parameterized sets of linear matrix inequalities (LMIs). Using the results of this paper, we then investigate analysis conditions to guarantee the asymptotic stability and ??_∞ performance of fault‐tolerant control (FTC) systems, in which instability may take place for a short period of time due to the false identification of the fault signals provided by a fault detection and isolation (FDI) module. The numerical examples are used to illustrate the qualification of the proposed analysis and synthesis results for addressing brief instability in time‐delay systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Identification of multi-model LPV models with two scheduling variables

In order to model complex industrial processes, this work studies the identification of linear parameter varying (LPV) models with two scheduling variables. The LPV model is parameterized as blended linear models, which is also called multi-model structure. Several weighting functions, linear, polynomial and Gaussian functions, are used and compared. The usefulness of the method is tested using a high purity distillation column model in a case study. The case study shows that a good fit of identification data is not enough to verify model quality and can even be misleading in nonlinear process identification; other measures related to process knowledge should be used in model validation. The case study also shows that commonly used LPV model based on parameter interpolation can fail for the high purity distillation column. Finally, several pitfalls in nonlinear process identification are pointed out.