This paper presents an algorithm for solving optimization problems with bilinear matrix inequality constraints. The algorithm is based on a combination of gradient-based optimization and LMIs, which makes it fast and enables it to handle a large number of decision variables. It is applied to two controller synthesis problems: static output feedback controller synthesis and robust controller synthesis for linear parameter varying (LPV) systems using the idea of quadratic separation. Since the second problem has large number of decision variables, a hybrid approach is applied, in which LMI solvers are used for the evaluation of the cost function. The algorithm is applied to two examples, and results are compared with some existing approaches.

This paper presents an algorithm for solving optimization problems with bilinear matrix inequality (BMI) constraints, which frequently appear in controller synthesis. The algorithm is based on a combination of gradient-based optimization and linear matrix inequalities (LMIs), which makes it fast and enables it to handle a large number of decision variables. Here it is used to synthesize fixed-structure and low-order gain-scheduled controllers for linear parameter varying (LPV) systems, using the idea of quadratic separation. It is known that the synthesis problem based on quadratic separation leads to BMIs. The synthesis technique is applied to design fixed-structure and low-order gain-scheduled controllers for a spark ignition engine, and results are compared with existing approaches to solve BMI constraint optimization problems. It turns out that the proposed algorithm gives solutions where other approaches may fail.

In this paper a method is proposed that allows the identification of input-output quasi-linear parameter-varying (LPV) models based on ergodic signals. In this case the use of the instrumental variables (IV) method leads to a consistent estimation of the quasi-LPV model parameters. Moreover, an indirect closed-loop identification technique, which has been proposed for the identification of linear time-invariant (LTI) models in closed-loop, is extended here to consistently identify input-output LPV models in closed loop using the IV method. Two cases are considered: LPV systems with noise-free external scheduling signals and quasi-LPV systems with noisy scheduling signals. Several simulation examples are presented to illustrate the method.

This document proposes the nonlinear control of an industrial three-degrees-of-freedom (3-DOF) robotic manipulator as a benchmark problem for controller synthesis methods, that are applicable to complex plants, but can provide implementation with low complexity. Full details on the nonlinear model of the industrial robotic manipulator Thermo CRS A465 are provided. Furthermore, a solution is presented by considering linear parameter-varying (LPV) controller synthesis based on a reduced parameter set. Stability and performance guarantees are rendered void as the plant's parameter dependency is first approximated by means of principle component analysis. The guarantees are recovered by tools which have previously been reported.

A difficulty encountered in applying linear parameter-varying (LPV) control is the complexity of synthesis and implementation for large numbers of scheduling parameters. Often, heuristic solutions involve neglecting individual scheduling parameters, such that LPV controller synthesis methods become applicable. However, stability and performance guarantees are rendered void, if a controller design based on an approximate model is implemented on the original plant. In this paper, a posteriori conditions are proposed to assess closed-loop stability and performance and possibly recover guarantees. The controller - synthesized based on a reduced parameter set - is first transformed back to depend on the original parameters. Then analysis is performed with respect to the original plant model, which is considered to be accurate. Moreover, an iterative approach for optimizing controllers with few scheduling parameters is sketched. A two-degrees-of-freedom (2-DOF) robotic manipulator is considered as an illustrative example. Experimental results indicate a significant increase in performance.

This paper considers the synthesis of linear parameter-varying (LPV) controllers for plant models given in input-output LPV form. For SISO systems, a method for synthesizing LPV gain-scheduled controllers in input-output form has been proposed recently, where the a priori choice of a central polynomial plays a critical role, and the synthesis problem is solved using a sum-of-squares relaxation. In this paper we propose a way of simplifying this design procedure, by replacing the sum-of-squares approach by representing the closed-loop model in polytopic input-output LPV form and then using a gradient-based optimization to solve the synthesis BMI. In this procedure the central polynomial is tuned while the closed-loop performance index is minimized over the decision variables, which include the controller parameters. The proposed method is illustrated with simulation examples.

In this paper, low-complexity linear parameter-varying (LPV) modeling and control of a two-degrees-of-freedom robotic manipulator is considered. A quasi-LPV model is derived and simplified in order to facilitate LPV controller synthesis. An LPV gain-scheduled, decentralized PD controller in linear fractional transformation form is designed using mixed sensitivity loop shaping to take - in addition to high tracking performance - noise and disturbance rejection into account, which are not considered in model-based inverse dynamics or computed torque control schemes. The controller design is based on the existence of a parameter-dependent Lyapunov function - employing the concept of quadratic separators - thus reducing the conservatism of design. The resulting bilinear matrix inequality (BMI) problem is solved using a hybrid gradient-LMI technique. Experimental results illustrate that the LPV controller clearly outperforms a decentralized LTI-PD controller and achieves almost the same accuracy as a model-based inverse dynamics and a full-order LPV controllers in terms of tracking performance while being of significantly lower complexity.

This paper considers the controller design problem for parameter-varying distributed systems, whose time/space-varying dynamics can be characterized by temporal/spatial linear parameter-varying (LPV) models defined at the spatially-discretized subsystems. Assuming a rational functional dependence on the scheduling parameters, the distributed LPV model in linear fractional transformation (LFT) form renders analysis and synthesis conditions at the subsystems level with the application of Finsler's lemma and the full block S-procedure technique. The designed distributed controller inherits the interconnected structure of the plant and has a (predefined) fixed structure. Simulation results using a spatially-varying heat equation demonstrate the satisfactory performance of the proposed control design method.

This paper proposes a non-iterative, Lyapunov-based distributed model predictive control (MPC) design for invariant spatially-interconnected systems comprised of a network of subsystems with coupled dynamcis and subject to local state and/or input constraints. Considered here is the distributed MPC design for linear systems in input-output form with fixed-structure local state-feedback-like control law. The proposed distributed MPC design approach ensures asymptotic stability and recursive feasibility, and its online implementation can be formulated as solving a linear matrix inequality (LMI) problem defined at the subsystem level. Simulation results using a heat equation in one-dimensional space demonstrate the merits and effectiveness of the proposed approach.

In this paper a novel LPV controller synthesis approach to design fixed-structure LPV controllers in input output (IO) form is presented. The LPV-IO model and the LPV-IO controller are assumed to depend affinely as well as statically on the scheduling variable. By using an implicit representation of the system model and the controller, an exact representation of the closed-loop behavior is achieved. Using Finsler's Lemma, novel stability conditions are derived in the form of linear matrix inequalities (LMIs). Based on these conditions a quadratic performance synthesis approach is introduced in form of bilinear matrix inequalities (BMIs) and solved using a DK-iteration based approach.

In this note, novel linear matrix inequality (LMI) analysis conditions for the stability of linear parameter-varying (LPV) systems in input–output (IO) representation form are proposed together with bilinear matrix inequality (BMI) conditions for fixed-structure LPV-IO controller synthesis. Both the LPV-IO plant model and the controller are assumed to depend affinely and statically on the scheduling variables. By using an implicit representation of the plant and the controller interaction, an exact representation of the closed-loop behavior with affine dependence on the scheduling variables is achieved. This representation allows to apply Finsler's Lemma for deriving exact stability as well as exact quadratic performance conditions. A DK-iteration based solution is carried out to synthesize the controller. The main results are illustrated by a numerical example.

This paper proposes a method for frequency-weighted discrete-time linear parameter varying (LPV) model reduction with bounded rate of parameter variation, using structurally balanced truncation with a priori (non-tight) upper error bounds for each fixed parameter. For systems with both input and output weighting filters, guaranteed stability of the reduced-order model is proved as well as existence of solutions, provided that the full-order model is stable. A technique based on cone complementarity linearization is proposed to solve the associated LMI problem. Application to the model of a gantry robot illustrates the effectiveness of the approach. Moreover, a method is proposed to make the reduced order model suitable for practical LPV controller synthesis.

This paper presents an identification technique to identify models for Parameter-Varying Spatially Interconnected systems. The main focus of the note is the case when there is additive colored noise in the output of the data generating system. A Refined Instrumental Variable method is proposed to identify parameter-varying spatially interconnected models with Box-Jenkins structure. The technique allows identification of models for general multi-dimensional systems, which may be separable or non-separable, causal, semi-causal (spatially interconnected systems) or non-causal. The effectiveness of the method is shown with application to simulation example. © 2011 AACC American Automatic Control Council.

This article presents an identification technique for distributed systems with identical units using linear recurrent neural networks and exploiting the replicated structure of the units inside the system. The proposed method is applicable both to open-loop and closed-loop identification, takes into consideration boundary conditions and available information about the structure of the system, and is capable of identifying systems with heterogeneous units. The approach provides parameters estimate with minimum bias for unstable plant models when there is additive colored noise in the data. The method is described for two-dimensional systems (one for time and one for space), but is equally applicable to systems having more dimensions in space. The effectiveness of the method is demonstrated by two examples. © 2011 IFAC.

This paper presents an identification technique based on linear recurrent neural network to identify spatially interconnected systems both in open and closed-loop form. The latter has not been addressed in the literature for the systems under consideration. The paper considers identification of two-dimensional (time and space) systems; the method can be easily extended to have more than one dimension in space. In this paper we consider a semi-causal (causal in time and non-causal in space) two-dimensional (2-D) system, which may be separable or non-separable but the method can also be used for 2-D systems which are causal in both dimensions. Furthermore the algorithm can handle boundary conditions. The effectiveness of the method is shown with application to simulation examples.

In this paper a Linear Recurrent Neural Network (LRNN) approach is used to consistently identify input-output Linear Parameter Varying (LPV) systems with additive output noise in input-output representation. Moreover, an indirect identification approach based on structured LRNN is proposed for consistent identification of input-output LPV models in closed-loop. The structured LRNN is trained to identify the closed-loop system from the reference to the output signal, where the controller parameters are presented as fixed weights and the parameters of the LPV model as unknown weights. The open-loop model can then be easily extracted from the identified closed-loop model. The proposed approach is illustrated with simulation examples, and a comparison with an existing approach is given.

This paper is one of two joint papers, each presenting and utilizing a different representation of a feedforward neural network for controller design. Here a neural state-space model is transformed into a linear fractional transformation (LFT) representation to obtain a discrete-time quasi-linear parameter-varying (LPV) model of a nonlinear plant, whereas in the joint paper (Abbas and Werner [2008]) a method is proposed to transform the neural state-space into a discrete-time polytopic quasi-LPV model. As a practical application, air charge control of a Spark-Ignition (SI) engine is used in both papers as example to illustrate two different synthesis methods for fixed structure low-order discrete-time LPV controllers. In this paper, a method that combines modelling using a multilayer perceptron network and controller synthesis using linear matrix inequalities (LMIs) and evolutionary search is proposed. In the first step a neural state-space model is transformed into a linear fractional transformation (LFT) representation to obtain a discrete-time quasi-LPV model of a nonlinear plant from input-output data only. Then a hybrid approach using LMI solvers and genetic algorithm, which is based on the concept of quadratic separators, is used to synthesize a discrete-time LPV controller.

This paper presents the design and successful experimental validation of a linear parameter-varying (LPV) control strategy for a four-degrees-of-freedom control moment gyroscope (CMG). First, a linearized model with moving operating point is used to construct an LPV model. Then, a gridding-based LPV state-feedback control is designed that clearly outperforms linear time-invariant (LTI) controllers. Moreover, a way is proposed to select pre-filter gains for reference inputs that can be generalized to a large class of mechanical systems. Overall, the strategy allows a simple implementation in real-time. Experimental results illustrate that the proposed LPV controller achieves indeed a better performance in a much wider range of operation than linear controllers reported in the literature. © 2013 AACC American Automatic Control Council.

This paper presents an application of Linear-Parameter-Varying (LPV) control to an electromechanically driven landing gear of an aircraft. The LPV approach is motivated by the highly nonlinear characteristics of the kinematic. First, a nonlinear model is derived using physical modeling tools. A quasi-LPV model is then derived by using an approach which is based on linearisation and additional measurements of the nonlinear model. Using mixed sensitivity loop shaping, a polytopic LPV controller based on a single Lyapunov function is designed. Then a method is developed for this controller which compensates any wind up effects due to a reconstruction and without any further calculation. Finally the designed controller is tested and compared to a Linear-Time- Invariant (LTI) controller in simulation studies. © 2010 AACC.

This paper presents the construction of a realistic linear parameter-varying (LPV) model of a robotic manipulator using parameter set mapping, for the purpose of synthesizing an LPV gain-scheduled controller. A nonlinear dynamic model of the manipulator is obtained and a quasi-LPV model is derived. Since the quasi-LPV model has a large number of affine scheduling parameters and a large overbounding, parameter set mapping is used to reduce conservatism and complexity in controller design by finding tighter parameter regions with fewer scheduling parameters. Then, a polytopic LPV gain-scheduled controller is synthesized and implemented experimentally on an industrial robot for a trajectory tracking task. Comparison of results with a decentralized PD controller illustrates that the designed LPV controller improves the tracking error significantly. Moreover, it achieves a slightly better accuracy than a model-based inverse dynamics controller while being of lower complexity.