Sufficient lyapunov-like conditions for stabilization

In this paper we study the stabilizability problem for nonlinear control systems. We provide sufficient Lyapunov-like conditions for the possibility of stabilizing a control system at an equilibrium point of its state space. The stabilizing feedback laws are assumed to be smooth except possibly at the equilibrium point of the system.     

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.     

Distributed multivariable control system design for coal-fired boilers

This paper describes the multivariable characteristics of industrial coal-fired boilers and associated mathematical models, such as combustion model, a water drum level model and a superheated steam model. The purpose of the paper is to design multivariable control systems using multivariable system frequency domain design theory and the Smith-predictor technique. A specific application shows how to design a model-based distributed multivariable control system for coal-fired boilers in a small-scale power station.     

Self-tuning regulators for a class of multivariable systems

Control of a class of multivariable systems described by linear vector difference equations with constant but unknown parameters is discussed. A multivariable minimum variance strategy is first presented. This gives a generalization of the minimum variance strategy for single-input single-output systems. A multivariable self-tuning regulator based on the minimum variance strategy is then proposed. It uses a recursive least squares estimator and a linear controller obtained directly from the current estimates. The asymptotic properties of the algorithm are discussed. If the estimated parameters converge, the resulting controller will under certain conditions give the minimum variance strategy. The analysis also gives insight into the case when several single-input single-output self-tuning regulators are operating in cascade mode.     

Geometric state-space theory in linear multivariable control: A status report

With the renewed emphasis in control theory on qualitative structural issues, as distinct from techniques of optimization, the last decade has brought significant growth in the application of geometric ideas to the formulation and solution of problems of controller synthesis. In this article we review the status of geometric state space theory as developed for application to systems that are linear, multivariable and time-invariant. After a brief summary of the underlying geometric concepts ((A, B)-invariant subspaces and (A, B)-controllability subspaces) we outline two standard problems of feedback control that have been successfully attacked from this point of view, and briefly survey recent results in a range of other topic areas. Then we discuss certain issues of methodology, and conclude with some remarks on computational procedures.     

On-line structure selection for multivariable state-space models

An algorithm is described for the selection of model structure for identifying state-space models of ‘black box’ character. The algorithm receives as ‘input’ a given system in a given parametrization. It is then tested whether this parametrization is suitable (well conditioned) for identification purposes. If not, a better one is selected and the transformation of the system to the new representation is performed. This algorithm can be used as a block both in an iterative, off-line identification procedure, and for recursive, on-line identification. It can be called whenever there is some indication that the model structure is ill-conditioned. It is discussed how the model structure selection algorithm can be interfaced with an off-line identification procedure. A complete procedure is described and tested on real and simulated data.     

A self-tuning regulator for multivariable systems

The controller described in this paper is designed for multivariable plants with constant, unknown parameters. The algorithm operates on-line with the a priori information about the time delay. The order of the system may be given a priori. In the case where the order of the system is unknown it can be determined by a generalized likelihood-ratio statistical test which is described in this paper. The multivariable self tuning regulator consists of the two tasks of estimation and regulation. Estimation of the input-output system model parameters is based on the least-squares principle. The control is computed to minimize the combined cost of output deviation and control energy. Asymptotic properties of the estimation are discussed. Usefulness and simplicity of this approach are illustrated by examples.     

Asymptotic linearization of uncertain systems by variable structure control

A nonlinear control system with uncertain dynamics described by a single ordinary differential equation with scalar control and available state is given. Based on knowledge of upper and lower estimates of the unknown dynamics, we show that the system can be transformed to an asymptotically equivalent linear model (arbitrarily fixed) described by a single linear ordinary differential equation of the same order, by using an (explicitly described) discontinuous feedback control law of variable structure type.The linear behaviour is obtained up to an (arbitrarily fast) exponentially decaying error term.     

Design of pole-placement compensators for multivariable systems

The paper describes a two-stage method for the design of dynamic compensators for pole placement in linear multivariable systems. In the first stage, a number of poles are assigned by means of constant output feedback. In the second stage, the assigned poles are preserved and a number of additional poles are placed using dynamic output feedback. The pole placement is achieved using a compensator of lower order than required by the existing methods, since now the compensator has non-unity rank transfer function matrix. In particular, for a compensator of given order, a larger number of poles can be placed using this method compared to the existing methods.     

A multivariable self-tuning controller

A multivariable self-tuning controller is derived extending the scalar version of Clarke and Gawthrop (1975). Because the control terms are penalized in the cost function, fluctuations and peaking in control signals are reduced compared with the multivariable minimum variance self-tuning controller (Borisson, 1979). Time-varying reference signals as well as certain nonminimum-phase systems can be handled without difficulty with the proposed controller. Several examples illustrate the power of the derived self-tuning controller.     

System identification for generic model control

System identification methods build mathematical models of dynamical systems based on observed data. The intended use of the model should always be reflected in the methods and techniques used for identification. In this paper an identification scheme is derived for the case where the model is going to be used for GMC controller design. The aim of GMC control is to make the output approach a setpoint along a given desired trajectory. This is reflected in the identification scheme which is non-standard in two ways. Firstly, the emphasis is on the output trajectories of the models, and secondly we try to make the prediction errors follow an error trajectory determined by the controller parameters. Simulation studies are included which show that the derived identification scheme performs well.     

Adaptive dynamic surface control for linear multivariable systems

In this paper, an output-feedback adaptive control is presented for linear time-invariant multivariable plants. By using the dynamic surface control technique, it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated. The proposed scheme has the following features: (1) The L_∞ performance of the system’s tracking error can be guaranteed, (2) it has least number of updated parameters in comparison with other multivariable adaptive schemes, and (3) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.     

Stability issues for dynamic traffic assignment

This paper explores stability issues for operational route guidance control strategies for vehicular traffic networks equipped with advanced information systems, and develops a general procedure for the stability analysis of the associated dynamic traffic assignment (DTA) problems. The route guidance control strategies are modeled as dynamical systems, and the associated solution procedure enables computational tractability for real-time deployment. An important study insight is that the Lyapunov functions for the route guidance control models are their corresponding objective functions under DTA. This overcomes the key difficulty of constructing meaningful Lyapunov functions for DTA problems.     

A multivariable self-tuning controller with integral action

In this paper a novel stochastic self-tuning control algorithm for multivariable linear systems described by Controlled Autoregressive Integrating Moving Average (CARIMA) models is proposed. In particular, the presence of an integral action on each component of the error vector ensures the robust offset rejection for any constant load disturbance acting on the plant. The leading assumption is made that the system interactor matrix is known a priori. The algorithm is derived by resorting to the generalized minimum variance approach. Two simulation examples illustrate the main features of the method.     

Modal synthesis of multivariable systems with observers of specified order

The problem of pole assignment in multivariable linear systems with observers of a given order v is considered. By way of a simple proof, a very general result is established which constitutes an extension of all theorems known in the literature on pole assignment via observers. On its basis, an efficient design algorithm is worked out.     

A multivariable selftuning regulator to control a double effect evaporator

A multivariable selftuning regulator has been applied in control of a pilot plant double effect evaporator. The selftuning regulator consists of a recursive least squares algorithm combined with a single step optimal control strategy which minimizes a quadratic criterion. The algorithm is very fast and can be adjusted by an external operator in order to obtain satisfactory stationary regulator performance.     

An approach to multivariable system identification

Two prototype identifiable structures are presented which make possible the identification via an equation-error model reference adaptive system of linear plants with rational transfer function matrices. The structures include as specialisations many of the particular structures presented hitherto in the literature. Convergence properties are also discussed, and several modes of convergence are distinguished: model output to plant output, model transfer function matrix to plant transfer function matrix, and model parameters to plant parameters. Conditions are presented for exponentially fast convergence in the absence of noise.     

Robust camera pose and scene structure analysis for service robotics

Successful path planning and object manipulation in service robotics applications rely both on a good estimation of the robot’s position and orientation (pose) in the environment, as well as on a reliable understanding of the visualized scene. In this paper a robust real-time camera pose and a scene structure estimation system is proposed. First, the pose of the camera is estimated through the analysis of the so-called tracks. The tracks include key features from the imaged scene and geometric constraints which are used to solve the pose estimation problem. Second, based on the calculated pose of the camera, i.e. robot, the scene is analyzed via a robust depth segmentation and object classification approach. In order to reliably segment the object’s depth, a feedback control technique at an image processing level has been used with the purpose of improving the robustness of the robotic vision system with respect to external influences, such as cluttered scenes and variable illumination conditions. The control strategy detailed in this paper is based on the traditional open-loop mathematical model of the depth estimation process. In order to control a robotic system, the obtained visual information is classified into objects of interest and obstacles. The proposed scene analysis architecture is evaluated through experimental results within a robotic collision avoidance system.