Adaptive tracking-control synthesis for functionally uncertain systems via modified backstepping

The paper is concerned with the problem of adaptive tracking system control synthesis. It is assumed that a nonlinear, feedback linearizable object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that proportional state feedback plus parameter adaptation are able to assure its asymptotic stability. This form of controller permits online compensation of unknown model nonlinearities and exogenous disturbances, which results in satisfactory tracking performance. An interesting feature of the system is that the whole process control is performed without requisite asymptotic convergence of approximator parameters to the postulated ‘true’ values. It has been noticed that the parameters play rather a role of slack variables on which potential errors (that otherwise would affect the state variables) cumulate. The system's performance has been tested via Matlab/Simulink simulations via an example of ship path‐following problem. Copyright © 2009 John Wiley & Sons, Ltd.

A new form of nonlinear control scheme is presented in this brief where the concepts of feedback linearization and adaptive control schemes are combined together to design an adaptive partial feedback linearizing controller. The newly proposed scheme is exercised on a single machine infinite bus (SMIB) power system in order to design its excitation controller in order to eliminate the parameter sensitivity problems of the feedback linearization scheme. The SMIB system is first linearized using the partial feedback linearization technique and the parameters appearing in the feedback linearized model are estimated using the adaptive control scheme. The proposed adaptive partial feedback linearizing excitation controller of the SMIB system uses the estimated values of parameters. The stability of the SMIB system is also analyzed using the Lyapunov stability theory while using the proposed scheme. Simulation studies are carried out to demonstrate the effectiveness of the proposed control scheme over an existing partial feedback linearizing scheme.

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This article describes the design of a linear observer–linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in the case of nonlinear, multivariable, nonholonomic underactuated mobile manipulators. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and suitably extended, high-gain, linear Generalized Proportional Integral (GPI) observers, thus aiding the linear feedback controllers to provide an accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and perturbation inputs. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities, and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Simulations reveal the effectiveness of the proposed approach.

SUMMARY In this paper, several concepts of switching frequency are introduced to analyze the properties and performance of switched systems in infinite as well as finite-time intervals. The observation is very motivating that different system properties and performances depend on different switching frequencies. Sufficient conditions ensuring asymptotic stability, l2 gain performance, and state boundness are derived on the basis of the notions of switching frequency, respectively. Then, on the basis of the analysis results, the control synthesis problems are addressed. LMI-based design algorithms are proposed to meet different control synthesis requirements. Numerical design examples are provided to demonstrate our results. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, the non-linear speed/position-tracking controllers for the linear induction motor are proposed along with a non-linear transformation set being proposed to facilitate the process of the controller design. Moreover, the very unique end effect of the linear induction motor and the unknown payload are also taken care of in the proposed controller design. Stability analysis based on Lyapunov theory is also performed to guarantee the stability of the proposed control schemes. Finally, the computer simulations and experimental results are given to demonstrate the performance of the proposed speed/position controllers.

This paper considers the control synthesis problem and its solution using symbolic regression. Symbolic regression methods, which were previously called genetic programming methods, allow one to use a computer to find not only the parameters of a given regression function but also its structure. Unlike other works on solving the control synthesis problem using symbolic regression, the novelty of this paper is that for the first time this work employs a training dataset to address the problem of general control synthesis. Initially, the optimal control problem is solved from each point in a given set of initial states, resulting in a collection of control functions expressed as functions of time. A reference model is then integrated into the control object model, which generates optimal motion trajectories using the derived optimal control functions. The control synthesis problem is framed as an approximation task for all optimal trajectories, where the control function is sought as a function of the deviation of the object from the specified terminal state. The optimization criterion for solving the synthesis problem is the accuracy of the object’s movement along the optimal trajectory. The paper includes an example of solving the control synthesis problem for a mobile robot using a supervised machine learning method. A relatively new method of symbolic regression, the method of variational complete binary genetic programming, is studied and proposed for the solution of the control synthesis problem.

Chapter 7 - Advanced approaches to multiagent coordination

Nowadays the feedback linearization and backstepping techniques are introduced as methods for linearization of a system with coordinate transformation and nonlinear designing, respectively. The feedback linearization and backstepping techniques are robust methods, however this study indicates that combining of them and adding nonlinear disturbance observer increases the system robustness. In this paper, the system linearization with backstepping process has been studied. Combining of above mentioned techniques has been used for linearization in this method. The systems have been practically exposed to disturbances and uncertainties. Nonlinear disturbance observer has a good ability to estimate disturbances and nonlinear dynamics, so it is useful method for increasing performance of control methods, reducing the effects of disturbances and system uncertainties. The presented control method with nonlinear disturbance observer improves the system robustness against different types of uncertainties, so this method is a modified technique. The proposed design process consists of two steps: First, the nonlinear disturbance observer has been designed to estimate the uncertainties and external disturbances applied to system. Second, a controller has been designed using combined feedback linearization-backstepping method that used prior estimations to decrease the effects of external disturbances and uncertainties in the control input.

In this paper, the feedback linearization scheme is applied to the control of vehicle's lateral dynamics. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamical model is adopted for controller design. It was observed in Liaw and Chung (2006) that the saddle-node bifurcation would appear in vehicle dynamics with respect to the variation of the front wheel steering angle, which might result in spin and/or system instability. Feedback linearization control laws are proposed in this paper to stabilize the vehicle's dynamics at bifurcation points. Numerical simulations for an example model demonstrate the effectiveness of the analytical results

An identification control is a control of an object which mathematical model is unknown. For such objects initially the problem of identification is solved, and then for the resulting object model the problem of control synthesis is solved. As a result of control synthesis we obtain a multi-dimensional function that describes the dependence of control on the object state. After the implementation of this function in the control unit of the real object, it achieves the goal of control with optimal value of the quality criteria. To solve the identification and synthesis problems we use the method of network operator, which with the help of evolutionary algorithms finds the structure and parameters of the functions describing the model and functional dependence of control from the object state. In this paper, an example of using a network operator to solve the problem of identification control synthesis for a multilink robot is given.

The problem of precisely controlling (within sensor resolution) the height of a steel ball above the ground by levitating it against the force of gravity using an electromagnet is considered. The state variables used to model the system are the ball's position below the magnet, the ball's speed and the current in the electromagnet. Two state-space controllers are compared in terms of their performance in controlling the ball's position. The first controller is based on feedback linearization where a nonlinear state-space transformation along with nonlinear state feedback is used to linearize the system exactly. A linear controller is then used on the resulting system to control the ball's position. As a direct measurement of ball speed is not available, a nonlinear observer with linear error dynamics is used to estimate the speed. The second controller is a standard linear state feedback controller whose design is based on a linear model found by perturbing the nonlinear system model about an operating po...

This work eonsiden the H, norm control of structural systems with collocated sensors and actuators using an analytical upper bound approach. A parametrization of the output feedback control gains that achieve a desired H, norm bound is obtained using an analytical solution of the Bounded Real Lemma. This approach is verified experimentally on a cantilevered aluminum beam with two collocated pairs of piezoceramic patches that serve as sensors and actuators. The finite element model of this beam is developed and the simulations show a drop of -6 dB in the H, norm of the closed loop system. Experimental results verify the simulated results and demonstrate the effectiveness of this method. The proposed control methodology has obvious computational advantages compared to traditional H, control design methods, especially for lnrge scale systems. The control of structural systems with collocated sensors and actuators has been shown to provide great advantages from a stability, passivity, robustness and an implementation viewpoint. For example, collocated control can easily be achieved in a space structure when an attitude rate sensor is placed at the same point as a torque actuator.(l)(2) The actuator placement and sizing optimization for vibration sup pression of a collocated beam structure is discussed in Ref. (3).Collocation of sensors and actuators leads to symmetric transfer functions. Several other classes of engineering sys- tems, such as circuit systems, chemical reactors and power networks, can be modelled as systems with symmetric trans- fer functions. Stabilization, robustness, model reduction and control of such systems has been examined recently.(4)(5) The H, norm control of structural systems has attracted a lot of attention recently due to the interpretation of the H, norm in the frequency domain. In early work, D-K iteration method was used to design H, controllers for a non-collocated flexible shucture. Now state space H, control based on the standard Riccati equation approach or the linear matrix inequality (LMI) formulation is a well developed control synthesis tool. The optimal static state feedback and full-order dynamic output feedback H, con- trol synthesis problems can be solved using iterations on the corresponding Riccati solutions or via the computational solution of a convex LMI optimization problem.(7)(8) On the other hand, the static output feedback and the fixed-order dynamic output feedback H, control synthesis problems are difficult computational problems since they require the

In this paper, some basic dynamical properties of a four-dimensional autonomous hyperchaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this new hyperchaotic system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment. An efficient approaching is developed for global asymptotic stabilization of this four-dimensional hyperchaotic system. Based on the method of inverse optimal control for nonlinear systems, a linear state feedback is electronically implemented. It is remarkably simple as compared with other chaos control ways, like nonlinear state feedback.

This paper develops a general continuous-time stochastic framework for robustness analysis and robust control synthesis. We consider a stochastic minimax optimization problem for general stochastic uncertain systems. A general method is presented for converting problems of performance analysis or controller synthesis into unconstrained optimization problems.