Approximate Decoupling Flight Control Design with Output Feedback

International audience

In this paper finite-time stabilization of nonlinear affine systems, is considered. First we provide a formula for a finite-time stabilizing state feedback control law, for the last class of system. Then we extend the result to the case of a norm-bounded uncertain system and a polytopic uncertain system stabilization are given. Some numerical examples are given to illustrate the main result.

On observer-based fault detection for nonlinear systems

This paper studies the linear feedback control strategies for nonlinear systems. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function, which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations the Duffing oscillator and the nonlinear automotive active suspension system are provided to show the effectiveness of this method.

A robustness design of fuzzy control is proposed in this paper to overcome the effect of modeling error between nonlinear system and Takagi-Sugeno (T-S) fuzzy model. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of nonlinear interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected systems. Finally, an example is given to illustrate the concepts discussed throughout the paper.

This paper considers the output feedback adaptive controller design problem for a class of discrete-time nonlinear systems in output feedback form with unknown control directions and preceded by unknown hysteresis. The problem of lacking in a-priori knowledge on the control directions and unknown hysteresis are solved by using the discrete Nussbaum gain and Prandtl–Ishlinskii model, respectively. The system is transformed into the form of a nonlinear auto regressive moving average (NARMA) model to construct an output feedback control. To overcome the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead-zone technique are constructed on the basis of the NARMA model. The proposed control algorithm guarantees that all the signals in the controlled system are bound and the output tracking error is made to be neighbourhood around zero, ultimately. Finally, simulations are performed on a nonlinear system to show the effectiveness of the proposed method

This paper is concerned with control design for a generalized discrete-time Takagi-Sugeno fuzzy system. The Takagi-Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations. It is a great tool to analyze a nonlinear system and to design a stabilizing controller for it. However, there is a case where a controller design for a nonlinear system based on the Takagi-Sugeno fuzzy system becomes difficult due to its representation. A generalized fuzzy system to be considered in this paper describes even a wider class of nonlinear systems by representing locally nonlinear systems, and gives a different representation from the standard Takagi-Sugeno fuzzy system, which leads to a rather easy controller design. For such a generalized system, a stabilizing controller design method is proposed by introducing a new class of nonlinear controllers. Then, the resulting closed-loop system becomes a fuzzy system with linear system structures locally, which makes the control design easier. Stabilizing controller design conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. A relaxation method is used to reduce the conservatism of design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.

Direct feedback control design for nonlinear systems

The goal of this book is to present different methodologies of the adaptive-approximation-based control in a unified context to facilitate discussions and comparison. Some of the topics covered include: a review of typical terminology used in nonlinear system control; approximation theory; approximation structures; learning methodologies used for adaptive function approximation; the design of nonlinear control systems; analysis and synthesis of nonlinear adaptive-approximation-based control systems; higher-order systems; and the design and analysis of adaptive-approximation-based controllers as applied to a fixed-wing aircraft. The book includes two appendices, with the first giving a background knowledge for stability and control of nonlinear systems, and the second providing a useful guide for implementing and debugging adaptive-approximation-based controllers. The book is written in plain language and flows from chapter to chapter in a natural way. Each chapter concludes with a summary as well as the exercises and design problems. The book constitutes an excellent reference for scientists and engineers interested in the subject matter. It would also serve well as a text for senior undergraduate or first year graduate courses in the field.

Recent theoretical developments have improved the understanding of gain scheduled control and suggested new methods for design, analysis and implementation of such nonlinear control systems. An integrated software environment for gain scheduled local controller network design and analysis, including computer-aided modelling and system identification, is described. Some background theory is included, and a speed control design problem for an experimental vehicle illustrates the application of the approach.

Event-triggered controller design of nonlinear discrete-time networked control systems in T-S fuzzy model

An H∞ tracking-based adaptive fuzzy sliding mode controller (H∞ AFSMC) is proposed for a class of nonlinear systems involving system uncertainties and external disturbances. The H∞ tracking control design method and the adaptive fuzzy sliding mode control technique are combined in the design of the H∞ AFSMC controller. By the Lyapunov theory, it is shown that the proposed controller has the following advantages: it can inhibit the chattering phenomenon and can guarantee the H∞ tracking performance to attenuate the lumped uncertainties caused by the unmodelled dynamics, the approximation error and the external disturbances. Subsequently, the problem of H∞ AFSMC design is characterised in terms of an eigenvalue problem, which can be efficiently solved by using convex optimisation techniques. Finally, an inverted pendulum system is simulated to demonstrate the validity and effectiveness of the proposed controller.

This paper aims at the design and simulation of hybrid PI-fuzzy control system for the speed control of a brushless dc motor. The performance of the fuzzy logic controller (FLC) is better under transient conditions, while that of the proportional plus integral (PI) controller is superior near the steady-state condition. The combined advantages of these two controllers can be obtained with hybrid PI -fuzzy speed controller. Both the design of the fuzzy controller and its integration with the proportional-integral (PI) controller is to be done. The principle of the proposed control system is to use a PI controller, which performs satisfactorily in most cases, while keeping in the background, a fuzzy controller, which is ready to take over the PI controller when severe perturbations occur. By combining the two controllers, one can get the quick response of the PI controller while eliminating the overshoot possibly associated with it.

In this paper, a new stabilizing control law with respect to a control Lyapunov function (CLF) is presented. This control law is similar to the pointwise min-norm control law. This control law is designed to maximize the angle between the gradient of the control Lyapunov function and the time derivative of the state vector at the state trajectory, which is defined in what follows as the "pointwise maximum angle control law." A comparison with the pointwise minnorm control law is provided. A criterion of the stability performance of control laws that are designed with respect to a CLF is presented. Also, by proposing the concept of the "eigen-angle" for real square nonsingular matrices, the stabilization of some nonaffine nonlinear systems, and the construction of a CLF for such systems are reduced to the construction of CLFs for affine nonlinear (linear) systems. Finally, simulation results are provided to show the effectiveness of the proposed methodologies.