Output feedback control of discrete-time nonlinear quadratic systems with quantization effects and missing measurements

This paper is concerned with an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> output feedback control of Takagi-Sugeno fuzzy systems with immeasurable premise variables. Takagi-Sugeno fuzzy systems can usually approximate nonlinear systems and can even describe a certain class of nonlinear system exactly. When we consider the output feedback control of Takagi-Sugeno fuzzy systems, the selection of premise variables plays an important role. If the premise variable is the state of the system, then a fuzzy system describes a wide class of nonlinear systems. However, the state is not measurable in the output feedback control problem. In this case, a control design of the underlying nonlinear system based on its fuzzy system description is difficult. In this paper, we consider an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> output feedback control problem. In this problem, the premise variable may not be measurable. Thus we formulate an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> output feedback control problem of fuzzy systems as a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control of uncertain systems. Numerical examples are given to illustrate our theory

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Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS) was proposed by Okubo (1985). In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k))║≤α + β║v (k)║^γ , where α≥0, β≥0, 0≤γ≤1. When 0≤γ<1. It is easy to extend the method to discrete time systems. But in the case γ = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.

In this paper, the decentralized robust output-feedback tracking control problem is investigated for a class of uncertain nonlinear interconnected systems subject to high order time varying disturbances. Firstly, generalized-proportional-integral observers (GPIOs) are designed for every subsystems such that the disturbances and unmeasured states can be recovered. Then, based on the estimation information of GPIOs and the output-feedback domination approach, a composite decentralized output-feedback controller is constructed. The proposed decentralized control scheme can not only handle the uncertain nonlinear interconnected terms, but also remove the influences the disturbances effectively via feedforward compensation manner. Finally, a practical example is conducted to demonstrate the effectiveness of the proposed control approach.

This article studies the problem of H ∞ dynamic output‐feedback control of non‐linear networked discrete‐time systems with data packet dropouts. Specifically, the data missing happens randomly from the sensor to the controller and the controller to the actuator. A sequence of independent variables obeying the Bernoulli random binary distribution is introduced to account for the measurement missing. The Takagi–Sugeno fuzzy model is used to describe the non‐linear plant. In addition, the strategy of parallel distributed compensation is adopted to design the fuzzy dynamic output‐feedback controller. Here, attention is focused on obtaining the sufficient conditions to guarantee the closed‐loop system to be stochastically stable as well as the prescribed H ∞ performance. An approach based on fuzzy Lyapunov function is developed to solve it. To tackle the non‐convex problem, the cone‐complementarity linearisation procedure is adopted. Finally, a numerical example is employed to show the usefulness of the proposed result.

This paper uses a polynomial approach to present a necessary and sufficient condition for local controllability of single-input single-output (SISO) discrete-time non-linear systems. The condition is presented in terms of common factors of a non-commutative polynomial expression. This extends the result on controllability of linear systems and the recent result on controllability of continuous-time non-linear systems to expose controllability of discrete-time non-linear systems in the input–output framework. The controllability condition yields a finite step computing procedure for examining controllability of discrete-time input–output non-linear systems.

This paper is concerned with the finite-horizon H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> quantized control problem for a class of discrete time-varying nonlinear networked control systems with earliest deadline first (EDF) schedule. EDF schedule is employed in the channels both from sensor to controller and controller to actuator. Moreover, the measurement output signal and control signal are quantized by a logarithmic quantizer before they enter the controller and system, respectively. The main purpose of the problem addressed is to design a dynamical output-feedback controller such that the prespecified H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of the system is guaranteed over a given finite time-horizon. To this end, a sufficient condition is firstly established for the existence of the desired output-feedback controller. Then, the controller parameters are characterized by solving a recursive linear matrix inequality. Finally, a numerical example is given to illustrate the effectiveness of the proposed control approach.

The problem of output feedback control for a class of second-order nonlinear systems is investigated in this paper. Using the techniques of finite-time control and finite-time convergent observer, an observer-based finite-time output feedback controller is proposed which can guarantee that the system’s state converges to the equilibrium in a finite time. As an application of the proposed theoretical results, the problem of finite-time control without current signal for the DC–DC buck converters is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.

The H∞ dynamic output feedback control problem for a class of discrete‐time switched time‐delay systems under asynchronous switching is investigated in this paper. Sensor nonlinearity and missing measurements are considered when collecting output knowledge of the system. Firstly, when there exists asynchronous switching between the switching modes and the candidate controllers, new results on the regional stability and l2 gain analysis for the underlying system are given by allowing the Lyapunov‐like function (LLF) to increase with a random probability. Then, a mean square stabilizing output feedback controller and a switching law subject to average dwell time (ADT) are obtained with a given disturbance attenuation level. Moreover, the mean square domain of attraction could be estimated by a convex combination of a set of ellipsoids, the number of which depends on the number of switching modes. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Based on the backstepping technique, an adaptive neural network (NN) based output feedback controller is proposed to achieve a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict-feedback form. The neural networks are utilized to approximate unknown functions in the systems. The adaptive output feedback controller needs only to adjust less adaptive parameters, therefore it is clear that the proposed approach can reduce on-line computation burden. It is proven that all the signals in the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero by choosing the design parameters appropriately. A simulation example is used to verify the effectiveness of the proposed approach.

This paper considers the design problem of dynamic output feedback control for fractional-order (FO) Takagi-Sugeno fuzzy systems with uncertain parameters. Via the application of FO system stability theory, robust control method and the linear matrix inequality techniques, sufficient conditions are given for the stability analysis and the existence of the dynamic fuzzy output feedback controllers. The dynamic output feedback controller designed here guarantees the robust stability of the closed-loop system. Finally, a fractional order chaotic system simulation example is given to illustrate the effectiveness of the design approach here.

In this paper, the output feedback control problem is considered for a class of uncertain nonlinear time-delay systems. The system nonlinearities satisfy linear growth condition on unmeasured states multiplied by unknown growth rate and output polynomial function. With appropriate Lyapunov-Krasovskii functional, a memoryless adaptive output feedback controller is developed to guarantee global stability of the nonlinear time-delay systems. The precise knowledge of the time-delay is not required to be known a priori. Furthermore, only one dynamic gain is designed, which makes the controller easier to implement. A numerical example is used to illustrate the effectiveness of the proposed method.

This paper is focused on the static output feedback (SOF) control problem for a class of switched nonlinear systems with actuator faults. By means of the Takagi-Sugeno fuzzy model, the switched nonlinear plant is described by a family of switched fuzzy systems. Considering transmission failures may occur between controller and actuator, a reliable SOF controller against actuator faults is designed. Sufficient conditions are developed to guarantee the existence of the reliable SOF controller. Furthermore, an iterative algorithm is designed to determine the controller gains, which avoids the conservatism brought by the traditional singular value decomposition method. To validate the effectiveness of the proposed approach, a numerical example is exploited and simulation results are also presented.

A novel neural network (NN) -based output feedback controller with magnitude constraints is designed to deliver a desired tracking performance for a class of multi-input-multi-output (MIMO) discrete-time strict feedback nonlinear systems. Reinforcement learning in discrete time is proposed for the output feedback controller, which uses three NN: 1) a NN observer to estimate the system states with the input-output data; 2) a critic NN to approximate certain strategic utility function; and 3) an action NN to minimize both the strategic utility function and the unknown dynamics estimation errors. The magnitude constraints are manifested as saturation nonlinearities in the output feedback controller design. Using the Lyapunov approach, the uniformly ultimate boundedness (UUB) of the state estimation errors, the tracking errors and weight estimates is shown.