Continuous finite-time state feedback stabilizers for some nonlinear stochastic systems

This paper is concerned with the problem of finite-time stabilization for some nonlinear stochastic systems. Based on the stochastic Lyapunov theorem on finite-time stability that has been established by the authors in the paper, it is proven that Euler-type stochastic nonlinear systems can be finite-time stabilized via a family of continuous feedback controllers. Using the technique of adding a power integrator, a continuous, global state feedback controller is constructed to stabilize in finite time a large class of two-dimensional lower-triangular stochastic nonlinear systems. Also, for a class of three-dimensional lower-triangular stochastic nonlinear systems, a recursive design scheme of finite-time stabilization is given by developing the technique of adding a power integrator and constructing a continuous feedback controller. Finally, a simulation example is given to illustrate the theoretical results. © 2014 John Wiley & Sons, Ltd.

Reduced-order output feedback controllers for discrete-time systems

This article considers the stabilization by output feedback controllers for discrete-time systems. The controller can place all of the closed-loop poles within a specified disk D(-α, 1/β), centred at (-α,0) with radius 1/β, where | - α|  + 1/β < 1. The design method involves the decomposition of the system into two portions. The first portion comprises of all of the poles that are lying outside of the specified disk. A reduced-order model is constructed for this portion. The second portion comprises of all of the remaining poles of the system and is characterized by an H_∞-norm bound. The controller design is then accomplished by using H_∞-control theory. It is shown that, subject to the solvability of an algebraic Riccati equation, output feedback controllers can be systematically derived. The order of the controller is low, and can be as low as the number of the open-loop poles that are lying outside of the specified disk. A step-by-step design algorithm is provided. Numerical examples are given to illustrate the attractiveness of the design method.

Constrained pole placement for linear systems using low-order output feedback controllers

The paper presents a simple approach to the problem of designing low-order output feedback controllers for linear continuous systems. The controller can place all of the closed-loop poles within a circle, C(- , 1/ β) , with centre at - and radius of 1/ β in the left half s-plane. The design method is based on transformation of the original system and then applying the bounded-real-lemma to the transformed system. It is shown that subjected to the solvability of an algebraic Riccati equation (ARE), output feedback controllers can then be systematically derived. Furthermore, the order of the controller is low and equals only the number of the open-loop poles lying outside the circle. A step-by-step design algorithm is given. Numerical examples are given to illustrate the design method.

Determination of structurally constrained controllors

This paper reports on determination of structurally constrained controllers for linear uncertain time-invariant systems from state controllers. It is shown that practical structures such as output and decentralized controllers may be derived from state feedback controllers. A previously studied load frequency control of a two-area interconnected power system is considered to illustrate the proposed approach.

Exponential stabilization for state and input delay systems via output feedback

This paper considers the exponential stabilization problem via static and dynamic output feedback controllers of linear systems with a time delay in both the state and input. By using a change of the state variable and combining with the Lyapunov-Krasovskii method, new sufficient conditions for exponential stabilization via static and dynamic output feedback controllers are proposed. The conditions are expressed in terms of matrix inequalities but with only one parameter needs to be tuned and therefore can be efficiently solved by incorporating an one-dimensional search method into the Matlab’s LMI toolbox. Two numerical examples are provided to illustrate the obtained results.

Problem of precision missile guidance: LQR and H‡ control frameworks

Addressed here is the precision missile guidance problem where the successful intercept criterion has been defined in terms of both minimizing the miss distance and controlling the missile body attitude with respect to the target at the terminal point. We show that the H∞ control theory, when suitably modified, provides an effective framework for the precision missile guidance problem. The existence of feedback controllers (guidance laws) is investigated for the case of finite horizon and non-zero initial conditions. Both state feedback and output feedback implementations are explored.

Dynamic output feedback control of single-link flexible manipulators

This paper presents an efficient technique to design dynamic feedback control scheme for single-link flexible manipulators.  A linear model can be derived for the robotic system using the assumed-mode method.  Conventional techniques such as pole-placement or LQR require physical measurements of all systme states,  posing a stringent requirement for its implementation.  To overcome this problem, a low-order state functional observer is proposed here for reconstruction of the state feedback control action.  The observer design involves solving an optimisation problem with the objective to generate a feedback gain that is as close as possible to that of the required feedback controller.  A condition for robust stability of the closed-loop system under the observer-based control scheme is given.  The attractive features of the propsed technique are the resulted functional state observer is of a very low order and it requires only sensor measurements of only the output- the tip position of the arm.

A distributed approach to global feedback control of multi-agent systems

This paper presents a distributed approach to global state feedback control of for multi-agent systems. The proposed solution is obtained from the construction of decentralised functional observers. The required local control signal is generated asymptotically using only corresponding local output information. It is shown that a complete distribution of the control of a decentralised system having N agents can be achieved upon the satisfaction of some necessary conditions, and that the resulting controller can emulate the performance of a global state feedback controller. A step-by-step design algorithm is given. Its simplicity and correctness are illustrated through a numerical example.

Observer-based control for time-varying delay neural networks with nonlinear observation

This paper studies the problem of designing observer-based controllers for a class of delayed neural networks with nonlinear observation. The system under consideration is subject to nonlinear observation and an interval time-varying delay. The nonlinear observation output is any nonlinear Lipschitzian function and the time-varying delay is not required to be differentiable nor its lower bound be zero. By constructing a set of appropriate Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, some delay-dependent stabilizability conditions which are expressed in terms of Linear Matrix Inequalities (LMIs) are derived. The derived conditions allow simultaneous computation of two bounds that characterize the exponential stability rate of the closed-loop system. The unknown observer gain and the state feedback observer-based controller are directly obtained upon the feasibility of the derived LMIs stabilizability conditions. A simulation example is presented to verify the effectiveness of the proposed result.

New H∞ control design for polytopic systems with mixed time-varying delays in state and input

This paper concerns with the problem of state-feedback H∞ control design for a class of linear systems with polytopic uncertainties and mixed time-varying delays in state and input. Our approach can be described as follows. We first construct a state-feedback controller based on the idea of parameter-dependent controller design. By constructing a new parameter-dependent Lyapunov-Krasovskii functional (LKF), we then derive new delay-dependent conditions in terms of linear matrix inequalities ensuring the exponential stability of the corresponding closed-loop system with a H∞ disturbance attenuation level. The effectiveness and applicability of the obtained results are demonstrated by practical examples.

Load frequency control of power systems with electric vehicles and diverse transmission links using distributed functional observers

This paper presents a load frequency control scheme using electric vehicles (EVs) to help thermal turbine units to provide the stability fluctuated by load demands. First, a general framework for deriving a state-space model for general power system topologies is given. Then, a detailed model of a four-area power system incorporating a smart and renewable discharged EVs system is presented. The areas within the system are interconnected via a combination of alternating current/high voltage direct current links and thyristor controlled phase shifters. Based on some recent development on functional observers, novel distributed functional observers are designed, one at each local area, to implement any given global state feedback controller. The designed observers are of reduced order and dynamically decoupled from others in contrast to conventional centralized observer (CO)-based controllers. The proposed scheme can cope better against accidental failures than those CO-based controllers. Extensive simulations and comparisons are given to show the effectiveness of the proposed control scheme.

Robust terminal attitude navigation for autonomous vehicles

Here we define the terminal attitude of the pursuer with respect to a target and present a LQR and H¿ control approach to solving the problem of pursuer achieving a desired terminal attack/approach angle. The intercept or engagement criteria is defined in terms of both minimizing the miss distance and controlling the pursuer's body attitude with respect to the target at the terminal point. This approach in comparison to previous approaches consider the relativistic approach of the pursuer with respect to the target as opposed the absolute velocities of the two dynamic bodies, and have possible applications ranging from autonomous vehicle entry in to a mother craft to nossle engagements in on-flight refuelling or even in precision missile guidance. Here we also suitably formulate the H¿ control ideas directly applicable to the underlying problem and presents both state feedback and output feed back results for the case of finite horizon and non-zero initial conditions together with a optimal parameter value to achieve a desired terminal characteristic in terms of the original weighting parameters.

Observer-based control of multi-agent systems under decentralized information structure

This paper addresses the problem of decentralized implementation of a global state feedback controller for multi-agent systems. The system is assumed to be under the constraint of a complete decentralized information structure. The decentralization of the control task is achieved through the construction of low-order decentralized functional observers with the purpose of generating the required corresponding control signal for each local control station. A design procedure is developed for obtaining an approximate solution to the design of the observers. Stability analysis is provided for the global system using the proposed observer-based approach. A numerical example is given to illustrate the design procedure and cases when the observers' order increases from the lowest value.