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.

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.

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.

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.

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.

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.

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.

Observer-based decentralized approach to robotic formation control

Control of a group of mobile robots in a formation requires not only environmental sensing but also communication among vehicles. Enlarging the size of the platoon of vehicles causes difficulties due to communications bandwidth limitations. Decentralized control may be an appropriate approach in those cases when the states of all vehicles cannot be obtained in a centralized manner. This paper presents a solution to the problem of decentralized implementation of a global state-feedback controller for N mobile robots in a formation. The proposed solution is based on the design of functional observers to estimate asymptotically the global state-feedback control signals by using the corresponding local output information and some exogenous global functions. The proposed technique is tested through simulation and experiments for the control of groups of Pinoneer-based non-holonomic mobile robots.

A low-order linear functional observer for time delay systems

This paper presents an efficient technique to design low order state function observers for linear time-delay systems. Assuming the existence of a linear state feedback controller to achieve stability or some control performance criteria of the time-delay system, a design procedure is proposed for
reconstruction of the state feedback control action. The procedure involves solving an optimisation problem with the objective to generate a matrix that is as close as possible to the given feedback gain of the required feedback controller. A condition for robust stability of the time-delay system using the observer-based control scheme is given. The attractive features of the proposed design procedure are that the resulted linear functional state observer is of a very low order and it requires information of a small number of outputs. Numerical examples are given to demonstrate the design procedure and its merits.

Performance of first and second-order sliding mode observers for nonlinear systems

This paper presents a brief study on the design and performance comparison of conventional first-order and super-twisting second-order sliding mode observers for some nonlinear control systems. Estimation accuracy, fast response, chattering effect, peaking phenomenon and robustness are considered for nonlinear ystems under observer-based output feedback control and state feedback control.

A finite-time stability theorem of stochastic nonlinear systems and stabilization designs

This paper focuses on the finite-time stability and stabilization designs of stochastic nonlinear systems. We first present and discuss a definition on the finite-time stability in probability of stochastic nonlinear systems, then we introduce a stochastic Lyapunov theorem on the finite-time stability, which has been established by Yin et al. We also employ this theorem to design a continuous state feedback controller that makes a class of stochastic nonlinear systems to be stable in finite time. An example and a simulation are given to illustrate the theoretical analysis.

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.

Quasi-decentralized functional observers for the LFC of interconnected power systems

This letter presents a novel approach to the load-frequency control (LFC) of interconnected power systems. Based on functional observers theory, quasi-decentralized functional observers (QDFOs) are designed to implement any given global PI state feedback controller. The designed functional observers are decoupled from each other and also of low-order; thus, they are cost effective and easy to implement. Although the proposed approach is applicable to N- area power systems, an example of a two-area interconnected power system with reheat thermal turbines is considered for simplicity.