Dynamic surface control based on neural network for an air‐breathing hypersonic vehicle

In this paper, an adaptive dynamic surface control approach is presented for the longitudinal motion of an air‐breathing hypersonic vehicle. Fully tuned radial basis function neural network that regulates weights, width, and center of Gaussian function simultaneously is developed to estimate aerodynamic uncertainties and atmospheric disturbances. The nonlinear control law is subsequently designed by dynamic surface control approach for the vehicle model converted into strict block feedback form by input–output linearization method. Simulation results show that the velocity can be successfully tracked over a large range from Mach 11 to Mach 12 and an altitude range from 26 to 30 km. The presented approach has perfect ability of restraining unknown and time‐varying nonlinear dynamics during flight. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust static and fixed‐order dynamic output feedback control of discrete‐time parametric uncertain Luré systems: Sequential SDP relaxation approaches

Design methods are proposed for static and fixed‐order dynamic output feedback controllers for discrete‐time Luré systems with sector‐bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear matrix inequalities, which are nonconvex. By using convex relaxation methods, controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs) and iterative LMIs, which are associated with semidefinite programs. The proposed design methods are developed from stability conditions using parameter‐dependent Lyapunov functions, and existing iterative numerical methods are adapted to solve certain classes of nonconvex optimization problems for controller design. Several numerical examples are provided to illustrate and verify the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.     

An improved path‐following method for solving static output feedback control problems

This paper studies the static output feedback stabilization problems. An improved path‐following method is proposed for continuous‐time systems as well as for discrete‐time systems. The method has two advantages. Firstly, by virtue of a new linearization approach, the related bilinear matrix inequalities ensuring the stabilization of the systems are expanded and linearized around some points. The initialization methods for both systems are built. Then a wide range perturbation step is added to help the method escape from local optimum. The effectiveness and merits of the proposed method are shown through several examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Characterization and selection of global optimal output feedback gains for linear time‐invariant systems

The problem of global optimal static output feedback control for linear time‐invariant systems with linear quadratic index is investigated. The contributions of this paper are two‐fold. One is to investigate the dependence of the global optimal output feedback gain on the system initial conditions. The other is to construct a globally optimal feedback under a certain output measurement structure. Copyright © 2000 John Wiley & Sons, Ltd.     

Suboptimal digital LQ output feedback control design via LMI relaxations

This paper deals with suboptimal linear quadratic (LQ) output feedback control of linear discrete systems. It is shown that degree of freedoms by instrumental variables employed in this paper lead to much flexibility in obtaining a suboptimal LQ controller. An improved convex optimization method involving linear matrix inequalities (LMIs) is suggested to solve the matrix inequalities characterizing a solution of the suboptimal LQ problem. Of the major interest of this paper is an extension to a class of nonconvex LQ problems of large size arising in decentralized feedback, simultaneous control, periodic feedback control, etc. Illustrative examples demonstrate the validity of the proposed convex approximate approach to optimal LQ output feedback control. Also, it is shown that suboptimal LQ solutions obtained by the proposed method can be used as an initial feasible point of existing iterative LMI algorithms to improve the feasibility of the iterative methods. Copyright © 2007 John Wiley & Sons, Ltd.     

State and output feedback design for robust tracking of linear systems with rate limited actuators

A design technique (Control of Uncertain Systems with Bounded Inputs, Tarbouriech S, Garcia G, (Eds), Lecture Notes in Control and Information Sciences, vol. 227 , Springer: Berlin, 1997; 173–186) recently proposed for stabilization of a linear system with rate‐limited actuators is utilized to design feedback laws that cause the system output to track a desired command signal. This design technique combines two design techniques recently developed for linear systems with position limited actuators, piecewise‐linear LQ control (Automatica, 1994; 30 : 403–416) and low‐and‐high gain feedback (IEEE Trans. Automat. Control, 1996; 41 : 368–378), and hence takes advantage of both design techniques, while avoiding their disadvantages. In the case that only the output is available for feedback, the performance of the state feedback law is preserved by the use of a fast observer. An open‐loop exponentially unstable fighter aircraft is used to demonstrate the effectiveness of the proposed control design method. Copyright © 2002 John Wiley & Sons, Ltd.     

New results on dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information

This paper investigates the problem of delay‐dependent dynamic output feedback control for a class of discrete‐time Markovian jump linear systems (MJLSs). The systems under consideration are subject to time‐varying delay and defective mode information. The defective transition probabilities comprise of three types: exactly known, uncertain, and unknown. By employing a two‐term approximation for the time‐varying delay, the original MJLSs can be equivalently converted into a feedback interconnection form, which contains a forward subsystem with constant time‐delays and a feedback one with norm‐bounded uncertainties. Then, based on the scaled small‐gain theorem, the problem is therefore recast as an control problem in the face of uncertainties via an input–output framework. It is shown that the explicit expressions of the desired controller gains can be characterized in terms of strict linear matrix inequalities via some linearization techniques. Simulation studies are performed to illustrate the effectiveness and less conservatism of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Mixed H2/H∞ robust output feedback sliding mode control

This paper presents an output feedback sliding mode control scheme for uncertain dynamical systems. The design problem is solved in two steps, involving first a state feedback and then an output feedback problem. First, using the null space dynamics, the sliding surface for the unmatched uncertainty is designed. Then, by tuning the sliding surface, a robust controller is constructed for the whole uncertainty; this problem takes the form of static‐output feedback. Based on this, a dynamic output feedback controller for the system augmented with the sliding surface is designed. The synthesis involves the solution of an Linear Matrix Inequality (LMI) and Bilinear Matrix Inequality (BMI) problem; the BMI problem is solved iteratively. The proposed approach is illustrated by applying it to a well‐known robust benchmark problem and also experimentally on a spring mass system with variable stiffness. Simulation and experimental results show that the proposed method outperforms previous approaches in terms of robust performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Design of simultaneous static output feedback low‐gain H∞ controllers for a collection of time‐delay system

This paper considers the design of simultaneous static output feedback controllers for a finite collection of time‐delay linear systems. By solving a minimization problem, we try to find an output feedback low‐gain controller such that all resultant closed‐loop time‐delay systems are internally stable and satisfy a prespecified H_∞‐norm requirement. Based on the barrier method, necessary conditions for local optimum of the minimization problem are derived. An example is given for illustration.     

An optimal dynamic output feedback controller for a flexible spacecraft

The design of a low-order dynamic output feedback controller for a flexible spacecraft is carried out using modified linear quadratic Gaussian (LQG) theory. The necessary conditions for optimization are given. The linear equations governing a flexible spacecraft with a central rigid body and two sun-tracking solar panels are presented. The parameters of the Solar Electric Propulsion Spacecraft (SEPS) are selected for analysis and simulation. The optimal gains for the dynamic controller are estimated using an iterative algorithm. The sequential procedure which assures convergence is selected. The initial gains which stabilize the system are chosen on the basis of the principle of a PD controller. A third-order controller for pitch, roll and yaw axes of the 18th-order system, which includes sensor and actuator dynamics, is designed. Numerical simulations carried out to ascertain the performance of the controller show the performance to be satisfactory.     

Robust ℋ︁2 static output feedback design starting from a parameter‐dependent state feedback controller for time‐invariant discrete‐time polytopic systems

This paper investigates the problem of computing robust ??₂ static output feedback controllers for discrete‐time uncertain linear systems with time‐invariant parameters lying in polytopic domains. A two stages design procedure based on linear matrix inequalities is proposed as the main contribution. First, a parameter‐dependent state feedback controller is synthesized and the resulting gains are used as an input condition for the second stage, which designs the desired robust static output feedback controller with an ??₂ guaranteed cost. The conditions are based on parameter‐dependent Lyapunov functions and, differently from most of existing approaches, can also cope with uncertainties in the output control matrix. Numerical examples, including a mass–spring system, illustrate the advantages of the proposed procedure when compared with other methods available in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic output feedback of networked control systems with partially known Markov chain packet dropouts

In this paper, a class of networked control systems with output feedback control and H _∞ performance is discussed. It considers packet dropouts in both measurement (S/C) and actuation (C/A) channels. Markovian chain principle is used in modeling the packet dropouts in S/C and C/A channels. The time scale adopted in these two independent homogeneous Markov chain is linear with the physical time. The model also takes into consideration the late arriving packets. The effect of interaction between packet dropouts in both channels on the stability of system, when the networks of both (S/C) and (C/A) channels overlap is also examined. Sufficient condition for the existence of H _∞ output feedback controller is presented and it is shown that it is dependent on the upper bounds of the number of consecutive packet dropouts. The developed stability analysis and control scheme is also investigated with partially known transition probability matrices. Finally, a numerical example has been given to show the effectiveness of developed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive dynamic surface control using neural networks for hypersonic flight vehicle with input nonlinearities

This study proposes an effective adaptive dynamic surface control (DSC) method based on the radial basis function neural networks and the auxiliary system for hypersonic flight vehicle (HFV) systems in the presence of system uncertainties, external disturbances, and state variable and control input constraints. Firstly, to enhance the robustness of the system, the neural network is combined with the robust term to deal with the uncertainties and external disturbances of the system. Secondly, to prevent the deterioration of the dynamic performance of the system due to the over-adaptation of the neural networks and the robust terms caused by the state and control input constraints, the auxiliary system is added at each step in the DSC design to adjust the dynamic process of the reference signal and virtual control. Furthermore, the variable structure control is used to solve the problem of dead zone in the control input. Using the Lyapunov analysis method, all signals of the closed-loop system are semi-globally uniformly ultimate bounded. The simulation results illustrate the effectiveness of the proposed control scheme for the HFVs.     

Optimal trajectory control for a two‐link rigid‐flexible manipulator with ODE‐PDE model

In this paper, the optimal trajectory control problem for a two‐link rigid‐flexible manipulator is considered. Since the two‐link rigid‐flexible system is a distributed system, an ordinary differential equation and partial differential equation (ODE‐PDE) dynamic model of the manipulator is established by Hamilton's principle. Based on the ODE‐PDE model, an optimal trajectory controller is proposed in this paper, which includes 2 stages. In the first stage, the optimal trajectory is created by using the differential evolution algorithm. Energy consumption and deflection of the flexible link are chosen as performance indexes. Cubic spline interpolation is applied to obtain the continuous trajectory. In the second stage, the aim is to regulate 2 joints to follow the optimal trajectory and simultaneously suppress vibration of the flexible link. To achieve it, boundary control laws are designed and the stability analysis is given. In simulations, the effectiveness of the optimal controller is verified by MATLAB.     

The optimal feedback control of the linear‐quadratic control problem with a control inequality constraint

In this paper, we consider the linear‐quadratic control problem with an inequality constraint on the control variable. We derive the feedback form of the optimal control by the agency of the unconstrained linear‐quadratic control systems. Copyright © 2001 John Wiley & Sons, Ltd.     

An Optimal output feedback control method and application to a motor-generator system

A multi-input/multi-output feedback control system synthesis method with output feedback structure is proposed on the basis of an improved optimal regulator theory. The method is applied to a DC motor/AC generator system. The effectiveness of the method is demonstrated by simulation and experimental studies. An input-output relation is derived through the observable canonical form of the state equations of the controlled object, and an improved optimal regulator theory is applied to the relation. The controller consists of proportional actions, integral actions, difference actions and compensating actions for input delay times. The (l — 1) th-order difference actions are included in the controller for the controlled object in which an lth-order output subsystem is included. On the other hand, the (n — 1) th-order difference actions are included in the previous method for the same controlled object. In order to consider the transient response of the designed control system, the relations between the weighting factors in the defined performance index and the transient response are studied by simulation and experiment. Satisfactory responses for a two-input/two-output system are obtained in our experiments.     

Generalized sampled‐data hold functions for robust multivariable tracking and disturbance rejection

A new design procedure for a multivariable sampled‐data output feedback controller with generalized hold function is proposed. The controller can be designed for different operating points simultaneously. The design of the hold function is carried out in two steps: first the closed‐loop discrete‐time behaviour is determined by choosing a suitable output injection gain; integral action is incorporated to guarantee zero steady‐state error. In a second step this discrete‐time behaviour is approximately realized by output feedback with generalized hold. Minimization of a quadratic performance index simultaneously for all operating points yields hold functions with good intersample behaviour. A practical design example and experimental results illustrate the proposed method. Copyright © 2001 John Wiley & Sons, Ltd.     

A multi‐modality tracking,navigation and calibration for a flexible robotic drill system for total hip arthroplasty

Background

This paper presents a novel multi‐modality tracking and navigation system that provides a unique capability to guild a flexible drill tip inside the bone with accurate curved tunnelling.

Methods

As the flexible drill tip cannot be tracked optically inside the bone, this research focuses on developing a hybrid tracking and navigation system for tracking a flexible drill tip by using both optical and kinematic tracking. The tracking information is used to guide the THA (total hip arthroplasty) procedure, providing a real‐time virtual model of the flexible drill.

Results

The flexible and steerable drill tip system is then tested on total hip arthroplasty followed by evaluation of the positioning and orientation of femoral stem placement by femoral milling.

Conclusions

Based on this study, we conclude that the tracking and navigation system is able to guide the flexible drill to mill inside femoral canal.     

Dubins path‐based dynamic soaring trajectory planning and tracking control in a gradient wind field

This paper studies small unmanned aerial vehicle dynamic soaring for conserving onboard energy to extend flight endurance performance. A novel dynamic soaring path planning approach is proposed using the Dubins path. It enjoys a significant improvement in computational efficiency. In addition, a custom‐built trajectory tracking controller is developed for a nonlinear unmanned aerial vehicle dynamics model to verify the implementation of the proposed path planning approach. Extensive numerical simulations are conducted to demonstrate the effectiveness of the proposed design and development. Copyright © 2016 John Wiley & Sons, Ltd.