Dynamic output‐feedback control for continuous‐time singular Markovian jump systems

This paper considers a dynamic output‐feedback control for continuous‐time singular Markovian jump systems, whereas the existing research studies in literature focused on state‐feedback or static output‐feedback control. While they have only provided the sufficient conditions, this paper successfully obtains the necessary and sufficient condition for the existence of the dynamic output‐feedback control. Furthermore, this condition is expressed with linear matrix inequalities by the so‐called replacement technique. Two numerical examples show the validity of the resulting control.     

Robust output‐feedback control of state‐multiplicative noisy discrete‐time systems

Linear discrete‐time systems with stochastic and deterministic polytopic type uncertainties in their state‐space model are considered. A dynamic output‐feedback controller is obtained via a new approach that allows a derivation of a controller in spite of parameter uncertainty. In the proposed approach, the system is described via a difference equation and an augmented system is then used to obtain the output‐feedback controller parameters. The controller is obtained without assuming a specific structure to the quadratic Lyapunov function, and it is the first time that an output‐feedback controller is obtained for robust state‐multiplicative systems. The controller minimizes the stochastic L₂‐gain of the closed‐loop where a cost function is defined to be the expected value of the standard performance index with respect to the stochastic uncertainty. Two examples are given where the second of which demonstrates the applicability of our theory to a robot manipulator system. Copyright © 2016 John Wiley & Sons, Ltd.     

Gain‐scheduled dynamic output feedback control for discrete‐time LPV systems

This paper presents synthesis conditions for the design of gain‐scheduled dynamic output feedback controllers for discrete‐time linear parameter‐varying systems. The state‐space matrix representation of the plant and of the controller can have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameter. As an immediate extension, conditions for the synthesis of a multiobjective ??_∞ and ??₂ gain‐scheduled dynamic feedback controller are also provided. The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real‐time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the uncertainty domain are exploited to derive finite sets of linear matrix inequalities based on the existence of a homogeneous polynomially parameter‐dependent Lyapunov function. An application of the control design to a realistic engineering problem illustrates the benefits of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Probability‐dependent gain‐scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities

In this paper, the gain‐scheduled control problem is addressed by using probability‐dependent Lyapunov functions for a class of discrete‐time stochastic delayed systems with randomly occurring sector nonlinearities. The sector nonlinearities are assumed to occur according to a time‐varying Bernoulli distribution with measurable probability in real time. The multiplicative noises are given by means of a scalar Gaussian white noise sequence with known variances. The aim of the addressed gain‐scheduled control problem is to design a controller with scheduled gains such that, for the admissible randomly occurring nonlinearities, time delays and external noise disturbances, the closed‐loop system is exponentially mean‐square stable. Note that the designed gain‐scheduled controller is based on the measured time‐varying probability and is therefore less conservative than the conventional controller with constant gains. It is shown that the time‐varying controller gains can be derived in terms of the measurable probability by solving a convex optimization problem via the semi‐definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures. Copyright © 2012 John Wiley & Sons, Ltd.     

Gain‐scheduled leader‐follower tracking control for interconnected parameter varying systems

This paper considers the gain‐scheduled leader‐follower tracking control problem for a parameter varying complex interconnected system with directed communication topology and uncertain norm‐bounded coupling between the agents. A gain‐scheduled consensus‐type control protocol is proposed and a sufficient condition is obtained, which guarantees a suboptimal bound on the system tracking performance under this protocol. An interpolation technique is used to obtain a protocol schedule, which is continuous in the scheduling parameter. The effectiveness of the proposed method is demonstrated using a simulation example. Copyright © 2015 John Wiley & Sons, Ltd.     

Gain‐scheduled H∞ filtering of parameter‐varying systems

This paper deals with the gain‐scheduled H_∞ filtering problem for a class of parameter‐varying systems. A sufficient condition for the existence of a gain‐scheduled filter, which guarantees the asymptotic stability with an H_∞ noise attenuation level bound for the filtering error system, is given in terms of a finite number of linear matrix inequalities (LMIs). The filter is designed to be parameter‐varying and have a nonlinear fractional transformation structure. A numerical example is presented to demonstrate the application of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Output‐feedback control strategies of lower‐triangular nonlinear nonholonomic systems in any prescribed finite time

In this paper, output‐feedback control strategies are proposed for lower‐triangular nonlinear nonholonomic systems in any prescribed finite time. Specifically, by employing the input‐state–scaling technique, the controlled systems are firstly converted into lower‐triangular nonlinear systems, which makes it possible to study such systems using the high‐gain technique. Then, by introducing a scaling of the state by a function that grows unbounded toward the terminal time and proposing a high‐gain observer–prescribed finite time recovering the system states, the output‐feedback regulation control problem in any prescribed finite time is firstly achieved for nonlinear nonholonomic systems with unknown constant incremental rate. Moreover, by designing another time‐varying high gain, the output‐feedback stabilization control problem in any prescribed finite time is then achieved for nonlinear nonholonomic systems with a time‐varying incremental rate. Finally, a numerical example is introduced to show the effectiveness of proposed control strategies.     

Global robust practical output regulation for nonlinear systems in output feedback form by output‐based event‐triggered control

In this paper, we study the event‐triggered global robust practical output regulation problem for a class of nonlinear systems in output feedback form with any relative degree. Our approach consists of the following three steps. First, we design an internal model and an observer to form the so‐called extended augmented system. Second, we convert the original problem into the event‐triggered global robust practical stabilization problem of the extended augmented system. Third, we design an output‐based event‐triggered control law and a Zeno‐free output‐based event‐triggered mechanism to solve the stabilization problem, which, in turn, leads to the solvability of the original problem. Finally, we apply our result to the controlled hyperchaotic Lorenz systems.     

Robust H∞ output‐feedback control of retarded state‐multiplicative stochastic systems

Linear, state‐delayed, continuous‐time systems are considered with both stochastic and norm‐bounded deterministic uncertainties in the state–space model. The problem of robust dynamic H_∞ output‐feedback control is solved, for the stationary case, via the input–output approach where the system is replaced by a nonretarded system with additional deterministic norm‐bounded uncertainties. A delay‐dependent result is obtained which involves the solution of a simple linear matrix inequality. In this problem, a cost function is defined which is the expected value of the standard H_∞ performance cost with respect to the stochastic parameters. A practical example taken from the field of guidance control is given that demonstrates the applicability of the theory. Copyright © 2010 John Wiley & Sons, Ltd.     

Networked gain‐scheduled fault diagnosis under control input dropouts without data delivery acknowledgment

This paper investigates the fault diagnosis problem for discrete‐time networked control systems under dropouts in both control and measurement channel with no delivery acknowledgment. We propose to use a proportional integral observer‐based fault diagnoser collocated with the controller. The observer estimates the faults and computes a residual signal whose comparison with a threshold alarms the fault appearance. We employ the expected value of the arriving control input for the open‐loop estimation and the measurement reception scenario for the correction with a jump observer. The jumping gains are scheduled in real time with rational functions depending on a statistic of the difference between the control command being applied in the plant and the one being used in the observer. We design the observer, the residual, and the threshold to maximize the sensitivity under faults while guaranteeing some minimum detectable faults under a predefined false alarm rate. Exploiting sum‐of‐squares decomposition techniques, the design procedure becomes an optimization problem over polynomials. Copyright © 2015 John Wiley & Sons, Ltd.     

Parameterized LMIs for robust and state feedback control of continuous‐time polytopic systems

This paper presents new extended linear matrix inequality (LMI) characterizations for the synthesis of robust and state feedback controllers for continuous‐time linear time‐invariant systems with polytopic uncertainty. Based on a suitable change of variables and the Elimination Lemma, the proposed robust control design techniques are stated as extended LMI conditions parameterized in terms of 2 scalar parameters. One parameter is shown to belong to a bounded domain, thus limiting the scalar search domain. For the other parameter, a bounded subset is provided from numerical experiments. The benefits of the methodology are illustrated through numerical simulations performed on an uncertain model borrowed from the literature. It is shown that the proposed LMI relaxations can provide less conservative results with fewer scalar searches than some existing methods in the literature.     

Adaptive output‐feedback tracking for nonlinear systems with rather general control coefficients

This paper studies the problem of global practical tracking by output feedback for a class of uncertain nonlinear systems with unmeasured state‐dependent growth and unknown time‐varying control coefficients. Compared with the closely related works, the remarkableness of this paper is that the upper and lower bounds of unknown control coefficients are not required to be known a priori. Motivated by our recent works, by combining the methods of universal control and deadzone with the backstepping technique and skillfully constructing a novel Lyapunov function, we propose a new adaptive tracking control scheme with appropriate design parameters. The new scheme guarantees that the state of the resulting closed‐loop system is globally bounded while the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. Two examples, including a practical example, are given to illustrate the effectiveness of the theoretical results.     

Nonlinear output‐feedback control of torsional vibrations in drilling systems

This paper considers the design of a nonlinear observer‐based output‐feedback controller for oil‐field drill‐string systems aiming to eliminate (torsional) stick–slip oscillations. Such vibrations decrease the performance and reliability of drilling systems and can ultimately lead to system failure. Current industrial controllers regularly fail to eliminate stick–slip vibrations under increasingly challenging operating conditions caused by the tendency towards drilling deeper and inclined wells, where multiple vibrational modes play a role in the occurrence of stick–slip vibrations. As a basis for controller synthesis, a multi‐modal model of the torsional drill‐string dynamics for a real rig is employed, and a bit–rock interaction model with severe velocity‐weakening effect is used. The proposed model‐based controller design methodology consists of a state‐feedback controller and a (nonlinear) observer. Conditions, guaranteeing asymptotic stability of the desired equilibrium, corresponding to nominal drilling operation, are presented. The proposed control strategy has a significant advantage over existing vibration control systems as it can effectively cope with multiple modes of torsional vibration. Case study results using the proposed control strategy show that stick–slip oscillations can indeed be eliminated in realistic drilling scenarios in which industrial controllers fail to do so. Moreover, key robustness aspects of the control system involving the robustness against uncertainties in the bit–rock interaction and changing operational conditions are evidenced. Copyright © 2017 John Wiley & Sons, Ltd.     

Distributed output‐feedback finite‐time tracking control of nonaffine nonlinear leader‐follower multiagent systems

The distributed output‐feedback tracking control for a class of networked multiagents in nonaffine pure‐feedback form is investigated in this article. By introducing a low‐pass filter and some auxiliary variables, we first transform the nonaffine system into the affine form. Then, the finite‐time observer is designed to estimate the states of the newly derived affine system. By applying the fraction dynamic surface control approach and the neural network‐based approximation technique, the distributed output‐feedback control laws are proposed and it is proved that the tracking errors converge to an arbitrarily small bound around zero in finite time. Finally, some simulation examples are provided to confirm the effectiveness of the developed method.     

Output‐feedback stabilization for planar output‐constrained switched nonlinear systems

In this paper, globally asymptotical stabilization problem for a class of planar switched nonlinear systems with an output constraint via smooth output feedback is investigated. To prevent output constraint violation, a common tangent‐type barrier Lyapunov function (tan‐BLF) is developed. Adding a power integrator approach (APIA) is revamped to systematically design state‐feedback stabilizing control laws incorporating the common tan‐BLF. Then, based on the designed state‐feedback controllers and a constructed common nonlinear observer, smooth output‐feedback controllers, which can make the system output meet the predefined constraint during operation, are proposed to deal with the globally asymptotical stabilization problem of planar switched nonlinear systems under arbitrary switchings. A numerical example is employed to verify the proposed method.     

On static output‐feedback stabilization for multi‐input multi‐output positive systems

This paper revisits the static output‐feedback stabilization problem for positive systems. We first point out that for a class of positive systems whose output matrix has a particular row echelon form, this problem can be completely solved via linear programming. By duality, the result is also valid when the column echelon form of the input matrix has a particular structure. Along this line, by augmenting the output matrix as well as the feedback gain matrix, an iterative convex optimization algorithm is developed for the more general case. Finally, we show that the proposed method has advantages over existing works via several numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Global finite‐time stabilization via time‐varying output‐feedback for uncertain nonlinear systems with unknown growth rate

This paper considers the global finite‐time output‐feedback stabilization for a class of uncertain nonlinear systems. Comparing with the existing related literature, two essential obstacles exist: On the one hand, the systems in question allow serious parametric unknowns and serious time variations coupling to the unmeasurable states, which is reflected in that the systems have the unmeasurable states dependent growth with the rate being an unknown constant multiplying a known continuous function of time. On the other hand, the systems possess remarkably inherent nonlinearities, whose growth allows to be not only low‐order but especially high‐order with respect to the unmeasurable states. To effectively cope with these obstacles, we established a time‐varying output‐feedback strategy to achieve the finite‐time stabilization for the systems under investigation. First, a time‐varying state‐feedback controller is constructed by adding an integrator method, and by homogeneous domination approach, a time‐varying reduced‐order observer is designed to precisely rebuild the unmeasurable states. Then, by certainty equivalence principle, a desired time‐varying output‐feedback controller is constructed for the systems. It is shown that, as long as the involved time‐varying gain is chosen fast enough to overtake the serious parametric unknowns and the serious time variations, the output‐feedback controller renders that the closed‐loop system states converge to zero in finite time. Copyright © 2017 John Wiley & Sons, Ltd.     

An optimal approach to output‐feedback robust model predictive control of LPV systems with disturbances

An observer‐based output feedback predictive control approach is proposed for linear parameter varying systems with norm‐bounded external disturbances. Sufficient and necessary robust positively invariant set conditions of the state estimation error are developed to determine the minimal ellipsoidal robust positively invariant set and observer gain through offline computation. The quadratic upper bound of state estimation error is updated and included in an ‐type cost function of predictive control to optimize transient output feedback control performance. Recursive feasibility of the dynamic convex optimization problem is guaranteed in the proposed predictive control strategy. With the input‐to‐state stable observer, the closed‐loop control system states are steered into a bounded set. Simulation results are given to demonstrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive output‐feedback Lyapunov‐based model predictive control of nonlinear process systems

This work addresses the problem of output feedack control of nonlinear uncertain systems via adaptive Lyapunov‐based model predictive control design. To this end, at every control implementation, a moving horizon mechanism is first utilized to generate current estimates of the uncertainty and states. The model with the current estimated uncertainty is then used in a Lyapunov‐based model predictive controller to achieve uncertainty rejection. The key ideas are explained through an illustrative example and the application demonstrated on a networked reactor‐separator process subject to measurement noise and uncertainty.