Observer‐based decentralized adaptive control for large‐scale pure‐feedback systems with unknown time‐delayed nonlinear interactions

This paper presents an approximation design for a decentralized adaptive output‐feedback control of large‐scale pure‐feedback nonlinear systems with unknown time‐varying delayed interconnections. The interaction terms are bounded by unknown nonlinear bounding functions including unmeasurable state variables of subsystems. These bounding functions together with the algebraic loop problem of virtual and actual control inputs in the pure‐feedback form make the output‐feedback controller design difficult and challenging. To overcome the design difficulties, the observer‐based dynamic surface memoryless local controller for each subsystem is designed using appropriate Lyapunov‐Krasovskii functionals, the function approximation technique based on neural networks, and the additional first‐order low‐pass filter for the actual control input. It is shown that all signals in the total controlled closed‐loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, simulation examples are provided to illustrate the effectiveness of the proposed decentralized control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal controller location in wireless networked control systems

The control performance of wireless networked control systems (WNCS) has been shown to heavily depend on the packet delivery quality of both the sensor‐to‐controller and controller‐to‐actuator communications. Such quality relies on the relative distance between the wireless transmitter and receiver, which naturally raises the challenging problem of controller placement in WNCS for optimal control performance. In this paper, we investigate the optimal controller location (OCL) problem in WNCS based on linear‐quadratic‐Gaussian control strategy. For the one‐hop network case where the controller can only be placed at either the sensor side or the actuator side, we derive a simple yet effective criterion to determine the OCL. For the more general multi‐hop case where the controller can be located at either one of the sensors, relays, or actuators, we obtain the necessary and sufficient condition under which the closed‐loop system is guaranteed to be stable. On the basis of these results, we further transform the OCL problem into an optimization problem that can be solved efficiently. Numerical results are provided to verify our analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust linear parameter‐varying control of induction motors

The paper deals with the motion control of an induction motor. Because the nonlinear state equations describing the dynamics of such a machine can be embedded into a linear model with the rotor speed ω as a varying parameter, advantage is taken of some recent results on the control of linear parameter‐varying systems, thus ensuring stability independently of how the varying parameter changes in time within a compact set. The adopted control structure consists of a fast inner electric loop that controls the stator currents and an outer mechanical loop that generates the torque acting on the motor shaft. Of crucial importance is the design of the internal model controller for the current loop. In particular, it is proved that an algebraically equivalent electric motor model admits a Lyapunov function that, together with its Lyapunov derivative, is independent of ω and of all motor parameters. This result allows us to find an upper bound on the norm of the Youla–Kucera parameter that ensures robust stability against speed measurement errors. Simulations carried out on a benchmark motor model show that the adopted control strategy performs well. Copyright © 2014 John Wiley & Sons, Ltd.     

Informative conditions for a data set in a MIMO closed‐loop system with a switching controller

In system identification, a data set needs to be informativeto ensure that the identification criterion has a unique global minimum asymptotically, and the parameter estimation is consistent. To guarantee a data set in a MIMO closed‐loop system with a switching controller to be informative, we develop a group of flexible conditions for the controller's switching rule and feedback laws, which provide a trade‐off between these two aspects through adjustable parameters. Compared with the results in the existing literature, our result includes all kinds of switching rules and therefore is not limited by the constraints on the switching rule.Copyright © 2014 John Wiley & Sons, Ltd.     

Observer based repetitive learning control for a class of nonlinear systems with non‐parametric uncertainties

In this paper, a repetitive learning control (RLC) scheme is developed for a class of nonlinear systems to handle an output tracking problem, where two state observers are introduced concurrently to estimate the unavailable control system and reference states information. The estimation of reference state information is because of the lack of reference internal model in the RLC design. By virtue of the periodicity of reference signals and the associated learning capability in control mechanism, the involved unstructured nonlinear uncertainties can be handled. The Lyapunov‐like energy function method is adopted to facilitate the learning control design as well as property analysis thus achieve the asymptotical convergence of errors in state observation and output tracking simultaneously. Moreover, owing to the robustification of the learning controller that is addressed by incorporating projection, the proposed control scheme would be applicable in practice. In the end, an illustrative example is simulated to demonstrate the efficacy of the proposed RLC law. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐time H ∞ control for discrete‐time switched nonlinear systems with time delay

In this paper, the problem of finite‐time H _∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept of H _∞ finite‐time boundedness is first introduced for discrete‐time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay‐dependent sufficient conditions are derived to guarantee the H _∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐time H _∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐time H _∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water‐quality control system are provided to demonstrate the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.     

Connectivity maintenance and distributed tracking for double‐integrator agents with bounded potential functions

In this paper, we develop a set of decentralized control laws with bounded potential functions. The basic control law is a combination of attractive, repulsive, and alignment forces, which can keep connectivity, avoid collision, synchronize all agents, and further track a constant moving leader. Furthermore, we investigate the distributed tracking problem with a varying‐velocity leader, where the acceleration of the leader can not be measured. Two cases are considered; the acceleration of the leader is bounded, and the acceleration function satisfies Lipschitz condition. In the first case, the relative velocities of neighbors are integrated and transmitted as a new variable to account for the uncertain time‐varying acceleration. In the second case, two distributed estimators are added for the leader's position and velocity. Finally, some simulations are presented to show the effectiveness of the proposed algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

A limit set stabilization by means of the Port Hamiltonian system approach

A solution to the stabilization problem of a compact set by means of the Interconnection and Damping Assignment Passivity‐Based Control methodology, for an affine nonlinear system, was introduced. To this end, we expressed the closed‐loop system as a Port Hamiltonian system, having the property of almost all their trajectories asymptotically converge to a convenient limit set, except for a set of measure zero. It was carried out by solving a partial differential equation (PDE) or single matching condition, which allows the desired energy level or limit set E to be shaped explicitly. The control strategy was tested using the magnetic beam balance system and the pendulum actuated by a direct current motor (DC‐motor), having obtained satisfactory results. Copyright © 2014 John Wiley & Sons, Ltd.     

Consensus of heterogeneous first‐ and second‐order multi‐agent systems with directed communication topologies

In this paper, we consider the consensus problem for heterogeneous multi‐agent systems composed of some first‐order and some second‐order dynamic agents in directed communication graphs. Consensus protocols are proposed for the second‐ and first‐order dynamic agents, respectively. Under certain assumptions on the control parameters, for fixed communication topologies, necessary and sufficient conditions for consensus are given, and the consensus values of all agents are established. For switching topologies, sufficient conditions are given for all agents to reach consensus. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Less conservative stability criteria for linear systems with interval time‐varying delays

The problem of the stability of a linear system with an interval time‐varying delay is investigated. A new Lyapunov–Krasovskii functional that fully uses information about the lower bound of the time‐varying delay is constructed to derive new stability criteria. It is proved that the proposed Lyapunov–Krasovskii functional can lead to less conservative results than some existing ones. Based on the proposed Lyapunov–Krasovskii functional, two stability conditions are developed using two different methods to estimate Lyapunov–Krasovskii functional's derivative. Two numerical examples are given to illustrate that the two stability conditions are complementary and yield a larger maximum upper bound of the time‐varying delay than some existing results. Copyright © 2013 John Wiley & Sons, Ltd.