Reliable decentralized stabilization of linear systems

Reliable stabilization of linear time-invariant multi-input/multi-output plants is considered using a two-channel decentralized controller configuration. Necessary and sufficient conditions are obtained for existence of reliable controllers that maintain stability under the possible failure of either one of the two controllers. All decentralized controllers that achieve reliable stabilization are characterized     

Reliable stabilization with integral action in decentralized control systems

Reliable stabilization with integral action is studied in a linear, time-invariant, multi-input, multi-output, two-channel decentralized control system, where the plant is stable. The objective is to achieve closed-loop stability when both controllers act together and when each controller acts alone. Necessary and sufficient conditions are obtained for existence of block-diagonal decentralized controllers that ensure reliable stabilization, and integral action and all such decentralized controllers are parametrized. Explicit controller design approaches are discussed for the case of square channels.     

Control and stabilization of decentralized systems

The control and stabilization of decentralized systems attracted a great deal of attention in the late 1970s and 1980s, in part because the microprocessor revolution made it feasible to envision the control of large, complex systems. Most of the stability research undertaken during this era was analytic, focusing for example on various interpretations of weak or strong coupling between subsystems, the existence of multiple time-scales, etc. Motivated by the so-called ‘twin-lift’ problem, a problem of stabilizing the motion of two helicopters manoeuvring a single load, we develop a methodology for stabilizing classes of decentralized systems based on a more algebraic approach involving the external symmetries of decentralized systems. The study of the symmetry algebra of classes of such systems was initiated by Hazewinkel and Martin and in this language, we derive stabilizing, local feedback laws for any class of decentralized systems having a semi-simple algebra of symmetries. The twin-lift problem as well as certain problems involving stabilization of discretizations of distributed parameter problems have semi-simple algebras of symmetries.     

Universal stabilization of feedforward nonlinear systems

In recent years, many important results on global stabilization of feedforward nonlinear systems have been proposed. However, in all previous results, to develop a global stabilizer, one must know some a priori information on system nonlinearities. For example, it is required that the system nonlinearities be known, or be bounded by known functions, or be linearly parametrized, or satisfy some high order growth rate condition, etc. The contribution of this paper is proposing a universal global stabilizer design for a class of feedforward systems, which does not require a priori knowledge of system nonlinearities.     

On decentralized stabilization of interconnected systems

A decentralized control scheme is proposed for stabilization of interconnected systems consisting of arbitrarily connected, linear, time-invariant multivariable subsystems. Sufficient conditions are given for an interconnected system to be stabilized using only local state feedback. The obtained results are illustrated by an example.     

Reliable decentralized stabilization via extended linear matrix inequalities and constrained dissipativity

This paper considers the problem of reliable decentralized stabilization with multicontroller configurations when some of the controllers are faulty in the sense that they fail to act optimally or do not function in the way that they were originally intended to function. Specifically, we introduce a solution concept that requires controllers to respond optimally (i.e. in the sense of best‐response correspondences) to the nonfaulty controllers regardless of the identity or actions of the faulty controllers. At any time, we assume that the nonfaulty controllers know only that there can be at most one faulty controller in the system, but they know neither the identity of the faulty controller nor how this faulty controller behaves. We present a design framework using an extended linear matrix inequality technique for deriving reliable stabilizing state‐feedback gains; whereas a set of filters whose estimation‐error dynamics satisfy certain quadratic integral constraints is used as decentralized observers within the subsystems for extending the result to the output‐feedback case. Moreover, a sufficient condition for solvability of the problem is provided in terms of the minimum‐phase condition of the subsystems. We also present an application of the results to a power system problem. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive stabilization of time-delay feedforward nonlinear systems

In this paper, we consider the adaptive stabilization problem for feedforward nonlinear systems with time delays. An adaptive stabilizer is proposed. Our stabilizer takes a nested saturation feedback, and a set of switching logics is designed to tune online the saturation levels in a piecewise constant or switching manner. It has been shown that under our proposed control, all closed-loop states are bounded and asymptotic regulation is achieved.     

On the stabilization of decentralized control systems

This paper considers the problem of stabilizing a linear time-invariant multivariable system by using several local feedback control laws. Each local feedback control law depends only on partial system outputs. A necessary and sufficient condition for the existence of local control laws with dynamic compensation to stabilize a given system is derived. This condition is stated in terms of a new notion, called "fixed modes," which is a natural generalization of the well-known concept of uncontrollable modes and unobservable modes that occur in centralized control system problems. A procedure that constructs a set of stabilizing feedback control laws is given.     

Pseudo-decentralized adaptive stabilization of large-scale feedforward nonlinear systems

In this paper, we propose a pseudo-decentralized adaptive control scheme for a class of large-scale feedforward nonlinear systems with unknown nonlinear effects within subsystems and unknown nonlinear interactions among subsystems. The local controller of each subsystem takes a nested saturation feedback, using the state of its own subsystem, and the saturation levels are tuned online in a switching manner via a set of switching logics, which requires some binary flag communication among subsystems. Global asymptotic regulation of the closed-loop states is achieved.     

Global robust stabilization of feedforward systems with uncertainties

This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive design is developed for constructing a nested saturation control law. At each recursion, two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium point, respectively.     

Robust decentralized stabilization of uncertain large-scale discrete-time systems

This article describes the synthesis of robust decentralized controllers for large-scale discrete-time systems with uncertainties. Based on the Lyapunov method, a sufficient condition for robust stability is derived in terms of a linear matrix inequality (LMI). The solutions of the LMI can be easily obtained using efficient convex optimization techniques. A numerical example is given to illustrate the proposed method.     

Optimal stabilization of linear systems via decentralized outputfeedback

Presents an approach to the optimal stabilization of a linear time-invariant system via decentralized control. The class of controllers considered does not restrict the controller to be finite dimensional or time invariant. In fact, the controller structure proposed can be regarded as a form of time varying sampled data control. The main result of the paper presents a scheme for constructing a collection of decentralized controllers which stabilizes the system and is optimal with respect to a quadratic performance index     

On stabilization of decentralized dynamic output feedback systems

A dynamic output feedback law is presented for large scale interconnected systems. If the coupling terms between the subsystems are neglected, the control scheme can be interpreted as decentralized reconstruction of the state variables from the output of the subsystems. A class of systems stabilizable by decentralized state feedback is investigated. A sufficient condition is determined for systems to be stabilizable with local state feedback and reconstruction with observers of full order. The resulting closed-loop systems are connectively stable. Moreover, any prescribed degree of stability can be achieved and the closed-loop systems are robust with respect to bounded nonlinearities in the couplings between the subsystems.     

Practical stabilization of robotic systems by decentralized control

The practical stability of large-scale robotic systems with variable parameters is considered. The control should ensure the system state to belong to a finite region around the nominal trajectory for various values of parameters. The robotic system is considered as a set of decoupled subsystems each of which corresponds to one degree of freedom. For each decoupled subsystem a local controller is synthesized ensuring the practical stability of free subsystem. Then the practical stability of the coupled global system is analysed for various values of mechanical parameters. This permits the synthesis of decentralized control which provides practical stabilization of robotic systems in given finite regions and for the given set of allowable parameter values. Global control is also introduced. Decentralized control for a manipulation robot with variable payload is synthesized.     

Decentralized robust stabilization for large-scale feedforward non-linear systems

In this paper, we consider the decentralized robust stabilization problem for large-scale feedforward non-linear systems, which possess an upper-triangular structure, while in the decentralized control area the commonly studied large-scale feedback non-linear systems possess a lower-triangular structure. Our decentralized robust stabilizer for each subsystem takes a nested saturation feedback, with the saturation levels satisfying a set of equations and inequalities. Global asymptotic stability of the closed-loop large-scale system has been proved, and a simulation example is given.     

n-bit stabilization of n-dimensional nonlinear systems in feedforward form

A methodology is presented which allows to design encoder, decoder and controller for stabilizing a nonlinear system in feedforward form using saturated encoded state feedback basically under standard assumption, namely local Lipschitz property of the vector field defining the system. n (respectively, n + 1) bits are used to encode the state information needed to the purpose of semiglobally (globally) stabilizing an n-dimensional system. Minimality of the data rate is discussed.     

On the stabilization of feedforward systems with bounded control

For the global asymptotic stabilization of nonlinear—controllable in the first approximation—cascades consisting of a globally asymptotically—locally exponentially stable system driving a stable system, a Lyapunov-like design is proposed. This yields (bounded) control laws, where the control magnitude can be chosen arbitrarily large. This result provides an alternative to classical forwarding.     

On decentralized stabilization and structure of linear large scale systems

Connective stabilizability of large-scale systems, which are composed of interconnected subsystems, is considered using decentralized feedback. Both analytical and graph-theoretic conditions are derived directly in terms of the interconnection structure, which ensure that stability of the overall closed-loop system is invariant under the structural perturbations caused by disconnections and reconnections of links among the subsystems. The conditions characterize a large class of decentrally stabilizable systems, which includes all classes of connectively stabilizable interconnected systems considered so far.     

Feedback stabilization for high order feedforward nonlinear time-delay systems

This paper investigates the problem of global strong stabilization by state feedback, for a family of high order feedforward nonlinear time-delay systems. The uncertain nonlinearities are assumed to satisfy a polynomial growth assumption with an input or delayed input dependent rate. With the help of the appropriate Lyapunov–Krasovskii functionals, and a rescaling transformation with a gain to be tuned online by a dynamic equation, we propose a dynamic low gain state feedback control scheme. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.