Problem Of Output Feedback Stabilization Research Articles

Output Feedback Stabilization of Networked Control Systems with Random Delays

AbstractThis paper is concerned with the output feedback stabilization problem of networked control systems (NCSs) with random communication delays. Mean-square stability is derived for the closed-loop NCSs. Based on this, the one-mode-dependent output feedback controller is designed, and the explicit expressions of the controller gains are obtained in terms of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness and applicability of the proposed results.

Output-Feedback Stabilization of Stochastic High-Order Nonlinear Systems under Weaker Conditions

Under the weaker conditions on the power order and the nonlinear functions, this paper investigates the output-feedback stabilization problem for a class of stochastic high-order nonlinear systems. Based on the backstepping design method and homogeneous domination technique, the closed-loop system can be proved to be globally asymptotically stable in probability.

Global Output Feedback Stabilization of a Chemostat With an Arbitrary Number of Species

This technical note studies the global output feedback stabilization problem for a chemostat with an arbitrary number of species competing for a single nutrient source. It is shown that coexistence can be achieved by means of a feedback control of the substrate input concentration and an appropriate choice of a constant dilution rate. The input substrate feedback controller proposed is a dynamic time-varying output feedback, with the substrate concentration considered as the output. The result relies on the construction of a novel nonlinear observer and is established via a Lyapunov-based proof.

Stabilization for state/input delay systems via static and integral output feedback

This paper addresses the static and integral output feedback stabilization problems of continuous-time linear systems with an unknown state/input delay. By combining an augmentation approach and the delay partitioning technique, criteria for static and integral output feedback stabilizability are proposed in terms of nonlinear matrix inequalities with a free parameter matrix introduced. These new characterizations possess a special structure, which leads to linearized iterative computation. The effectiveness and merits of the proposed approach are shown through numerical examples.

Remarks on output feedback stabilization of two-species chemostat models

We consider a class of output feedback stabilization problems for chemostats with two species. We design dilution rate feedbacks that stabilize a componentwise positive equilibrium. Our feedbacks only depend on the sum of the species levels. The novelty of our treatment is in our dropping the usual condition on the relative sizes of the growth yield constants.

Stabilization of a chemostat model with Haldane growth functions and a delay in the measurements

The stabilization of equilibria in chemostats with measurement delays is a complex and challenging problem, and is of significant ongoing interest in bioengineering and population dynamics. In this paper, we solve an output feedback stabilization problem for chemostat models having two species, one limiting substrate, and either Haldane or Monod growth functions. Our feedback stabilizers depend on a given linear combination of the species concentrations, which are both measured with a constant time delay. The values of the delays are unknown. Instead, one only knows an upper bound on the delays, and we allow the upper bound to be arbitrarily large. The stabilizing feedback depends on the known upper bound for the delays as well. Our work is based on a Lyapunov–Krasovskii argument.

Linear matrix inequality approach to static output-feedback stabilisation of discrete-time networked control systems

This study is concerned with the static output-feedback stabilisation problem of discrete-time networked control systems. If the controlled plant is a discrete-time system, the networked control system with time-varying network-induced delays and data packet dropouts in the transmission is modelled as a discrete-time system with time-varying delays in the state. The network-induced delays are assumed to have both an upper bound and a lower bound. Next, an asymptotic stability condition for the networked control systems is established, which depends on the upper and lower bounds of delay times. Then, three approaches to the static output-feedback controller are proposed, where the effect of both network-induced delays and data packet dropouts has been considered. Furthermore, the robust stability condition and controller design method for such networked control systems with structured uncertainties are presented. All the results are formulated in the terms of linear matrix inequalities (LMIs), which are numerically very efficiently solved via LMI toolbox in the Matlab. Finally, three examples are worked out to illustrate the feasibility and effectiveness of the proposed method.

Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach

This paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical examples.

Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable

This brief paper investigates the problem of output-feedback stabilization for a class of high-order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input. Based on the ideas of the homogeneous systems theory and the adding a power integrator technique, an output-feedback controller is constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable (GAS) in probability. The efficiency of the output-feedback controller is demonstrated by a simulation example.

Observer and output feedback stabilisation for a class of nonlinear systems

The objective of the work is twofold. First, we investigate the problem of observer design for a class of systems in cascade form. We suppose that an observer exists for each subsystem and then prove that this interconnection is an observer for the overall system. One of both nonlinear functions is assumed to be not Lipschitz (e.g. to satisfy a quadratic constraint on the unmeasured part of the state). This first main result may be viewed as an improvement of Besançon and Hammouri (Besançon, G., and Hammouri, H. (1998), ‘On Observers Design for Interconnected Systems’, Journal of Mathematical Systems, Estimation and Control, 8, 377–380) in which the authors discussed the problem of the synthesis of interconnected observers. The second part is a generalisation of Ammar, Mabrouk, and Vivalda (Ammar, S., Mabrouk, M., and Vivalda, J.-C. (2009), ‘Observer and Global Output Feedback Stabilisation for Some mechanical Systems’, International Journal of Control, 82, 1070–1081) in which the authors study the problem of output feedback stabilisation for a class of Euler–Lagrange systems. The problem of global output feedback stabilisation of the practical system called the two-link manipulator system is solved. The output feedback scheme presented has better performance than the one exhibited in Ammar et al. (2009).

Output-feedback control of a class of high-order stochastic nonlinear systems

This article investigates the problem of output-feedback stabilisation for a class of high-order stochastic non-linear systems in which the diffusion terms depend on unmeasurable states besides the output. By introducing a new rescaling transformation, adopting an effective observer and choosing the appropriate Lyapunov function, an output-feedback controller is constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, the output can be regulated to the origin almost surely, and the problem of inverse optimal stabilisation in probability is solved. The efficiency of the output-feedback controller is demonstrated by several simulation examples.

Output feedback stabilisation of networked control systems via switched system approach

Output feedback stabilisation problem of networked control systems with bounded packet loss is addressed. Sufficient conditions for output feedback stabilisation are derived by using a packet-loss-dependent Lyapunov function. Different from existing results, we present a design for packet-loss-dependent output feedback controllers for two types of packet-loss processes: one is a arbitrary packet-loss process, and the other is a Markovian packet-loss process. Several numerical examples and simulations are worked out to demonstrate the effectiveness of the proposed design techniques.

Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems

In this paper, the adaptive neural network output-feedback stabilization problem is investigated for a class of stochastic nonlinear strict-feedback systems. The nonlinear terms, which only depend on the system output, are assumed to be completely unknown, and only an NN is employed to compensate for all unknown upper bounding functions, so that the designed controller is more simple than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the closed-loop system can be proved to be asymptotically stable in probability. The simulation results demonstrate the effectiveness of the proposed control scheme.

Observer and global output feedback stabilisation for some mechanical systems

The objective of the work is two-fold. A first part is devoted to the problem of constructing an observer to the practical system called overhead crane with the position as output. In a second part, the problem of global output feedback stabilisation is solved for a class of Euler–Lagrange systems when the variables of velocity are the unmeasured part of the state. The equations of these systems are non-linear with respect to the velocities. A new output feedback control scheme is proposed. It relies on the determination of a change of coordinates which gives to the systems a triangular form. To illustrate the approach, it is applied to a two-link manipulator.

On the Practical Output Feedback Stabilization for Nonlinear Uncertain Systems

In this paper, we treat the problem of output feedback stabilization of nonlinear uncertain systems. We propose an output feedback controller that guarantees global uniform practical stability of the closed loop system.

Spectral radius minimization for optimal average consensus and output feedback stabilization

In this paper, we consider two problems which can be posed as spectral radius minimization problems. Firstly, we consider the fastest average agreement problem on multi-agent networks adopting a linear information exchange protocol. Mathematically, this problem can be cast as finding an optimal W ∈ R n × n such that x ( k + 1 ) = W x ( k ) , W 1 = 1 , 1 T W = 1 T and W ∈ S ( E ) . Here, x ( k ) ∈ R n is the value possessed by the agents at the k th time step, 1 ∈ R n is an all-one vector and S ( E ) is the set of real matrices in R n × n with zeros at the same positions specified by a network graph G ( V , E ) , where V is the set of agents and E is the set of communication links between agents. The optimal W is such that the spectral radius ρ ( W − 1 1 T / n ) is minimized. To this end, we consider two numerical solution schemes: one using the q th-order spectral norm (2-norm) minimization ( q -SNM) and the other gradient sampling (GS), inspired by the methods proposed in [Burke, J., Lewis, A., & Overton, M. (2002). Two numerical methods for optimizing matrix stability. Linear Algebra and its Applications, 351–352, 117–145; Xiao, L., & Boyd, S. (2004). Fast linear iterations for distributed averaging. Systems & Control Letters, 53(1), 65–78]. In this context, we theoretically show that when E is symmetric, i.e. no information flow from the i th to the j th agent implies no information flow from the j th to the i th agent, the solution W s ( 1 ) from the 1-SNM method can be chosen to be symmetric and W s ( 1 ) is a local minimum of the function ρ ( W − 1 1 T / n ) . Numerically, we show that the q -SNM method performs much better than the GS method when E is not symmetric. Secondly, we consider the famous static output feedback stabilization problem, which is considered to be a hard problem (some think NP-hard): for a given linear system ( A , B , C ) , find a stabilizing control gain K such that all the real parts of the eigenvalues of A + B K C are strictly negative. In spite of its computational complexity, we show numerically that q -SNM successfully yields stabilizing controllers for several benchmark problems with little effort.

Nonlinear Control of the Viscous Burgers Equation: Trajectory Generation, Tracking, and Observer Design

In a companion paper we have solved the basic problem of full-state stabilization of unstable “shock-like” equilibrium profiles of the viscous Burgers equation with actuation at the boundaries. In this paper we consider several advanced problems for this nonlinear partial differential equation (PDE) system. We start with the problems of trajectory generation and tracking. Our algorithm is applicable to a large class of functions of time as reference trajectories of the boundary output, though we focus in more detail on the special case of sinusoidal references. Since the Burgers equation is not globally controllable, the reference amplitudes cannot be arbitrarily large. We provide a sufficient condition that characterizes the allowable amplitudes and frequencies, under which the state trajectory is bounded and tracking is achieved. We then consider the problem of output feedback stabilization. We design a nonlinear observer for the Burgers equation that employs only boundary sensing. We employ its state estimates in an output feedback control law, which we prove to be locally stabilizing. The output feedback law is illustrated with numerical simulations of the closed-loop system.

Sampled-Data Stabilization of a Class of Nonlinear Systems With Application in Robotics

The output feedback stabilization problem for the class of nonlinear Lipschitz systems is considered. A discrete-time feedback controller is designed for the sampled-data case, where the output of the plant is only available at discrete points of time and where the objective is to stabilize the system continuously using a discrete-time controller. We show that exact stabilization in this case can be achieved using a direct sampled-data design approach, based on H∞ optimization theory, in which neither the plant model nor the controller need to be discretized a priori. The proposed design is solvable using commercially available software and is shown to have important advantages over the classical emulation approach that has been used to solve similar problems. The applicability of the proposed techniques in the robotics field is thoroughly discussed from both the modeling and design perspectives.

Some Remarks on Output Feedback Stabilization of SISO Systems with I/O Network-Induced Delays

This note addresses the output feedback stabilization problem for a class of linear SISO systems subject to I/O network delays. More precisely, we are interested in the characterization of the set of delay- and gain-parameters guaranteeing the stability of the closed-loop system. To perform such an analysis, we adopt an eigenvalue perturbation-based approach.

A dual‐observer design for global output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities

AbstractThis paper employs a dual‐observer design to solve the problem of global output feedback stabilization for a class of nonlinear systems whose nonlinearities are bounded by both low‐order and high‐order terms. We show that the dual‐observer comprised of two individual homogeneous observers, can be implemented together to estimate low‐order and high‐order states in parallel. The proposed dual observer, together with a state feedback controller, which has both low‐order and high‐order terms, will lead to a new result combining and generalizing two recent results (Li J, Qian C. Proceedings of the 2005 IEEE Conference on Decision and Control, 2005; 2652–2657) and (Qian C. Proceedings of the 2005 American Control Conference, June 2005; 4708–4715). Copyright © 2008 John Wiley & Sons, Ltd.