Search

This paper investigates the decentralized linear quadratic optimization and stabilization problem for Itô systems, where the system's controller has two parts: the deterministic and random parts. Unlike previous works, with positive semi-definite weighting matrices, finite-horizon optimization and infinite-horizon stabilization problems are considered. The chief challenge lies in solving the forward and backward stochastic differential equations and selecting the Lyapunov function. The relationship between the forward and backward processes is established using a modified version of the four-step scheme combined with the information pattern of the problem. The equivalent condition for the optimization problem is obtained based on the Riccati differential equation. Besides, the necessary and sufficient conditions for the stabilization problem are presented using the Lyapunov function defined by the optimal cost function. Finally, numerical examples illustrate the validity of the presented strategies. [ABSTRACT FROM AUTHOR]

Most research on control of nonlinear systems using backstepping concentrates on construction of feedback controllers to achieve stability and/or steady-state tracking performance. Little research considers systematic methods for tuning nonlinear feedback controllers to guarantee the transient performance. This paper investigates how parameters of a backstepping controller can be determined to achieve the predefined settling time and overshoot, which are basic criteria for the transient performance. First, some modifications are made for the backstepping design method by introducing more parameters so that there are more degrees of freedom for parameter tuning. Second, the pole-placement method is used for the linear part of the closed-loop system corresponding to a backstepping controller. Third, an objective function is defined by summing the square of errors between the corresponding coefficients of the desired and real characteristic polynomials. Fourth, constraints are introduced to guarantee the negative semi-definiteness of the time derivative of the Lyapunov function. Fifth, the controller parameters can be found by minimizing the objective function. Finally, simulation and experimental results show that, compared with the existing method, the proposed method is more effective and efficient for fine tuning backstepping controllers. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization of an uncertain wave equation which describes the vibration dynamics of a flexible string. All the system parameters are unknown while the disturbance with unknown bound and period is allowed which lead to more serious uncertainties than the related literature, and hence result into the incapability of the traditional schemes. To solve the control problem, a novel condition-based adaptive control framework is developed in the paper. Specifically, as preparation for the adaptive control design, a state-feedback controller is first designed under the assumption that all the system parameters are known. Then, an adaptive controller, together with two continuous adaptive laws and a condition-based updating mechanism for the online tuning of the controller parameters, is proposed for the original uncertain system. Finally, it is proven that the updating of controller parameters under the proposed condition-based updating mechanism stops at a finite time instant, then the proposed controller guarantees the stability of the resulting closed-loop system. The proposed theoretical results are validated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper addresses the semi-global stabilization problem of linear systems with simultaneous presence of distributed infinite input delays and actuator saturations. Two low gain controllers are proposed, respectively, for two classes of linear systems with both infinite input delays and actuator saturations. It is shown that under our first controller, the semi-global stabilization problem can be solved for the first class of systems where all eigenvalues of the open loop system have no positive real parts. It is also shown that under our second controller, which is much simpler, the semi-global stabilization problem can be solved for the second class of systems where all eigenvalues of the open loop system are zero. Another contribution of this paper is that the bounds for the peak magnitude of the control signals can be explicitly given. Furthermore, our results include relevant results on bounded distributed delays and constant delays as their special cases. Simulation examples are finally provided to illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the sampled-data control for a class of linear time-varying system. A classic Halanay inequality is first extended to the time-varying sampled-data system. Then based on the comparison principle and the extended Halanay inequality, new criteria for globally uniformly exponential stability and globally uniformly asymptotic stability of the corresponding closed-loop system are derived. Furthermore, an algorithm is presented to solve the gain synthesis problem. Finally, one example is given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the stability, stabilization and L 1 -gain of linear periodic piecewise positive systems. The monotonicity of linear periodic piecewise positive systems is first studied. Then a time-varying co-positive Lyapunov function for periodic piecewise positive systems is employed and a sufficient condition for the asymptotic stability of the system is established. Based on the provided co-positive Lyapunov function and the sufficient stability condition, a state-feedback periodic piecewise controller to stabilize the system is formed and an upper bound of L 1 -gain of the system is given. Finally, numerical examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract We consider in this paper three different partial differential equations (PDEs) that can be exponentially stabilized using backstepping controllers. For implementation, a finite-dimensional controller is generally needed. The backstepping controllers are approximated and it is proven that the finite-dimensional approximated controller stabilizes the original system if the order is high enough. This approach is known as late-lumping. The other approach to controller design for PDEs first approximates the PDE and then a controller is designed; this is known as early-lumping. Simulation results comparing the performance of late-lumping and early-lumping controllers are provided. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the problems of optimal control and stabilization for networked control systems (NCSs), where the remote controller and the local controller operate the linear plant simultaneously. The main contributions are two-fold. Firstly, a necessary and sufficient condition for the finite horizon optimal control problem is given in terms of the two Riccati equations. Secondly, it is shown that the system without the additive noise is stabilizable in the mean square sense if and only if the two algebraic Riccati equations admit the unique solutions, and a sufficient condition is given for the boundedness in the mean square sense of the system with the additive noise. Numerical examples about unmanned aerial vehicles model are shown to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents limitations of energy signal-to-noise ratio (SNR) in control of discrete-time linear systems over noisy channels with and without feedback. The minimum SNR required for stabilization is shown to be the modulus of the product of unstable poles of the plants. Two types of optimal control laws that achieve this minimum are constructed based on the gains for expensive control, that is, LQ optimal control without input weight. It is observed that channel feedback does not improve the SNR limitation, which means feedback for control is efficient enough for communication. [ABSTRACT FROM AUTHOR]

In this paper, the stabilization problem is investigated for a class of linear discrete-time systems in a resource-constrained network environment where only the data with finite bits is permitted to transmit. The data transmissions from the sensors to the controller are subject to random packet dropouts. To improve the reliability of the data transmission, a novel dynamical multiple description coding scheme is developed with guaranteed convergence of the decoding error. By recurring to the matrix inequality theory and the stochastic analysis technique, sufficient conditions are established to ensure the stochastic stability of the closed-loop system. Furthermore, a parametric relationship is discovered that characterizes the influences from the packet-dropout probabilities and the encoder parameters on the stability of the closed-loop system. Finally, a numerical example is provided to illustrate the validity of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Abstract This paper furnishes a new system-theoretic interpretation to the product of unstable poles of discrete-time linear systems. This index has been known to represent limitations of feedback control in various situations. Our result shows that the index gives the limitation of the signal-to-noise ratio (SNR) with respect to amplitude when the feedback loop is stabilized through a multidimensional channel with bounded noise. [ABSTRACT FROM AUTHOR]

The problem of boundary stabilization of thermoacoustic oscillations in the Rijke tube is investigated using the backstepping method; as a first step, this work only considers the full-state design. This system consists of a vertical tube open at both ends and a heater placed in the lower half of the tube. To study this problem we consider that the mathematical model takes the form of 2 × 2 linear first-order hyperbolic partial differential equations (PDEs) with a point source term (induced by the Dirac delta distribution) on the right hand side, plus the coupling of an ordinary differential equation (ODE), and control input at one boundary condition. The presence of the Dirac delta distribution implies that the system solution has a discontinuity on a point of the domain, but is continuous everywhere else. We use a coordinate transformation to rewrite the equations into a system of four transport PDEs convecting in opposite directions and to translate the discontinuity to the boundary conditions. Then, a full state feedback backstepping controller is designed to exponentially stabilize the origin. However, the model is non-strict-feedback making unfeasible the use of standard backstepping designs. This issue is tackled by formulating a well-posed and invertible integral transformation with Volterra and Fredholm terms that maps the Rijke system into a target system with desirable stability properties. An exact piecewise-differentiable expression for the kernels of this transformation is found, allowing us in turn to derive an explicit feedback control law. Simulation results are presented to illustrate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

We detail in this article the development of a delay-robust stabilizing feedback control law for a linear ordinary differential equation coupled with two linear first order hyperbolic equations in the actuation path. The proposed method combines the use of a backstepping approach, required to construct a canceling feedback for the in-domain coupling terms of the PDEs, with a second change of variables that reduces the stabilization problem of the PDE–ODE system to that of a time-delay system for which a predictor can be constructed. The proposed controller can be tuned, with some restrictions imposed by the system structure, either by adjusting a reflection coefficient left on the PDE after the backstepping transformation, or by choosing the pole placement on the ODE when constructing the predictor, enabling a trade-off between convergence rate and delay-robustness. The proposed feedback law is finally proved to be robust to small delays in the actuation. [ABSTRACT FROM AUTHOR]

In this paper, the stability analysis and H ∞ control problems for a class of continuous-time switched systems with a random switching signal are addressed. The dwell time of the switched systems is characterized with a fixed part and a random part. A new stability criterion, which is equivalent to a necessary and sufficient condition developed previously, is established first, and then it is reformulated in terms of linear matrix inequalities. Based on the stability analysis result, L 2 -gain performance analysis and H ∞ control problems are studied. Several numerical examples are given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization problem of linear systems with distributed infinite input delays. By introducing a stability result on systems with infinite delays, it is shown that a stabilizable linear system with distributed infinite input delays can be globally asymptotically stabilized with low gain controllers as long as the open-loop system is not exponentially unstable. Our result includes constant delay and bounded distributed delay as its special cases. It should be noted that the stabilization problem of systems with distributed infinite input delays, to our best knowledge, has not been considered in existing literatures. Simulation examples are provided to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, new conditions of stability and stabilization are proposed for periodic piecewise linear systems. A continuous Lyapunov function is constructed with a time-dependent homogeneous Lyapunov matrix polynomial. The exponential stability problem is studied first using square matricial representation and sum of squares form of homogeneous matrix polynomial. Constraints on the exponential order of each subsystem used in previous work are relaxed. State-feedback controllers with time-varying polynomial controller gain are designed to stabilize an unstable periodic piecewise system. The proposed stabilizing controller can be solved directly and effectively, which is applicable to more general situations than those previously covered. Numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Methods for scattering-based stabilization of interconnections of nonlinear systems are developed for the case where the subsystems are non-planar conic. The notion of non-planar conicity is a generalization of the conicity notion to the case where the cone’s center is a subspace with dimension greater than one. For a feedback interconnection of non-planar conic systems, a graph separation condition for finite-gain L 2 -stability is derived in terms of relationship between the maximal singular value of the product of projection operators onto the subsystems’ central subspaces and the radii of the corresponding cones. Furthermore, a new generalized scattering transformation is developed that allows for rendering the dynamic characteristics of a non-planar conic system into an arbitrary prescribed cone with compatible dimensions. The new scattering transformation is subsequently applied to the problem of stabilization of interconnections of non-planar conic systems, with and without communication delays. Applications of the developed scattering-based stabilization methods to the problems of stable robot–environment interaction and bilateral teleoperation with multiple heterogeneous communication delays are discussed. [ABSTRACT FROM AUTHOR]

A new technique is proposed to construct observers and to achieve output feedback stabilization of a class of continuous-time switched linear systems with a time-varying delay in the output. The delay is a piecewise continuous bounded function of time and no constraint is imposed on the delay derivative. For stability analysis, an extension of a recent trajectory based approach is used; this is fundamentally different from classical Lyapunov function based methods. A stability condition is given in terms of the upper bound on the time-varying delay to ensure global uniform exponential stability of the switched feedback system. The main result applies in cases where some of the subsystems of the switched system are not stabilizable and not detectable. [ABSTRACT FROM AUTHOR]

We consider stabilization of an equilibrium point via infinite horizon discounted optimal control in discrete-time. In addition to applications in economics and social sciences, discounted optimal control is a commonly used numerical technique guaranteeing solvability of certain classes of optimal control problems. In this paper, we present conditions based on strict dissipativity that ensure that the optimally controlled system is asymptotically stable or practically asymptotically stable. These conditions are shown to be complementary to recently proposed conditions based on a detectability property. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability and stabilization issues for a family of discrete-time stochastic switching systems with bounded sojourn time. The stochastic switching systems are modeled by semi-Markov jump linear systems and the semi-Markov kernel approach is employed to handle the stability and stabilization problems. The sojourn time of each system mode is considered to have both upper and lower bounds, which is more general than the scenarios in previous literature that only consider the upper bound of sojourn time. The concept of σ -error mean square stability is put forward in a new form by taking into account the lower bounds of sojourn time for all system modes. By virtue of a Lyapunov function that not only depends on the current system mode but also on the elapsed time the system has been in the current mode, together with certain techniques eliminating powers of matrices, numerically testable stability and stabilization criteria in the sense of the proposed σ -error mean square stability are obtained for the closed-loop stochastic switching system. Finally, a numerical example and a practical example of a DC motor are utilized to demonstrate the effectiveness of the proposed control strategy and the superiority of allowing for the lower bound of sojourn time. [ABSTRACT FROM AUTHOR]

Motivated by the seminal work of Dupire (2009) on functional Itô formulas, this work investigates asymptotic properties of systems represented by stochastic functional differential equations (SFDEs). Stability of general delay-dependent SFDEs is investigated using degenerate Lyapunov functionals, which are only positive semi-definite rather than positive definite as used in the classical work. This paper first establishes boundedness and regularity of SFDEs by using degenerate Lyapunov functionals. Then moment and almost sure exponential stabilities are obtained based on degenerate Lyapunov functionals and the semi-martingale convergence theorem. As an application of the stability criteria, consentability of stochastic multi-agent systems with nonlinear dynamics is studied. [ABSTRACT FROM AUTHOR]

In this paper, we study state-feedback control of Markov jump linear systems with partial information about the mode signal responsible for switching between dynamic modes. We assume that the controller can only access random samples of the mode signal according to a hidden-Markov observation process. Our formulation provides a novel framework to analyze and design feedback control laws for various Markov jump linear systems previously studied in the literature, such as the cases of ( i ) clustered observations, ( ii ) detector-based observations, and ( iii ) periodic observations. We present a procedure to transform the closed-loop system with hidden-Markov observations into a standard Markov jump linear system while preserving stability, H 2 norm, and H ∞ norm. Furthermore, based on this transformation, we propose a set of Linear Matrix Inequalities (LMI) to design feedback control laws for stabilization, H 2 suboptimal control, and H ∞ suboptimal control of discrete-time Markov jump linear systems under hidden-Markov observations of the mode signals. We conclude by illustrating our results with some numerical examples. [ABSTRACT FROM AUTHOR]

We solve the problem of stabilizing a linear ODE having a system of a linearly coupled hyperbolic PDEs in the actuating path. The control design is based on a backstepping approach and yields exponential closed-loop stability of the zero equilibrium. The existence of a Volterra transformation relies on a relatively general well-posedness result for hyperbolic backstepping kernel equations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method, by designing an unknown input type state observer, to stabilize an unstable 1-d heat equation with boundary uncertainty and external disturbance. The state observer is designed in terms of a disturbance estimator. A stabilizing state feedback control is designed for the observer by the backstepping transformation, which is an observer based output feedback stabilizing control for the original system. The well-posedness and stability of the closed-loop system are concluded. The numerical simulations show that the proposed scheme is quite effectively. This is a first result on active disturbance rejection control for a PDE with both boundary uncertainty and external disturbance. [ABSTRACT FROM AUTHOR]

The conditions for existence of solutions and stability, asymptotic and exponential, of a large class of boundary controlled systems on a 1D spatial domain subject to nonlinear dynamic boundary actuation are given. The consideration of such class of control systems is motivated by the use of actuators and sensors with nonlinear behavior in many engineering applications. These nonlinearities are usually associated to large deformations or the use of smart materials such as piezo actuators and memory shape alloys. Including them in the controller model results in passive dynamic controllers with nonlinear potential energy function and/or nonlinear damping forces. First it is shown that under very natural assumptions the solutions of the partial differential equation with the nonlinear dynamic boundary conditions exist globally. Secondly, when energy dissipation is present in the controller, then it globally asymptotically stabilizes the partial differential equation. Finally, it is shown that assuming some additional conditions on the interconnection and on the passivity properties of the controller (consistent with physical applications) global exponential stability of the closed-loop system is achieved. [ABSTRACT FROM AUTHOR]

Based on semi-tensor product of matrices, global robust stability and stabilization of Boolean network (BN) with disturbances are investigated. Firstly, the definition of global robust stability for BN with disturbances is presented. By using the algebraic state space representation of disturbed BN, some necessary and sufficient criteria are obtained to ensure the global robust stability with respect to (w.r.t.) a fixed point or w.r.t. a limit cycle. In contrast, if a given disturbed BN is not globally robust stable w.r.t. a fixed point or w.r.t. a limit cycle, system can achieve stability by a matrix transformation technique. However, it is a difficult task to find such a suitable matrix transformation. In this paper, a pinning state feedback control design is proposed to find a suitable transformation. The obtained results are well illustrated by numerical example. [ABSTRACT FROM AUTHOR]

Robust stabilization of nonlinear systems has been extensively studied subject to both static and dynamic uncertainties. In particular, a class of nonlinear controllers can be explicitly constructed based on recursively applying the small gain theorem. In this paper, we further investigate the so-called robust input-to-output stabilization problem for systems with additional external input (or perturbation, rather than the control input). It aims to explicitly construct a controller such that the system is input-to-output stable (IOS) from the external input to the specified output, moreover, with a specified IOS gain. [ABSTRACT FROM AUTHOR]

This paper studies the stabilization of linear systems with both state and input delays where the input delay can be arbitrarily large yet exactly known. Observer–predictor based controllers are designed to predict the future states so that the input delay can be properly compensated. Necessary and sufficient conditions guaranteeing the stability of the closed-loop system are provided in terms of the stability of some simple linear time-delay systems refereed to as observer-error systems, by which the separation principle is discovered. Moreover, approaches in terms of linear matrix inequalities are also provided to design both the state feedback gains and observer gains. Finally, a numerical example illustrates that the proposed approaches are more effective and safe to implement than the existing methods. [ABSTRACT FROM AUTHOR]

A reverse-transfer method is proposed to study the stabilization problem of k -valued logical control networks (LCNs). Main results consist of two parts. (1) Two necessary and sufficient stabilization conditions are derived for k -valued LCNs. The stabilization results are much superior to the existing relevant results in the literature. (2) Based on the above conditions, some algorithms for solving the open-loop stabilization problem of k -valued LCNs are developed. These algorithms cut useless control paths off as many as possible, which, compared with existing results, reduce the related computational cost markedly. [ABSTRACT FROM AUTHOR]

The stabilization and set stabilization of a multivalued logical system are investigated in this paper by using pinning control. First, new algorithms are presented to redesign the transition matrix of the multivalued logical system such that the system is stable or set stable. Then, by using reconstruction theory of a k -valued logical system, the pinning nodes are selected. In addition, the transition matrix of the pinning control is given by solving some logical matrix equations. Then, a pinning control design algorithm is provided. Finally, an example is employed to illustrate the proposed control design procedure. [ABSTRACT FROM AUTHOR]

We provide a new control design for chemostats, under constant substrate input concentrations, using piecewise constant delayed measurements of the substrate concentration. Our growth functions can be uncertain and are not necessarily monotone. The dilution rate is the control. We use a new Lyapunov approach to derive conditions on the largest sampling interval and on the delay length to ensure asymptotic stabilization properties of a componentwise positive equilibrium point. [ABSTRACT FROM AUTHOR]

In this contribution we investigate the input delay compensation for neutral type time-delay systems with both state and input delays. A nested predictor is established to predict the future states such that the input delay that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed-loop system in the presence of input delay possesses the same characteristic equation as the closed-loop system in the absence of input delay. An implementation scheme by adding input filters is also proposed. Under an additional assumption, explicit nested predictor feedback controllers involving only 1-fold integrals are established. A numerical example is carried out to support the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization problem for controllable and observable linear systems with saturated outputs, in which direct feedthrough term is involved. The necessity of considering the direct feedthrough term is clarified. We present a constructive design strategy to achieve globally asymptotic stability of the systems by output feedback. The controller is continuous during the interval we drive a specific output component out of saturation in order to handle the direct feedthrough term. Moreover, the parameters to be designed for the controller have close relationship with the transfer function and direct feedthrough matrix. Numerical simulations are included to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses on the design problem for a class of continuous-time linear systems under the saturated linear feedbacks. The concerned problem becomes an exponential stabilization one through the further refined treatment on the saturation nonlinearity, including a property of absolute value and the S -procedure lemma. Then, sufficient linear matrix inequality (LMI) conditions for its local exponential stabilizability are derived in the sense of Lyapunov stability criterion. A numerical example is provided to show the reduced conservatism of the proposed design conditions. [ABSTRACT FROM AUTHOR]

The stabilization problem of rigid spacecraft is essential for space explorations and operations. This paper studies the model predictive stabilization problem of a class of underactuated rigid spacecrafts with two bounded control torques. A novel model predictive control (MPC) algorithm is designed by making use of the homogeneity of the system dynamics. In addition, a local homogeneous Lyapunov function is constructed based on which the approach to designing the terminal set and other parameters are developed. Finally, the conditions for ensuring algorithm feasibility and closed-loop stability are provided. We show that under the given conditions, the designed MPC algorithm is feasible, and the closed-loop system is asymptotically stable. Simulation and comparison studies verify that the developed results are effective and valid, and the designed controller fulfills the constraint satisfaction and achieves much faster convergence rate in comparison with conventional continuous time-varying controllers. [ABSTRACT FROM AUTHOR]

This paper studies the dynamic event-triggered intermittent control (D-ETIC) for the stabilization of delayed dynamical systems (DDS). The stabilization of DDS via general intermittent control is formulated as a problem of delay-dependent minimal activation time rate (MATR). A D-ETIC scheme with input delay is proposed to stabilize DDS. The delay-dependent MATR is estimated. And the maximal input delay allowed in D-ETIC is estimated for quasi-linear DDS. Both theoretical and numerical comparisons are given among D-ETIC, static ETIC (S-ETIC), and the recently developed static intermittent control schemes, including time-triggered intermittent control and event-triggered aperiodic intermittent control. It is shown that the proposed D-ETIC achieves the lowest MATR. It is also shown that larger delays, including the time delay in DDS and the input delay in D-ETIC, may lead to more control activation time for the stabilization. [ABSTRACT FROM AUTHOR]

The problem of synchronization and balancing around simple closed polar curves is addressed for unicycle-type multi-agent systems. Leveraging the concept of barrier Lyapunov function in conjunction with bounded Lyapunov-like curve-phase potential functions, we propose distributed feedback control laws and show that the agents asymptotically stabilize to the desired closed curve in synchronized and balanced curve-phase patterns, and their trajectories remain bounded within a compact set. Our control design methodology is based on the proposition of two models, namely the parametric-phase control model and the curve-phase control model. We also characterize the trajectory-constraining set based on the magnitude of the safe distance of the exterior boundary from the desired curve. We further establish a connection between the perimeters and areas of the trajectory-constraining set with the perimeter and area of the desired curve. We obtain bounds on different quantities of interest in the post-design analysis and provide simulation results to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Transient response of linear systems with non-zero initial conditions was at the center of attention for engineers and researchers at early stages of classical control theory. However this field was not intensively investigated later. For instance, the breakthrough result on unavoidable peaking effect for systems with strong damping factor was obtained by Izmailov in 1987, but it did not attract much attention. We try to continue this line of research and provide explicit worst-case lower bound. Then we exhibit large deviation effects for other pole locations and estimate lower bounds for them. The upper bounds for deviations of trajectories are much better studied; to obtain the smallest deviations by static linear feedback the techniques of linear matrix inequalities can be exploited. We demonstrate that for such closed-loop systems the upper and lower bounds have the same asymptotic behavior. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization problem of discrete-time linear systems with infinite distributed input delays. A novel framework is adopted to analyze the stability of the concerned systems. Under this framework, two truncated predictor feedback controllers are developed for two classes of discrete-time linear systems with infinite distributed input delays via the low gain method respectively. It is shown that under the designed controllers, those two classes systems are globally exponentially stable. To the best of our knowledge, this is the first time that the stabilization problem of discrete-time linear systems with infinite distributed input delays is considered. Two simulation examples are provided to illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

This paper is concerned with mean field linear quadratic social control with common noise, where the weight matrices of individual costs are indefinite We first obtain a set of forward–backward stochastic differential equations (FBSDEs) from variational analysis, and then construct a centralized feedback representation by decoupling the FBSDEs. By using solutions of two Riccati equations, we design a set of decentralized control laws, which is further shown to be asymptotically social optimal. The necessary and sufficient conditions are given for uniform stabilization of the systems by exploiting the relation between population state average and aggregate effect. An explicit expression of the optimal social cost is given in terms of two Riccati equations. Besides, the decentralized optimal solution is provided for mean field social control problem with finite agents. [ABSTRACT FROM AUTHOR]

This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel control barrier functions/functionals for the safety problem. The proposed control Lyapunov and barrier functions/functionals extend the existing ones from the delay-free case to the time-delay case, and allow for designing the stabilizing and safety controllers in closed-form. Since analytical solutions to time-delay optimal control problems are hard to be achieved, a sliding mode control based approach is developed to merge the proposed control Lyapunov and barrier functions/functionals. Based on the sliding surface functional, a feedback control law is established to investigate the stabilization and safety objectives simultaneously. In particular, the properties of the sliding surface functional are analyzed, and further how to construct the sliding surface functional is discussed. Finally, the proposed approaches are illustrated via two numerical examples from the connected cruise control problem of automotive systems and the synchronization problem of multi-agent systems. [ABSTRACT FROM AUTHOR]

With the development of digital control technology, sampled-data control shows its prominent superiority for most practical industries. In the framework of sampled-data control, this paper studies the stabilization problem for a class of switched linear neutral systems meanwhile taking into account asynchronous switching. By utilizing the relationship between the sampling period and the dwell time of switched neutral systems, a bond between the sampling period and the average dwell time is revealed to form a switching condition, under which and certain control gains conditions exponential stability of the closed-loop systems is guaranteed. A simple example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We solve the problem of stabilizing a general class of linear first-order hyperbolic systems. Considered systems feature an arbitrary number of coupled transport PDEs convecting in either direction. Using the backstepping approach, we derive a full-state feedback law and a boundary observer enabling stabilization by output feedback. Unlike previous results, finite-time convergence to zero is achieved in the theoretical lower bound for control time. [ABSTRACT FROM AUTHOR]

The analysis of discontinuous extremum seeking (ES) controllers, e.g. those applicable to digital systems, has historically been more complicated than that of continuous controllers. We establish a simple and general extension of a recently developed bounded form of ES to a general class of oscillatory functions, including functions discontinuous with respect to time, such as triangle or square waves with dead time. We establish our main results by combining a novel idea for oscillatory control with an extension of functional analytic techniques originally utilized by Kurzweil, Jarnik, Sussmann, and Liu in the late 80s and early 90s and recently studied by Dürr et al. We demonstrate the value of the result with an application to inverter switching control. [ABSTRACT FROM AUTHOR]

We consider boundary stabilization for one-dimensional systems of linear hyperbolic partial differential equations with relaxation structure. Such equations appear in many applications. By combining weighted Lyapunov functions, the structure is used to derive new stabilization results. The result is illustrated with an application to boundary stabilization of water flows in open canals. [ABSTRACT FROM AUTHOR]

The present work addresses continuous-time approximation of distributed parameter systems governed by linear one-dimensional partial differential equations. While approximation is usually realized by lumped systems, that is finite dimensional systems, we propose to approximate the plant by a time-delay system. Within the graph topology, we prove that, if the plant admits a coprime factorization in the algebra of BIBO-stable systems, any linear distributed parameter plant can be approximated by a time-delay system, governed by coupled differential–difference equations. Considerations on stabilization and state-space realization are carried out. A numerical method for constructive approximation is also proposed and illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we design, in a systematic way, an infinite-dimensional disturbance estimator by the active disturbance rejection control approach. The proposed disturbance estimator can be used to extract real signal from corrupted velocity signal. Its variant form can also be served as a tracking differentiator. The result is applied to stabilization for a multi-dimensional wave equation with position and corrupted velocity measurements. [ABSTRACT FROM AUTHOR]

We provide a new backstepping result for time-varying systems with input delays. The novelty of our work is in the bounds on the controls, and the facts that (i) one does not need to compute any Lie derivatives to apply our controls, (ii) the controls have no distributed terms, and (iii) we do not require any differentiability conditions on the available controls for the subsystems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the static output-feedback stabilization with optimal L 1 -gain for positive linear systems. We aim to construct a static output-feedback controller such that the closed-loop system is positive, asymptotically stable and the L 1 -gain from the exogenous input to the regulated output is minimized. We show that when the control input or the measured output is a scalar, this problem can be directly solved via linear programming by adding a one dimensional search. Moreover, it is pointed out that the results can be extended to solve the L ∞ -optimal controller synthesis problem. Finally, several illustrative examples are given to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The problem of stabilizing a linear continuous-time system with discrete-time measurements and a sampled input with a pointwise constant delay is considered. In a first part, we design a continuous–discrete observer which converges when the maximum time interval between two consecutive measurements is sufficiently small. In a second part, we construct a dynamic output feedback by using a technique which is strongly reminiscent of the reduction model approach. It stabilizes the system when the maximal time between two consecutive sampling instants is sufficiently small. No limitation on the size of the delay is imposed and an ISS property with respect to additive disturbances is established. [ABSTRACT FROM AUTHOR]