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Showing papers on "Lyapunov function published in 2017"


Journal ArticleDOI
TL;DR: This paper develops a methodology that allows safety conditions—expression as control barrier functions—to be unified with performance objectives—expressed as control Lyapunov functions—in the context of real-time optimization-based controllers.
Abstract: Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions—expressed as control barrier functions —to be unified with performance objectives—expressed as control Lyapunov functions—in the context of real-time optimization-based controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds.

992 citations


Journal ArticleDOI
TL;DR: Two theorems are provided to show that all the signals in the closed-loop system are bounded, the outputs are driven to follow the reference signals and all the states are ensured to remain in the predefined compact sets.

657 citations


Book
27 Feb 2017

369 citations


Journal ArticleDOI
TL;DR: This article presents basic concepts and recent research directions about the stability of sampled-data systems with aperiodic sampling, and indicates the sources of conservatism, the problems that remain open and the possible directions of improvement.

344 citations


Journal ArticleDOI
TL;DR: It is shown that by invoking the redundancy properties induced by the descriptor formulation, combined with some convexifying techniques, the existence of the desired reliable controller can be explicitly determined by the solution of a convex optimization problem.
Abstract: This article studies the robust and reliable $\mathscr {H}_{\infty }$ static output feedback (SOF) control for nonlinear systems with actuator faults in a descriptor system framework. The nonlinear plant is characterized by a discrete-time Takagi-Sugeno (T-S) fuzzy affine model with parameter uncertainties, and the Markov chain is utilized to describe the actuator-fault behaviors. Specifically, by adopting a state-output augmentation approach, the original system is firstly reformulated into the descriptor fuzzy affine system. Based upon a novel piecewise Markovian Lyapunov function (LF), the $\mathscr {H}_{\infty }$ performance analysis condition for the underlying system is then presented, and furthermore the robust and reliable SOF controller synthesis is carried out. It is shown that by invoking the redundancy properties induced by the descriptor formulation, combined with some convexifying techniques, the existence of the desired reliable controller can be explicitly determined by the solution of a convex optimization problem. Finally, simulation studies are applied to confirm the effectiveness of the developed method.

316 citations


Journal ArticleDOI
TL;DR: By explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances, and constitute one of the first examples of provably safe and robust control for robotic systems with complex nonlinear dynamics that need to plan in real time in environments with complex geometric constraints.
Abstract: We consider the problem of generating motion plans for a robot that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, and disturbances. Furthermore, we...

305 citations


Journal ArticleDOI
TL;DR: It is proved that asymptotic stability of such a DMPC can be achieved through an explicit sufficient condition on the weights of the cost functions, by using the sum of local cost functions as a Lyapunov candidate.
Abstract: This paper presents a distributed model predictive control (DMPC) algorithm for heterogeneous vehicle platoons with unidirectional topologies and a priori unknown desired set point. The vehicles (or nodes) in a platoon are dynamically decoupled but constrained by spatial geometry. Each node is assigned a local open-loop optimal control problem only relying on the information of neighboring nodes, in which the cost function is designed by penalizing on the errors between the predicted and assumed trajectories. Together with this penalization, an equality-based terminal constraint is proposed to ensure stability, which enforces the terminal states of each node in the predictive horizon equal to the average of its neighboring states. By using the sum of local cost functions as a Lyapunov candidate, it is proved that asymptotic stability of such a DMPC can be achieved through an explicit sufficient condition on the weights of the cost functions. Simulations with passenger cars demonstrate the effectiveness of the proposed DMPC.

305 citations


Journal ArticleDOI
TL;DR: Adaptive neural network (NN) dynamic surface control (DSC) is discussed for a class of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics and a one to one nonlinear mapping is introduced.

305 citations


Journal ArticleDOI
TL;DR: New stability conditions are established for systems with a designed switching strategy where fast switching and slow switching are respectively applied to unstable and stable subsystems, via choosing multiple discontinuous Lyapunov functions in the quadratic form.
Abstract: In this technical note, the problem of stability for a class of slowly switched systems is investigated. By developing a novel multiple discontinuous Lyapunov function approach and exploring the feature of mode-dependent dwell time switching, new stability conditions are established for systems with a designed switching strategy where fast switching and slow switching are respectively applied to unstable and stable subsystems. In particular, stability conditions for linear switched systems are also given via choosing multiple discontinuous Lyapunov functions in the quadratic form. Moreover, stability criteria for the systems consisting of stable subsystems are also derived. It is shown that our proposed results cover some existing ones in literature as special cases, and provide tighter bounds on the dwell time. Finally, some simulation results are provided to show the advantages of the theoretic results obtained.

296 citations


Journal ArticleDOI
TL;DR: This paper proposes a new Lyapunov function, which is continuous and does not include any sign function, and hence, the chattering phenomenon in most of the existing results is overcome and an optimal algorithm is proposed for the estimation of the settling time.
Abstract: Dealing with impulsive effects is one of the most challenging problems in the field of fixed-time control. In this paper, we solve this challenging problem by considering fixed-time synchronization of complex networks (CNs) with impulsive effects. By designing a new Lyapunov function and constructing comparison systems, a sufficient condition formulated by matrix inequalities is given to ensure that all the dynamical subsystems in the CNs are synchronized with an isolated system in a settling time, which is independent of the initial values of both the CNs and the isolated system. Then, by partitioning impulse interval and using the convex combination technique, sufficient conditions in terms of linear matrix inequalities are provided. Our synchronization criteria unify synchronizing and desynchronizing impulses. Compared with the existing controllers for fixed-time and finite-time techniques, the designed controller is continuous and does not include any sign function, and hence, the chattering phenomenon in most of the existing results is overcome. An optimal algorithm is proposed for the estimation of the settling time. Numerical examples are given to show the effectiveness of our new results.

287 citations


Journal ArticleDOI
TL;DR: In order to overcome the difficulty of controller design for nonstrict-feedback system in backstepping design process, a variables separation method is introduced and an adaptive fuzzy controller is designed to guarantee all the signals of the resulting closed-loop system to be bounded.
Abstract: This paper investigates the problem of adaptive fuzzy state-feedback control for a category of single-input and single-output nonlinear systems in nonstrict-feedback form. Unmodeled dynamics and input constraint are considered in the system. Fuzzy logic systems are employed to identify unknown nonlinear characteristics existing in systems. An appropriate Lyapunov function is chosen to ensure unmodeled dynamics to be input-to-state practically stable. A smooth function is introduced to tackle input saturation. In order to overcome the difficulty of controller design for nonstrict-feedback system in backstepping design process, a variables separation method is introduced. Moreover, based on small-gain technique, an adaptive fuzzy controller is designed to guarantee all the signals of the resulting closed-loop system to be bounded. Finally, two illustrative examples are given to validate the effectiveness of the new design techniques.

Journal ArticleDOI
TL;DR: If each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique.
Abstract: The bipartite consensus problem for a group of homogeneous generic linear agents with input saturation under directed interaction topology is examined. It is established that if each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique. The convergence analysis of the proposed control strategy is performed by means of the Lyapunov method which can also specify the convergence rate. At last, the validity of the theoretical findings is demonstrated by two simulation examples.

Journal ArticleDOI
TL;DR: A Lyapunov function is proposed to prove the closed-loop system stability and the semi-global uniform ultimate boundedness of all state variables and a series of simulation results indicate that proposed controllers can track desired trajectories well via selecting appropriate control gains.
Abstract: The research of this paper works out the attitude and position control of the flapping wing micro aerial vehicle (FWMAV). Neural network control with full state and output feedback are designed to deal with uncertainties in this complex nonlinear FWMAV dynamic system and enhance the system robustness. Meanwhile, we design disturbance observers which are exerted into the FWMAV system via feedforward loops to counteract the bad influence of disturbances. Then, a Lyapunov function is proposed to prove the closed-loop system stability and the semi-global uniform ultimate boundedness of all state variables. Finally, a series of simulation results indicate that proposed controllers can track desired trajectories well via selecting appropriate control gains. And the designed controllers possess potential applications in FWMAVs.

Journal ArticleDOI
TL;DR: A continuous output feedback control scheme rendering the closed-loop double integrator system globally stable in finite-time is presented and the efficiency of the proposed algorithms is illustrated by numerical simulations.

Journal ArticleDOI
TL;DR: The control problem for flexible wings of a robotic aircraft is addressed by using boundary control schemes based on the original coupled dynamics, and bounded stability is proved by introducing a proper Lyapunov function.
Abstract: In this brief, the control problem for flexible wings of a robotic aircraft is addressed by using boundary control schemes Inspired by birds and bats, the wing with flexibility and articulation is modeled as a distributed parameter system described by hybrid partial differential equations and ordinary differential equations Boundary control for both wing twist and bending is proposed on the original coupled dynamics, and bounded stability is proved by introducing a proper Lyapunov function The effectiveness of the proposed control is verified by simulations

Journal ArticleDOI
TL;DR: This paper addresses the problem of an event-triggered non-parallel distribution compensation (PDC) control for networked Takagi–Sugeno (T–S) fuzzy systems, under consideration of the limited data transmission bandwidth and the imperfect premise matching membership functions.
Abstract: This paper addresses the problem of an event-triggered non-parallel distribution compensation (PDC) control for networked Takagi–Sugeno (T–S) fuzzy systems, under consideration of the limited data transmission bandwidth and the imperfect premise matching membership functions. First, a unified event-triggered T–S fuzzy model is provided, in which: 1) a fuzzy observer with the imperfect premise matching is constructed to estimate the unmeasurable states of the studied system; 2) a fuzzy controller is designed following the same premise as the observer; and 3) an output-based event-triggering transmission scheme is designed to economize the restricted network resources. Different from the traditional PDC method, the synchronous premise between the fuzzy observer and the T–S fuzzy system are no longer needed in this paper. Second, by use of Lyapunov theory, a stability criterion and a stabilization condition are obtained for ensuring asymptotically stable of the studied system. On account of the imperfect premise matching conditions are well considered in the derivation of the above criteria, less conservation can be expected to enhance the design flexibility. Compared with some existing emulation-based methods, the controller gains are no longer required to be known a priori . Finally, the availability of proposed non-PDC design scheme is illustrated by the backing-up control of a truck-trailer system.

Journal ArticleDOI
TL;DR: It is proved through Lyapunov analyses that the proposed control protocol ensures that all the signals of the closed-loop system are globally bounded and the system output tracking error can exponentially converge to a residual which can be made arbitrarily small.

Journal ArticleDOI
TL;DR: A sliding mode controller is synthesized to drive the underlying closed-loop system onto the sliding surface in finite time, locally for a given sliding region, which also guarantees the stochastic stability of sliding mode dynamical system.

Journal ArticleDOI
TL;DR: Improved delay-dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality (LMI).

Journal ArticleDOI
TL;DR: The time-varying asymmetric barrier Lyapunov functions (TABLFs) are employed in each step of the backsstepping design and a novel control TABLF scheme is established to ensure the asymptotic output tracking performance.
Abstract: In this paper, we address an adaptive control problem for a class of nonlinear strict-feedback systems with uncertain parameter. The full states of the systems are constrained in the bounded sets and the boundaries of sets are compelled in the asymmetric time-varying regions, i.e., the full state time-varying constraints are considered here. This is for the first time to control such a class of systems. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions (TABLFs) are employed in each step of the backsstepping design and we also establish a novel control TABLF scheme to ensure the asymptotic output tracking performance. The performances of the adaptive TABLF-based control are verified by a simulation example.

Journal ArticleDOI
TL;DR: A new function which consisted of two quadratic functions with a special structural matrix is established to be a Lyapunov functional candidate to decrease the conservatism of derived conditions.

Journal ArticleDOI
TL;DR: In this paper, an integral sliding mode controller (ISMC) for a general type of underwater robots based on multiple-input and multiple-output extended-state-observer (MIMO-ESO) was developed.
Abstract: This paper develops a novel integral sliding mode controller (ISMC) for a general type of underwater robots based on multiple-input and multiple-output extended-state-observer (MIMO-ESO). The difficulties associated with the unmeasured velocities, unknown disturbances, and uncertain hydrodynamics of the robot have been successfully solved in the control design. An adaptive MIMO-ESO is designed not only to estimate the unmeasurable linear and angular velocities, but also to estimate the unknown external disturbances. An ISMC is then designed using Lyapunov synthesis, and an adaptive gain update algorithm is introduced to estimate the upper bound of the uncertainties. Rigorous theoretical analysis is performed to show that the proposed control method is able to achieve asymptotical tracking performance for the underwater robot. Experimental studies are also carried out to validate the effectiveness of the proposed control, and to show that the proposed approach performs better than a conventional potential difference (PD) control approach.

Journal ArticleDOI
TL;DR: A neural-network-based observer is integrated to recover the system internal states from the measurable feedback to reduce the computation cost and transmission load of the event-triggered adaptive dynamic programming control method.
Abstract: This paper proposes a novel event-triggered adaptive dynamic programming (ADP) control method for nonlinear continuous-time system with unknown internal states. Comparing with the traditional ADP design with a fixed sample period, the event-triggered method samples the state and updates the controller only when it is necessary. Therefore, the computation cost and transmission load are reduced. Usually, the event-triggered method is based on the system entire state which is either infeasible or very difficult to obtain in practice applications. This paper integrates a neural-network-based observer to recover the system internal states from the measurable feedback. Both the proposed observer and the controller are aperiodically updated according to the designed triggering condition. Neural network techniques are applied to estimate the performance index and help calculate the control action. The stability analysis of the proposed method is also demonstrated by Lyapunov construct for both the continuous and jump dynamics. The simulation results verify the theoretical analysis and justify the efficiency of the proposed method.

Journal ArticleDOI
TL;DR: Two new approaches to the reliable SOF controller analysis and synthesis are proposed for the underlying stochastic fuzzy-affine systems based on a Markovian Lyapunov function combined with Itô differential formula, S-procedure, and some matrix inequality convexification procedures.
Abstract: This paper deals with the problem of reliable and robust $\mathscr {H}_{\infty }$ static output feedback (SOF) controller synthesis for continuous-time nonlinear stochastic systems with actuator faults. The nonlinear stochastic plant is expressed by an Ito-type Takagi–Sugeno fuzzy-affine model with parametric uncertainties, and a Markov process is employed to model the occurrence of actuator fault. The purpose is to design an admissible piecewise SOF controller, such that the resulting closed-loop system is stochastically stable with a prescribed disturbance attenuation level in an $\mathscr {H}_{\infty }$ sense. Specifically, based on a Markovian Lyapunov function combined with Ito differential formula, S-procedure, and some matrix inequality convexification procedures, two new approaches to the reliable SOF controller analysis and synthesis are proposed for the underlying stochastic fuzzy-affine systems. It is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness and advantages of the developed methods.

Journal ArticleDOI
TL;DR: An extended reciprocALLY convex matrix inequality is developed to replace the popular reciprocally convex combination lemma (RCCL) with potential to reduce the conservatism of the RCCL-based criteria without introducing any extra decision variable due to its advantage of reduced estimation gap using the same decision variables.
Abstract: This paper is concerned with the stability analysis of discrete-time neural networks with a time-varying delay. Assessment of the effect of time delays on system stability requires suitable delay-dependent stability criteria. This paper aims to develop new stability criteria for reduction of conservatism without much increase of computational burden. An extended reciprocally convex matrix inequality is developed to replace the popular reciprocally convex combination lemma (RCCL). It has potential to reduce the conservatism of the RCCL-based criteria without introducing any extra decision variable due to its advantage of reduced estimation gap using the same decision variables. Moreover, a delay-product-type term is introduced for the first time into the Lyapunov function candidate such that a delay-variation-dependent stability criterion with the bounds of delay change rate is established. Finally, the advantages of the proposed criteria are demonstrated through two numerical examples.

Journal ArticleDOI
TL;DR: The novel control strategy unifies the construction of Lyapunov functions, which are used to deal with high-order and low-order nonlinear growth rates separately in the existing results.

Journal ArticleDOI
TL;DR: A new time-dependent discontinuous Lyapunov functional, namely, free-matrix-based time- dependent discontinuous (FMBTDD) Lyapinov functional is introduced for stability analysis of sampled-data systems.
Abstract: In this paper, a new time-dependent discontinuous Lyapunov functional, namely, free-matrix-based time-dependent discontinuous (FMBTDD) Lyapunov functional is introduced for stability analysis of sampled-data systems. First, a modified free-matrix-based integral inequality (MFMBII) is derived based on the existing free-matrix-based integral inequality [1] and it is applied to develop a stability criterion for sampled-data systems. And then, inspired by MFMBII, FMBTDD term is established that leads to efficient stability conditions. Four numerical examples are given to demonstrate the effectiveness of the proposed methods.

Journal ArticleDOI
TL;DR: A neural networks-based tracking control method is developed for uncertain nonlinear systems with unmodeled dynamics and nonlower triangular form and it is shown that the proposed controller is able to ensure the semi-global boundedness of all signals of the resulting closed-loop system.
Abstract: This paper considers the problem of adaptive neural control of nonlower triangular nonlinear systems with unmodeled dynamics and dynamic disturbances. The design difficulties appeared in the unmodeled dynamics and nonlower triangular form are handled with a dynamic signal and a variable partition technique for the nonlinear functions of all state variables, respectively. It is shown that the proposed controller is able to ensure the semi-global boundedness of all signals of the resulting closed-loop system. Furthermore, the system output is ensured to converge to a small domain of the given trajectories. The main advantage about this research is that a neural networks-based tracking control method is developed for uncertain nonlinear systems with unmodeled dynamics and nonlower triangular form. Simulation results demonstrate the feasibility of the newly presented design techniques.

Journal ArticleDOI
TL;DR: In this article, a distributed continuous-time projected algorithm for convex cost functions with local constraints is proposed, in which each agent knows its local cost function and local constraint set, and proves that all the agents of the algorithm can find the same optimal solution.
Abstract: This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its local cost function and local constraint set, for the constrained optimization problem. Then we prove that all the agents of the algorithm can find the same optimal solution, and meanwhile, keep the states bounded while seeking the optimal solutions. We conduct a complete convergence analysis by employing nonsmooth Lyapunov functions for the stability analysis of differential inclusions. Finally, we provide a numerical example for illustration.

Journal ArticleDOI
TL;DR: A novel second-order sliding mode (SOSM) control method to handle sliding mode dynamics with mismatched term, so as to reduce the terms in the control channel is proposed and the validity of the proposed approach is verified.