Simultaneous Stabilization Problem Research Articles

Event-triggered simultaneous tracking control and stabilization of underactuated USVs

This study addresses the control problem of simultaneous tracking control and stabilization for underactuated unmanned surface vessels (USVs) with only two available inputs in the surge and yaw directions. Firstly, two velocity modifications are introduced to transform the error dynamics into two decoupled subsystems. Then, a novel error transforming scheme is presented to reduce the complexity of controller expressions and overcome the difficulties caused by underactuated dynamics. Based on the above transforming scheme and the event-triggered control (ETC) mechanism, a unified control method is designed to guarantee that the error states converge to a bounded neighborhood of the origin while excluding the Zeno behavior of the controllers. In addition, two radial basis function neural networks (RBFNNs) are applied to approximate the unknown dynamics and additional control errors caused by the ETC mechanism. Finally, comparative simulation experiments are performed to validate the effectiveness of the proposed controller.

Finite‐time robust simultaneous stabilization control for two nonlinear singular time‐delay systems

AbstractIn this paper, the finite‐time simultaneous stabilization problem of two nonlinear singular time‐delay Hamiltonian systems is investigated. Firstly, the two general nonlinear singular time‐delay Hamiltonian systems are transformed into their Hamiltonian differential‐algebraic forms by equivalent transformation, respectively, they are then converted to two strictly dissipative Hamiltonian forms via the state feedback method, and two strictly dissipative Hamiltonian systems are extended into a Hamiltonian one. Based on which, a suitable Hamiltonian function is constructed to analyze the finite‐time simultaneous stability and finite‐time robust simultaneous stabilization problem. Finally, an illustrative example is given to show the effectiveness of the results obtained. It should be pointed out that since there does not exist a finite‐time stability criterion on the nonlinear singular delay system, we adopt a new double compound asymptotic method.

Cooperative Spacing Sampled Control of Vehicle Platoon Considering Undirected Topology and Analog Fading Networks

The work on this paper studies the combined effect of vehicle dynamics, sampling period and the quality of inter-vehicle sensing and communication on the performance of platoon control. First, we induce the sampled control protocol from continuous–time linear consensus protocol by employing zero–order hold circuit and periodic sampling technology, then by virtue of the obtained sampled control protocol, the continuous–time platoon system is equivalently transformed into a discrete–time system. Second, for the inter–vehicle communication with ideal channel and under undirected information flow topology (UIFT), the stability thresholds of control gains are explicitly established by solving a discrete–time simultaneous stabilization problem, bilinear transformation and the Routh-Hurwitz stability criterion. Meanwhile, to ensure the fastest asymptotic stability of the platoon dynamics, we propose an optimal asymptotic convergence factor and a correspondingly optimal sampled control protocol. Third, For the inter–vehicle communication with identical fading networks and under UIFT, through solving a modified Riccati inequality, we provide a sampled control protocol depending not only on information flow topology (IFT) and sampling period, but also on the statistics of the inter–vehicle communication channel. Besides, employing Lyapunov inequality in probability theory, we show a necessary condition for the sampled control protocol ensuring the platoon dynamics mean square stable. Finally, simulations are performed to demonstrate the theory’s discoveries.

On the simultaneous stabilization of stochastic nonlinear systems

SummaryIn this paper, the problem of simultaneous stabilization in probability by state feedback is investigated for a class of stochastic nonlinear systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Under the assumption that a collection of stochastic control Lyapunov functions (SCLFs) is known and based on the generalized stochastic Lyapunov theorem, we derive sufficient conditions for the simultaneous stabilization in probability by a continuous state feedback controller that we explicitly compute. We also derive a necessary condition when the system coefficients satisfy some regularity conditions. This work generalizes previous results on the simultaneous stabilization of stochastic nonlinear systems. The obtained results are illustrated by a numerical example.

Finite-Dimensional Controllers for Consensus in a Leader-Follower Network of Marginally Unstable Infinite-Dimensional Agents

We consider the output-feedback state consensus problem for a homogeneous multi-agent system consisting of one leader agent and N follower agents. The dynamics of each of these agents is governed by a single-input single-output regular linear system (RLS), with the input to the leader agent being zero at all times. The transfer function of this RLS has all its poles in the closed left-half of the complex-plane, with only a finite number of them lying on the imaginary axis. Each follower agent can access the relative output of all its neighboring agents and some of the follower agents can access the relative output of the leader. The communication graph associated with the exchange of relative outputs is directed. Under this setting, we first establish that a controller solves the above leader-follower consensus problem if and only if it can simultaneously stabilize N regular linear systems. We then adapt a recently developed frequency-domain technique to construct a stable finite-dimensional output-feedback controller which solves the simultaneous stabilization problem, and hence the consensus problem. We demonstrate the efficacy of our controller design technique using a numerical example.

Simultaneous exponential stabilization for stochastic port-controlled Hamiltonian systems with actuator saturations, fading channels and delays

This paper is concerned with the simultaneous exponential stabilization problem for a set of stochastic port-controlled Hamiltonian (PCH) systems. Due to the limited bandwidth of the channels, the phenomena of fading channels and transmission delays which are described by a time-varying stochastic model always occur in the communication channels from the controller to the actuator. Meanwhile, actuator saturation constraint is taken into account. On the basis of dissipative Hamiltonian structural and saturating actuator properties, those stochastic PCH systems are combined to generate an augmented system. By utilizing the stochastic analysis theory, sufficient criterions are given for the simultaneous stabilization controller design ensuring that the closed-loop system is simultaneously exponentially mean-square stable (SEMSS). For the case that there exist external disturbances in the systems, some results on stability analysis and controller design are given. The developed controller design scheme is proved by a three-helicopter model simulation example.

Leader–follower formation stabilization and tracking control for heterogeneous planar underactuated vehicle networks

In this paper, we solve the distributed leader–follower simultaneous formation stabilization and tracking control problem for heterogeneous planar underactuated vehicle networks without global position measurements of the followers. The vehicles in the network are modeled as generic 3-DOF planar rigid bodies with two control inputs, and are allowed to have identical or non-identical dynamics. By incorporating graph theory, passivity-based control, partial stability theory, Matrosov’s theorem and the persistence of excitation concept, a smooth formation control scheme is proposed to simultaneously address the formation stabilization and formation tracking problems without switching. Moreover, the structure of the controller is relatively simple compared to the existing controllers in the literature, and thus, is practical and easy to implement. Simulations on a group of underactuated vehicles including nonholonomic mobile robots and surface vessels are presented to demonstrate the effectiveness of the proposed control scheme.

Robust simultaneous stabilization of multiple n‐degree‐of‐freedom robot systems

AbstractIn this paper, the robust simultaneous stabilization problem of multiple n‐degree‐of‐freedom (n‐DOF) robot systems is studied by using Hamiltonian function method, and the corresponding L2 interference suppression controller is designed. First, we investigate the general simultaneous stabilization of the multiple n‐DOF robot systems without external disturbance. On this basis, we further study the robust simultaneous stabilization control problem for multiple n‐DOF robot systems with external disturbance and design a simultaneous stabilization controller. Finally, the simulation results show that the simultaneous stabilization controller designed for the paper is very effective in stabilizing multiple robot systems at the same time.

Global Consensus of Positive Edge System With Sector Input Nonlinearities

This paper investigates the positive edge consensus problems for undirected networks, where each edge is modeled by a continuous-time positive system with sector input nonlinearities. Based on a given nodal network, the corresponding edge network is presented, and some relationships between the given nodal network and its edge network are given. The observer-based protocol for non-negative consensus is proposed. Rigorous theoretical analysis which considers both the input nonlinearities and the positivity constraint is introduced to achieve a global consensus result. Simultaneous stabilization problems are constructed for edge-based non-negative consensus using the maximum and the minimum nonzero eigenvalues of the edge Laplacian matrix. Furthermore, the robustness of the positive edge consensus to parameter perturbation is illustrated. Sufficient non-negative consensus conditions related to the bounds of system matrices are given, and the non-negative edge consensus conditions for star nodal networks are also given only using the vertex number. Iterative linear matrix inequalities (LMIs)/LMI algorithm is presented to obtain the feedback matrix and the observer matrix. The given theoretical results are finally illustrated by some simulations.

Finite-Time Simultaneous Stabilization for Stochastic Port-Controlled Hamiltonian Systems over Delayed and Fading Channels

In this paper, a finite-time simultaneous stabilization problem is investigated for a set of stochastic port-controlled Hamiltonian (PCH) systems over delayed and fading noisy channels. The feedback control signals transmitted via a communication network suffer from both constant transmission delay and fading channels which are modeled as a time-varying stochastic model. First, on the basis of dissipative Hamiltonian structural properties, two stochastic PCH systems are combined to form an augmented system by a single output feedback controller and then sufficient conditions are developed for the semiglobally finite-time simultaneous stability in probability (SGFSSP) of the resulting closed-loop systems. The case of multiple stochastic PCH systems is also considered and a new control scheme is proposed for the systems to save costs and achieve computational simplification. Finally, an example is provided to verify the feasibility of the proposed simultaneous stabilization method.

Pseudo predictor feedback stabilisation of linear systems with both state and input delays

This paper proposes a pseudo predictor feedback control scheme for stabilisation of linear systems with both input and state delays. It is proved that the stability of the closed-loop system is determined by the stability of the target closed-loop system, along with the stability of an associated integral delay system, which describes the additional dynamics induced by the pseudo predictor. It is shown that in case of commensurate delays, the control law can be directly expressed as a function of the original system matrices, widening the applicability of analysis and design tools. For the synthesis of the feedback gains, a numerical procedure is presented to solve the simultaneous stabilization problem of the target system and the associated integral delay system. Numerical experiments are carried out to illustrate the effectiveness of the methodology.

Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

SummaryThis paper investigates the finite‐time robust simultaneous stabilization problem of a set of nonlinear time‐delay systems with general forms and proposes some new simultaneous stabilization results. First, by developing an equivalent form and applying augmented technique, this paper obtains an augmented equivalent form of the original systems. Secondly, based on the equivalent form, we study finite‐time simultaneous stabilization problem and present some new stabilization results by constructing some suitable Lyapunov functionals. Thirdly, using the simultaneous stabilization results obtained, this paper investigates the finite‐time robust simultaneous stabilization problem for the set systems and proposes a delay‐dependent robust simultaneous stabilization result. Finally, the study of an illustrative example shows that the results obtained by this paper work well in the finite‐time robust simultaneous stabilization the set systems. It is shown that, by using the method in this paper, the developed conditions do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden in studying nonlinear time‐delay systems.

3-D Flight Path Tracking Control for Unmanned Aerial Vehicles Under Wind Environments

This paper provides a new design framework for 3D flight path tracking control of unmanned aerial vehicles (UAVs) under wind environments. The new design framework simultaneously achieves the following three points: (i) 3D path tracking error system representation using the Serret-Frenet frame under wind environments, (ii) guaranteed cost control, (iii) simultaneous stabilization by a single controller for different 3D paths with a common interval parameter setting in the Serret-Frenet frame. To realize the three points, a path tracking error system based on the 3D kinematic model of UAVs under wind environments is constructed in the Serret-Frenet frame. The path tracking error system is exactly represented with the Takagi-Sugeno (T-S) fuzzy model in considered operation domains. As an advantage of the T-S fuzzy model construction, this paper considers a guaranteed cost controller design that minimizes the upper bound of a given performance function. The guaranteed cost controller design problem is cast in terms of linear matrix inequalities (LMIs). Thus, the designed controller guarantees not only the path stabilization but also the guaranteed cost control even in path tracking control for a given desired 3D flight path under wind environments. In addition, a simultaneous stabilization problem is also considered in terms of finding a common solution in a set of the LMIs. The simulation results show the utility of the proposed 3D flight path tracking control under wind environments.

Adaptive Robust Simultaneous Stabilization of Two Dynamic Positioning Vessels Based on a Port-Controlled Hamiltonian (PCH) Model

In this paper, the adaptive robust simultaneous stabilization problem of two ships is studied. Firstly, the water surface three-degree-of-freedom ship models are transformed into port-controlled Hamiltonian (PCH) models. Using a single output feedback controller, the two PCH systems are combined to generate an enhanced PCH system based on Hamiltonian structural attributes. Then, considering the situation with both external interference and structural parameter perturbation in the systems, an adaptive robust output feedback controller is designed to stabilize the two systems simultaneously. Finally, the effectiveness of the controller proposed in this paper is illustrated by a simulation example.

Design of pseudo-predictor feedback for neutral-type linear systems with both state and input delays

In this paper, the stabilization problem of neutral-type linear time-delay systems with both state and input delays is studied. A pseudo-predictor feedback (PPF) approach is established to predict the future states such that the input delay is compensated properly. It is shown that the considered system can be stabilized by the PPF controller if and only if an associated integral delay system is asymptotically stable. Moreover, it is proved that the PPF controller can be safely implemented without involving any input filters. The computation of the feedback gains problem is successfully converted to a simultaneous stabilization problem, which is solved by adopting a direct optimization approach. The proposed PPF approach is also extended to neutral-type time-varying time-delay systems. A numerical example is carried out to illustrate the effectiveness of the proposed controllers.

Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances

In motor system control design, a single controller is usually employed to simultaneously control two or more motors for saving costs, which also achieves the computational simplification of control. In practical Hamiltonian systems control, more systems also need to be stabilized by a single controller under some working conditions. Thus, this paper studies simultaneous stabilization problem of two nonlinear Port-controlled Hamiltonian (PCH) systems with disturbances by a composite controller. Based on the Hamiltonian structure properties, two PCH systems are combined together to generate an augmented PCH system by utilizing output feedbacks firstly. Then, to estimate disturbances effectively, it is essential to design a nonlinear disturbance observer (NDOB) and the estimate is employed to feedforward compensate the effects of disturbances. Next, combining the output feedback part and the disturbance compensation part together, a simultaneous stabilization controller is developed. Subsequently, it is proved that the closed-loop system under the proposed controller is asymptotically stable. Finally, an example with simulations reveals that the proposed method is effective.

Simultaneous stabilization of a collection of uncertain discrete-time systems with time-varying state-delay via discrete-time sliding mode control

This paper considers the simultaneous stabilization problem which concerns finding a single controller to simultaneously stabilize a finite collection of discrete-time nonlinear systems with time-varying state delay and norm-bounded uncertainties. For this purpose, a simultaneously stabilizing discrete-time sliding mode controller (DT-SMC) is synthesized. Based on the delay-dependent Lyapunov–Krasovskii functional method, sufficient conditions are derived which guarantee the existence of a common sliding surface in terms of a nonconvex feasibility problem. The cone complementarity linearization approach is exploited to transform the nonconvex conditions into a convex optimization problem. Finally, the robust simultaneously stabilizing DT-SMC is designed in order to draw the closed-loop trajectories of each system onto the common sliding surface in finite time and to maintain it thereafter. The effectiveness of the proposed method is investigated by simulation of a practical example.

Simultaneous local stabilisation and fault detection for continuous‐time T‐S fuzzy systems

In this study, a simultaneous local stabilisation and fault detection (FD) problem for Takagi-Sugeno (T-S) fuzzy systems is investigated. The authors' attention is focused on synthesising an FD observer and an observer-based controller to achieve the objectives of local stabilisation and FD simultaneously. First, by establishing the relationship among the reachable set, the ellipsoid set and the objective area, a new local stabilisation criterion is proposed. The presented criterion guarantees that the state trajectory starting from a given local region can remain in this region even when the system is subject to disturbances and faults. Meanwhile, the FD observer is designed under a mixed framework such that the residual signal is robust to the persistent disturbance and sensitive to the fault. Different from some existing methods, via the proposed scheme, the state can be restricted into the modelling area so that the non-linear control problem can be addressed by the T-S fuzzy model approach effectively. Additionally, two different methods are utilised in the co-design of the observer and the controller such that the disturbance is not required to be energy-bounded. Finally, the effectiveness of the proposed approach is demonstrated by an example.

On the simultaneous stabilization for a family of time‐varying linear systems under the transmission condition

AbstractThis paper deals with the simultaneous stabilization problem for a family of discrete time‐varying linear systems in the framework of nest algebra. Under the transmission condition, a necessary and sufficient condition for simultaneous "stabilizability" is established in terms of single strong representation for only one controller in the transmission condition, in which the resulting characterization involves no strong representation of the plants compared to previous work.

Consensusability of Discrete-Time Multiagent Systems With Communication Delay and Packet Dropouts

In this paper, we study the mean-square consensusability problem of discrete-time linear multiagent systems over directed networks with constant communication delay and packet dropouts. When the packet dropouts in different communication channels are identical, the consensusability problem is transformed into a simultaneous mean-square stabilization problem of systems with constant time delay and packet dropout. When the packet dropouts are nonidentical, we build the dynamics over edges based on the notion of compressed edge Laplacian for directed graphs to separate the packet dropouts from the network topology. Sufficient consensusability conditions are obtained for both cases in terms of the communication delay, the packet dropout rates, the communication network topology, and the agent dynamics.