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This paper studies scalable global state synchronization of discrete-time double integrator multi-agent systems in presence of input saturation based on localized information exchange. A scale-free collaborative linear dynamic protocols design methodology is developed for discrete-time multi-agent systems with both full and partial-state couplings. And the protocol design methodology does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Meanwhile, the protocols are parametric based on a parameter set in which the designed protocols can guarantee the global synchronization result. Furthermore, the proposed protocol is scalable and achieves synchronization for any arbitrary number of agents.

This paper studies scalable global state synchronization of discrete-time double integrator multi-agent systems in presence of input saturation based on localized information exchange. A scale-free collaborative linear dynamic protocols design methodology is developed for discrete-time multi-agent systems with both full and partial-state couplings. And the protocol design methodology does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Meanwhile, the protocols are parametric based on a parameter set in which the designed protocols can guarantee the global synchronization result. Furthermore, the proposed protocol is scalable and achieves synchronization for any arbitrary number of agents., Comment: This article is the complete version of the paper that was accepted by CCC 2022, Hefei China, July 25th-28th, 2022. arXiv admin note: text overlap with arXiv:1908.06535, arXiv:2004.13479

This paper studies synchronization of homogeneous and heterogeneous discrete-time multi-agent systems. A class of linear dynamic protocol design methodology is developed based on localized information exchange with neighbors which does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. The main contribution of this paper is that the proposed protocols are scale-free and achieve synchronization for arbitrary number of agents.

This paper studies output synchronization problems for heterogeneous networks of continuous- or discrete-time right-invertible linear agents in presence of unknown, non-uniform and arbitrarily large input delay based on localized information exchange. It is assumed that all the agents are introspective, meaning that they have access to their own local measurements. Universal linear protocols are proposed for each agent to achieve output synchronizations. Proposed protocols are designed solely based on the agent models using no information about communication graph and the number of agents or other agent models information. Moreover, the protocols can tolerate arbitrarily large input delays., 9 pages, 3 figures, short version of this paper will be presented at Chinese Control Conference 2020. arXiv admin note: text overlap with arXiv:2002.06577, arXiv:2001.02117, arXiv:1908.06535, arXiv:2004.09498

This paper studies regulated state synchronization of discrete-time homogeneous networks of non-introspective agents in presence of unknown non-uniform input delays. A scale free protocol is designed based on additional information exchange, which does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. The proposed protocol is scalable and achieves state synchronization for any arbitrary number of agents. Meanwhile, an upper bound for the input delay tolerance is obtained, which explicitly depends on the agent dynamics., Comment: This article focuses on the synchronization of DISCRETE-TIME multi-agent systems (MAS) in present of unknown non-uniform input delays. It is the discrete-time version of article arXiv:2001.02117. Even though the same problem (the synchronization of MAS) is dealt with in these two papers, the analysis and design tools and the resulting protocols are completely different

This paper studies regulated state synchronization of homogeneous networks of non-introspective agents in presence of unknown nonuniform input delays. A scale-free protocol is designed based on additional information exchange, which does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. The proposed protocol is scalable and achieves state synchronization for any arbitrary number of agents. Meanwhile, an upper bound for the input delay tolerance is obtained, which explicitly depends on the agent dynamics., Comment: arXiv admin note: text overlap with arXiv:1908.06535

In this paper, we consider scalable output and regulated output synchronization problems for heterogeneous networks of right-invertible linear agents based on localized information exchange where in the case of regulated output synchronization, the reference trajectory is generated by a so-called exosystem. We assume that all the agents are introspective, meaning that they have access to their own local measurements. We propose a scale-free linear protocol for each agent to achieve output and regulated output synchronizations. These protocols are designed solely based on agent models and they need no information about communication graph and the number of agents or other agent models information., Comment: The short version of this paper is presented in 2020 American Control Conference Denver, CO, USA. arXiv admin note: text overlap with arXiv:2007.03478, arXiv:2004.13014, arXiv:2004.09498, arXiv:1908.06535, arXiv:2004.13479

This paper studies global and semi-global regulated state synchronization of homogeneous networks of non-introspective agents in presence of input saturation based on additional information exchange where the reference trajectory is given by a so-called exosystem which is assumed to be globally reachable. Our protocol design methodology does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Moreover, the proposed protocol is scalable and achieves synchronization for any arbitrary number of agents., Comment: 8 pages, 6 figures, extended version of the paper submitted to 58th Conference on Decision and Control - Nice, France - December 11th-13th 2019

We consider the H∞ almost output synchronization and regulated output synchronization problem for heterogeneous directed networks with external disturbances where agents are introspective (i.e., agents have access to a part of their own states). A decentralized protocol is designed for each agent, without exchanging internal controller states with neighboring agents, to achieve output synchronization and regulated output synchronization while making the H∞ norm from the disturbances to the synchronization errors in the network arbitrarily small. Furthermore, the idea for output synchronization is applied to a formation problem in the presence of disturbances. The method is illustrated by simulation examples.

The main contribution of this paper is to point out the vast difference between a discrete-time double integrator subject to actuator saturation and a continuous-time double integrator subject to actuator saturation. In continuous-time, any linear state feedback control law which locally stabilizes the double integrator, also globally stabilizes the double integrator in the presence of actuator saturation. In discrete-time, the equivalent of the double integrator has intrinsically different behavior. Some linear feedbacks which locally stabilize the double integrator, also globally stabilize the double integrator in the presence of actuator saturation. However, other linear feedbacks which locally stabilize the double integrator, do not globally stabilize the double integrator in the presence of actuator saturation. We classify a class of linear feedback laws which achieve local stability but also yield nonzero periodic solutions in the presence of actuator saturation and therefore cannot achieve global asymptotic stability.

We consider stochastic almost output synchronization for time-varying directed networks of nonidentical and non-introspective (i.e., agents have no access to their own states or outputs) agents under external stochastic disturbances. The network experiences switches at unknown moments in time without chattering. A purely decentralized (i.e., the additional communication channel among agents is dispensed) time-invariant protocol based on a low- and high-gain method is designed for each agent to achieve stochastic almost output synchronization, while reducing the impact of stochastic disturbances.Moreover, we extend the problem to the case where stochastic disturbances can have nonzero mean or other disturbances are present with known frequencies. Another purely decentralized protocol is designed to completely reject the impact of disturbances with known frequencies on the synchronization error.

We consider the H∞ almost output synchronization and regulated output synchronization problem for heterogeneous directed networks with external disturbances where agents are introspective (i.e. agents have access to a part of their own state). A decentralized protocol is designed for each agent, without exchanging internal controller states with neighboring agents, to achieve output synchronization and regulation while holding back the H∞ norm from the disturbances to the synchronization errors in the closed-loop transfer function of the network. The method is illustrated by simulation examples.

This paper studies the synchronization problem for a network of identical discrete-time agents with unknown uniform constant communication delay. When the agents are non-introspective, the problem is solvable via a decentralized low-gain-based synchronization controller if the delay satisfies the proposed upper bound. When the agents are introspective, the synchronization problem can be solved with arbitrary bounded communication delay.

In this paper, we consider the output synchronization problem for heterogeneous networks of right-invertible linear agents. We assume that all the agents are introspective, meaning that they have access to their own local measurements. Under this assumption, we then propose a decentralized control scheme for solving the output synchronization problem for a set of network topologies. The proposed scheme can also be applied to solve the output formation problem with arbitrary formation vectors. We also consider the regulation of output synchronization problem, where the output of each agent has to track an a priori specified reference trajectory, generated by an exosystem. In this case, we assume that the root agent has access to its own output relative to the reference trajectory.

In this paper, we study the disturbance response of open-loop neutrally stable linear systems with saturating linear feedback controller. It is shown that the closed-loop states remain bounded if the disturbances con- sists of those signals that do not have large sustained frequency components corresponding to the system’s eigenvalues on the imaginary axis (continuous-time) or on the unit circle (discrete-time).

The main contribution of this paper is to completely characterize the dynamic behavior of the discrete-time double integrator with a saturated locally stabilizing linear state feedback law. In continuous-time setting, any linear state feedback control law that locally stabilizes the double integrator also globally stabilizes the system in the presence of actuator saturation. In discrete-time setting, the equivalent of the double integrator does not have the same property. In this paper, we completely characterize the global behavior of saturated locally stabilizing linear state feedback laws for the discrete-time double integrator.

In this paper, we study control of a chain of integrators under actuator saturation and non-additive dis- turbances. We shall show that boundedness of the states can be ensured if the disturbances are matched and integral-bounded, misaligned and magnitude-bounded, or a combination of the two, using either a static or a dynamic low-gain state feedback. This result is an extension of our earlier work on double integrator.

Linear systems with constraints on inputs and states are ubiquitous. Control of such systems has been a long-time challenge to control engineers and will continue to remain so. Indeed, the challenge of constraints is intense and dauntingly formidable and familiar. This book focuses on the very fundamental and primary goal of providing internal stability as well as external stability in the presence of disturbances and reference inputs. The focus is on both the analysis and design for both continuous- and discrete-time systems. A taxonomy of constraints paves distinct paths showing what is feasible and what is not. Internal and External Stabilization of Linear Systems with Constraints is an excellent reference for practicing engineers, graduate students, and researchers in control systems theory and design. The book may also serve as an advanced graduate text for a course or a seminar in nonlinear control systems theory and design in applied mathematics or engineering departments. Minimal prerequisites include a first graduate course in state-space methods as well as a first course in control systems design.

In this paper we study control under input saturation and disturbances of neutrally stable and critically unstable linear systems. It is shown that a feedback controller can be designed so that the closed-loop states remain bounded for disturbances which belong to two different classes depending on the specific system structure and the equilibrium is globally asymptotically stable.

We study in this paper the control of discrete-time neutrally stable and critically unstable linear systems subject to input saturation and disturbances. It is shown that a feedback controller can be designed so that the closed-loop states remain bounded for two classes of disturbances and the equilibrium is globally asymptotically stable.

For stabilization of linear systems subject to input saturation, there exist four different approaches of low-gain design all of which are independently proposed in the literature, namely direct eigenstructure assignment, $H_2$ and $H_\infty$ algebraic Riccati equation (ARE) based methods, and parametric Lyapunov equation based method. It is shown in earlier work that for continuous-time linear systems, all these methods are rooted in and can be unified under two fundamental control theories, $H_2$ and $H_\infty$ theory. In this paper, we extend such a result to a discrete-time setting. Both the $H_2$ and $H_\infty$ ARE-based methods are generalized to consider systems where all input channels are not necessarily subject to saturation, and explicit design methods are developed.

In this paper, we consider three problems, namely, the output consensus problem, the model-reference output consensus problem, and the regulation of output consensus problem, for a network of non-identical right-invertible linear agents. The network provides each agent with a linear combination of multiple agents' outputs. We assume that all the agents are introspective, meaning that they have access to their own local measurements. Under this assumption, we then propose a distributed linear protocol to solve each problem for a broad class of network topologies, including not only Laplacian topologies for a directed graph which contains a directed spanning tree, but a wide family of asymmetric topologies.

A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched between linear systems. We focus first on single-layer sandwich systems, which consist of a single saturation sandwiched between two linear systems. For such systems, we present necessary and sufficient conditions for semi-global and global stabilization problems by state feedback, and develop design methodologies to achieve the prescribed stabilization. We extend the results to single-layer sandwich systems subject to additional actuator saturation. Finally, we discuss further extension to general multi-layer sandwich systems with an arbitrary number of saturations sandwiched between linear systems, both with and without actuator saturation. The design methodologies can be viewed as extensions of classical low-gain design methodologies developed during the 1990s in the context of stabilizing linear systems subject to actuator saturation.

In this paper, we consider three problems, namely, the consensus (synchronization) problem, the model-reference consensus problem, and the regulation of consensus problem, for a network of identical linear time-invariant (LTI) multi-input and multi-output (MIMO) agents. For each problem, we propose a distributed LTI protocol to solve such a problem for a broad class of time-invariant network topologies including not only Laplacian topologies, but a wide family of asymmetric topologies.

For stabilization of linear systems subject to input saturation, there exist four different approaches of low-gain design all of which are independently proposed in the literature, namely direct eigenstructure assignment, H2 and H∞ algebraic Riccati equation (ARE) based methods, and parametric Lyapunov equation based method. We show here all these methods are rooted in and can be unified under two fundamental control theories, H2 and H∞ theory. Moreover, both the H2 and H∞ ARE based methods are generalized to consider systems where all input channels are not subject to saturation, and explicit design methods are developed.

This paper investigates time-invariant linear systems subject to input and state constraints. We study discrete-time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non-right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time-invariant linear systems with non-right invertible constraints, necessary and sufficient conditions are developed under which semi-global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well.

We are concerned here with the stabilization of a linear time invariant system subject to actuator saturation via decentralized control while using linear time invariant dynamic controllers. When there exists no actuator saturation, i.e. when we consider just linear time invariant systems, it is known that global stabilization can be done via decentralized control while using linear time invariant dynamic controllers only if the so-called decentralized fixed modes of it are all in the open left half complex plane. On the other hand, it is known that for linear time invariant systems subject to actuator saturation, semi-global stabilization can be done via centralized control while using linear time invariant dynamic controllers if and only if the open-loop poles of the linearized model of the given system are in the closed left half complex plane. This chapter establishes that the necessary conditions for semi-global stabilization of linear time invariant systems subject to actuator saturation via decentralized control while using linear time invariant dynamic controllers, are indeed the above two conditions, namely (a) the decentralized fixed modes of the linearized model of the given system are in the open left half complex plane, and (b) the open-loop poles of the linearized model of the given system are in the closed left half complex plane. We conjecture that these two conditions are also sufficient in general. We prove the sufficiency for the case when the linearized model of the given system is open-loop conditionally stable with eigenvalues on the imaginary axis being distinct. Proving the sufficiency is still an open problem for the case when the linearized model of the given system has repeated eigenvalues on the imaginary axis.

Having studied during the last decade several aspects of several control design problems for linear systems subject to magnitude and rate constraints on control variables, during the last two years the research has broadened to include magnitude constraints on control variables as well as state variables. Recent work by Han et al. (2000), Hou et al. (1998) and Saberi et al. (2002) considered linear systems in a general framework for constraints including both input magnitude constraints as well as state magnitude constraints. In particular, Saberi et al. consider internal stabilization while Han et al. consider output regulation in different frameworks, namely a global, semiglobal, and regional framework. These problems require very strong solvability conditions. Therefore, a main focus for future research should focus on finding a controller with a large domain of attraction and some good rejection properties for disturbances restricted to some bounded set

Objective(s): The aim of this study was to evaluate the final outcome of nerve regeneration across the eggsell membrane (ESM) tube conduit in comparison with autograft. Materials and Methods: Thirty adult male rats (250-300 g) were randomized into (1) ESM conduit, (2) autograft, and (3) sham surgery groups. The eggs submerged in 5% acetic acid. The decalcifying membranes were cut into four pieces, rotated over the teflon mandrel and dried at 37°C. The left sciatic nerve was surgically cut. A 10-mm nerve segment was cut and removed. In the ESM group, the proximal and distal cut ends of the sciatic nerve were telescoped into the nerve guides. In the autograft group, the 10 mm nerve segment was reversed and used as an autologous nerve graft. All animals were evaluated by sciatic functional index (SFI) and electrophysiology testing. Results:The improvement in SFI from the first to the last evalution in ESM and autograft groups were evaluated. On days 49 and 60 post-operation, the mean SFI of ESM group was significantly greater than the autograft group (P< 0.05). On day 90, the mean nerve conduction velocity (NCV) of ESM group was greater than autograft group, although the difference was not statistically significant (P> 0.05). Conclusion:These findings demonstrate that ESM effectively enhances nerve regeneration and promotes functional recovery in injured sciatic nerve of rat.