Problem Of Linear Systems Research Articles

Output Consensus Problem for Linear Heterogeneous Multiagent Systems With Dynamic Event-Based Impulsive Control

This article has a research on the problem of output consensus for linear heterogeneous multiagent systems (LHMASs) by using dynamic event-based impulsive control. First, according to whether the transfer of information from different agents is continuous or not, two corresponding control approaches are provided, respectively. Second, for the case of continuous information transfer, the corresponding dynamic event-triggered condition is obtained. Third, for the case that the information communication from each agent only occurs at the event-triggered time instant, two different dynamic event-triggered conditions according to whether the event-triggered time instant for each agent is same or not are proposed, respectively. For all these event-triggered mechanisms, both the output consensus conditions and the proofs of avoiding Zeno-behavior are given. Moreover, the effect of the dynamic variables belong to these dynamic event-triggered conditions on the minimum event-triggered time interval is also discussed. Finally, the analysis for a numerical example with two control approaches and the corresponding event-triggered conditions provided in this article is obtained to support our opinions.

Shifting Zeros of Pulse Modulation Driven Systems via Exact Linearization Using Multi-Degree-of-Freedom Pulses

This study deals with a control problem for continuous-time linear time-invariant systems driven by a pulse-modulation-type control input. Although pulse-driven systems are nonlinear in terms of manipulable variables, the behavior at the sampling instants can be made to obey a linear law by varying the number and location of the pulses on each control interval, in addition to the pulse widths. This study discusses various systems for the above exact linearization framework, where the zeros of the derived model can be shifted to the stable area by restricting the region of each control interval in which the pulses are assigned. The zero-stabilization ability is useful in achieving high-speed and high-accuracy positioning/path-following because the inverse of a model that consists of only stable zeros can be used as a feedforward controller. To confirm the effectiveness of the proposed method, a control design for a galvanometer scanner is demonstrated in this study.

Regularization of classical optimality conditions in optimization problems for linear Volterra-type systems with functional constraints

Regularization of classical optimality conditions in optimization problems for linear Volterra-type systems with functional constraints

On LQ Control Problem for Linear Discrete-Time Systems with Singular Weightings

On LQ Control Problem for Linear Discrete-Time Systems with Singular Weightings

Parameterized Synthesis of Discrete-Time Positive Linear Systems: A Geometric Programming Perspective

This letter focuses on optimization problems of discrete-time positive linear systems. To this end, the synthesis problem is presented by introducing parameterized system coefficient matrices and optimizing system parameters directly. Based on results concerning positive linear systems and nonnegative matrix theory, we demonstrate that optimization problems of minimizing the parameter tuning cost while satisfying the H2 norm, H∞ norm, and ℓ1/ℓ∞ Hankel norm constraints can be reduced to corresponding geometric programming problems. In turn, by imposing reasonable assumptions on system matrices, these geometric programming problems can be further transformed into convex optimization problems owing to the convexity of the logarithm transformation on posynomials. Finally, simulation experiments on a numerical example and epidemic spreading process example are used to show the validity of the main results.

Distributed State and Input Estimation Over Sensor Networks Under Deception Attacks

This paper is concerned with the joint state and input estimation problem for linear discrete time-varying systems over peer-to-peer sensor networks, in which deception attacks are taken into account. By resorting to singular value decomposition, a local estimator structure is proposed to jointly estimate the system states and unknown inputs. Then, a distributed state estimator is constructed by fusing local estimates and covariance matrices. In addition, a sufficient condition is provided to ensure the uniformly bounded estimation error (in mean square) in each node. Finally, a numerical example is provided to show the effectiveness of the proposed estimation algorithm.

Multi-Symmetric Lyapunov Equations

This letter studies multi-symmetric Lyapunov equations and their application to stochastic control. It is shown how Lyapunov recursions can be used to efficiently compute the tensor-valued cumulants of the transient- and limit distributions of stochastic linear systems. This analysis is based on the assumption that the process noise distribution admits a moment expansion but, apart from this, all derivations and numerical algorithms are kept entirely general—without introducing any further assumptions on the distribution. Moreover, it is shown both theoretically and numerically how to exploit these recursions to construct accurate approximations of a rather general class of stochastic optimal control problems for linear discrete-time systems with conditional-value-at-risk constraints.

Distributed consensus of discrete time-varying linear multi-agent systems with event-triggered intermittent control.

The consensus problem of discrete time-varying linear multi-agent systems (MASs) is studied in this paper. First, an event-triggered intermittent control (ETIC) protocol is designed, aided by a class of auxiliary functions. Under this protocol, some sufficient conditions for all agents to achieve consensus are established by constructing an error dynamical system and applying the Lyapunov function. Second, in order to further reduce the communication burden, an improved event triggered intermittent control (I-ETIC) strategy is presented, along with corresponding convergence analysis. Notably, the difference between the two control protocols lies in the fact that the former protocol only determines when to control or not based on the trigger conditions, while the latter, building upon this, designs new event trigger conditions for the update of the controller during the control stage. Finally, two numerical simulation examples are provided to demonstrate the effectiveness of the theoretical results.

Условие оптимальности типа принципа максимума Понтрягина в задаче управления линейными разностными уравнениями дробного порядка

The optimal control problem of fractional order linear two-dimensional difference equations sys-tems is considered. It is assumed that the control function is included in the boundary condition, and the functional is linear. A necessary and sufficient optimality condition is proved in the discrete maximum principal form. A sufficient optimality condition is proved in the nonlinear but convex cost functional case.

H2 suboptimal leader-follower consensus control of multi-agent systems

In this paper, we investigate the distributed H2 suboptimal leader-follower consensus control problem for linear multi-agent systems using dynamic output feedback. By considering an autonomous leader, a number of followers, and an associated H2 cost functional, we aim to design a distributed protocol to ensure that the leader-follower consensus is achieved while the associated H2 cost is smaller than an a priori given upper bound. To this end, we first show that the H2 suboptimal leader-follower consensus control problem can be equivalently derived as the H2 suboptimal control problem of a set of independent systems. Based on this, we then present a design method for computing a distributed protocol. The computation of the feedback gains involves two Riccati inequalities whose dimension matches the state dimension of the agents. A simulation example is provided to demonstrate the performance of the proposed protocol.

Stability analysis of robust control problems in linear descriptor systems with matching conditions

We investigate the optimal control equivalent and state feedback approach to linear time-invariant descriptor systems with norm-bounded uncertainty in matrix A(q). The goal is to find a controller that can stabilize the system even in the presence of random perturbations and to study the effect of initial conditions on the system’s stability. The systems with matching conditions and also linear algebraic equations with the full rank of the algebraic coefficient matrix are investigated. The solution to the optimal control problem (OCP) for the linear descriptor system (LDS) is the solution to the robust linear descriptor control problem provided. We will show that with theorems and examples.

Observer-Based Distributed Event-Triggered Secure Consensus of Multi-Agent System With DoS Attack

This paper addresses the distributed secure consensus problem for linear multi-agent systems (MAS) with unmeasurable states and Denial-of-Service (DoS) attacks. The observer is designed to be used in estimating unmeasurable states of agents. Then, an observer-based distributed event-triggered control protocol is proposed to save network resources. By using the piecewise Lyapunov function approach, several sufficient conditions for ensuring secure consensus are obtained. Further, a rigorous theoretical analysis shows that the given event-triggering scheme exhibits no Zeno behavior. Finally, the effectiveness of the proposed method is verified by numerical simulation.

Regulator Problem for Linear Continuous-Time Delay Dynamical Systems With Symmetrical Constrained Control

Regulator Problem for Linear Continuous-Time Delay Dynamical Systems With Symmetrical Constrained Control

Non-asymptotic System Identification for Linear Systems with Nonlinear Policies

This paper considers a single-trajectory system identification problem for linear systems under general nonlinear and/or time-varying policies with i.i.d. random excitation noises. The problem is motivated by safe learning-based control for constrained linear systems, where the safe policies during the learning process are usually nonlinear and time-varying for satisfying the state and input constraints. In this paper, we provide a non-asymptotic error bound for least square estimation when the data trajectory is generated by any nonlinear and/or time-varying policies as long as the generated state and action trajectories are bounded. This significantly generalizes the existing non-asymptotic guarantees for linear system identification, which usually consider i.i.d. random inputs or linear policies. Interestingly, our error bound is consistent with that for linear policies with respect to the dependence on the trajectory length, system dimensions, and excitation levels. Lastly, we demonstrate the applications of our results by safe learning with robust model predictive control and provide numerical analysis.

An optimal control perspective on the dynamic allocation problem for linear systems*

In this paper the problem of dynamic control allocation for input redundant, continuous-time linear systems is studied in the context of optimal control theory. Providing a new framework for the subject and relying on a well-established theoretical setting, an equivalent problem formulation is given and its solution is determined and discussed, also highlighting its simpler structure with respect to the one provided by approaches purely in the context of control allocation alone.

Closed-form and robust expressions for data-driven LQ control

This article provides an overview of certain direct data-driven control results, where control sequences are computed from (noisy) data collected during offline control experiments without an explicit identification of the system dynamics. For the case of noiseless datasets, we derive several closed-form data-driven expressions that solve a variety of optimal control problems for linear systems with quadratic cost functions of the state and input (including the linear quadratic regulator problem, the minimum energy control problem, and the linear quadratic control problem with terminal constraints), discuss their advantages and drawbacks with respect to alternative data-driven and model-based approaches, and showcase their effectiveness through a number of numerical studies. Interestingly, these results provide an alternative and explicit way of solving classic control problems that, for instance, does not require the solution of an implicit and recursive Riccati equation as in the model-based setting. For the case of noisy datasets, we show how the closed-form expressions derived in the noiseless setting can be modified to compensate for the bias induced by noise, and perform a sensitivity analysis to reveal favorable asymptotic robustness properties of the derived data-driven controls. We conclude the paper with some considerations and a discussion of outstanding questions and directions of future investigation.

Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation

When faced with a quantum-solving problem for partial differential equations, people usually transform such problems into Hamiltonian simulation problems or quantum-solving problems for linear equation systems. In this paper, we propose a third approach to solving partial differential equations that differs from the two approaches. By using the duality quantum algorithm, we construct a quantum-solving algorithm for solving the first-order wave equation, which represents a typical class of partial differential equations. Numerical results of the quantum circuit have high precision consistency with the theoretical d'Alembert solution. Then the routine is applied to the wave equation with either a dissipation or dispersion term. As shown by complexity analysis for all these cases of the wave equation, our algorithm has a quadratic acceleration for each iteration compared to the classical algorithm.

Impact limit cycles in the planar piecewise linear hybrid systems

This paper aims to study impact limit cycles in the planar piecewise linear hybrid systems formed by center type vector fields and reset maps on the impact surfaces. Motivated by Llibre & Teixeira, 2018, where an open problem was posed: Piecewise linear differential systems with only centers can create limit cycles? We answer this problem for piecewise linear hybrid systems separated by one or two parallel straight lines. By using Poincaré map and first integral, we present an estimate of the maximum number of two-zone and three-zone impact limit cycles. When the hybrid systems are separated by a unique straight line, they can have at most 1 two-zone impact limit cycle. When they are separated by two parallel straight lines, we show that such hybrid systems can have at most 2 three-zone impact limit cycles. Furthermore, we employ some numerical examples to illustrate our main results and show that this upper bound can indeed be reached.

Moment observability and output feedback stabilisation for linear stochastic impulsive systems

ABSTRACT This paper is concerned with the observability of linear stochastic impulsive systems with multiplicative noise. The concept of 2pth moment observability is first introduced. Then, to explore the moment observability, a deterministic expanded system is established for the linear stochastic impulsive systems by the generalised -representation technique. It shows that the linear stochastic impulsive system is 2pth moment observability if and only if the expanded system is completely observable. Subsequently, a series of algebraic criteria and geometric criteria for 2pth moment observability of linear stochastic impulsive systems are established by analysing the solution of the expanded system. The impulsive observer-based stabilisation problem for linear stochastic systems is further studied based on these observability criteria. Finally, two numerical examples illustrate the proposed theoretical results.

Stabilization of discrete-time linear systems with infinite distributed input delays

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.