Automatica最新文献

By computing Lyapunov functions of a certain, convenient structure, Lyapunov-based methods guarantee stability properties of the system or, when performing synthesis, of the relevant closed-loop or error dynamics. In doing so, they provide conclusive affirmative answers to many analysis and design questions in systems and control. When these methods fail to produce a feasible solution, however, they often remain inconclusive due to (a) the method being conservative or (b) the fact that there may be multiple causes for infeasibility, such as ill-conditioning, solver tolerances or true infeasibility. To overcome this, we develop linear-matrix-inequality-based theorems of alternatives based upon which we can guarantee, by computing a so-called certificate of nonexistence, that no poly-quadratic Lyapunov function exists for a given linear parameter-varying system. We extend these ideas to also certify the nonexistence of controllers and observers for which the corresponding closed-loop/error dynamics admit a poly-quadratic Lyapunov function. Finally, we illustrate our results in some numerical case studies.

The stabilizing switching signal design of discrete-time linear compartmental switched systems (DT-LCSSs) has been heretofore unsolved. It has been proven that a DT-LCSS is stabilizable if and only if it is stabilizable by a periodic switching signal. However, it still needs to be determined whether the period of a stabilizing switching signal can be confined within a bound. Moreover, the existing design method for stabilizing periodic switching signals requires the diagonal entries of system matrices of all subsystems to be strictly positive. In this study, we propose a novel approach to solve this problem completely. We construct a discrete-time Markov chain for a given DT-LCSS, termed the associated Markov chain, and prove the equivalence of stability and stabilizability between the DT-LCSS and the associated Markov chain. Based on this, verifiable necessary and sufficient conditions for stability and stabilizability are derived. Especially, the period of a stabilizing switching signal for an $n$-dimensional DT-LCSS can always be chosen within the bound $n^2-n+1$. We propose a state-independent stabilizing switching signal design method for general stabilizable DT-LCSSs. We also prove the equivalence between stabilizability by state-independent switching laws and stabilizability by state-dependent switching laws. A state-dependent global stabilizing switching signal design method is also proposed. Additionally, the proposed results are applied to the consensus analysis of discrete-time leader–follower multi-agent systems with switching communication digraphs. The effectiveness of the theoretical results is demonstrated by examples.

This paper considers output feedback stabilization of linear systems with both distributed infinite input and output delays. We first propose a PDE-based observer to deal with distributed infinite output delays. The main idea is to transform infinite-delayed output into a transport PDE with a semi-infinite domain. It is proved that the resulted error systems are exponentially stable and thus the observer is effective. Furthermore, relying on the PDE-based observer, a predictor-based output feedback stabilization controller is provided. This work removes a restrictive condition on eigenvalues of open-loop system in the previous work, which is a distinctive advantage of this work. A simulation example is given to illustrate the effectiveness of our proposed observer and controller.

This paper shows how the interconnection of two controlled Irreversible port Hamiltonian Systems has to be state and co-state modulated in order to ensure the closed-loop Irreversible port Hamiltonian structure, satisfying the first and second laws of Thermodynamics. It proposes a precise parametrization of this modulation from the open-loop systems structures in order to guarantee the consistency of the closed loop energy and entropy balance equations. The results are illustrated by means of the examples of a heat-exchanger, a gas-piston system and a chemical reaction.

We give a simple proof of the (perhaps not so) well known fact that exponential polynomials of order $k$ with real exponents have at most $k-1$ real zeros. We deduce several results that relate to impulsive controllability and sampled observability of finite-dimensional linear time-invariant dynamical systems. We prove that the initial state of a continuous-time linear time-invariant dynamical system of dimension $n$ can be uniquely reconstructed from the sampled output regardless of its sampling time sequence of length $n$ if and only if the system is observable and all the eigenvalues of the system matrix are real. This result thus characterizes sampled observability with arbitrary sampling times. Likewise, we prove that the system is controllable by means of $n$ impulses regardless of when they occur if and only if the system is controllable and all the eigenvalues of the system matrix are real. We also show that, if the system is observable and all the eigenvalues of the system matrix are real, then there exists an initial state such that the times where the output crosses a prescribed threshold are prescribed $m$ times with $m<n$.

In this paper, disturbance rejection approaches are suggested to stabilize Korteweg–de Vries–Burgers (KdVB) equation under the averaged measurements. Here two approaches—active disturbance rejection control (ADRC) and disturbance observer-based control (DOBC), are introduced to reject the external unknown disturbance actively. The main challenging issue is to design the effective extended state observer (ESO)/disturbance observer (DO) for KdVB equation respectively. As for ADRC strategy, the disturbance is rejected on the basis of an ESO. As for DOBC strategy, a DO is constructed to estimate the disturbance formulated by an exogenous system. Continuous-time and event-triggered anti-disturbance controllers are further presented for distributed stabilization of KdVB system. To significantly reduce the amount of control updates, an event-triggering mechanism is utilized and the Zeno behaviour is avoided. Sufficient stability conditions are established via Lyapunov functional method. The effectiveness of proposed approaches is verified by simulation results.

This paper addresses a nonsmooth aggregative game to control multiple noncooperative players, each with a nonsmooth cost function that depends not only on its own decision but also on some aggregate effect among all the agents. In addition, the decision of each player is restricted by private and coupling constraints. To address these concerns, a distributed generalized Nash equilibrium (GNE) seeking algorithm is proposed. Two features distinguish our methods from the existing GNE seeking algorithms. Firstly, an adaptive penalty method is introduced to drive each player’s action to enter the set of private constraints. The adaptive term ensures automatic adjustment of penalty parameter based on the degree of constraint violation excluding any prior calculation. Secondly, a distributed dynamic event-triggered mechanism is designed for each player to lessen communication energy. In comparison to the static event-triggered mechanism, the proposed dynamic mechanism possesses larger inter-execution time intervals. As the discontinuity of the event-triggered mechanism can impact the existence of a solution to the closed-loop system in the classical sense, we adapt a nonsmooth analysis technique, including differential inclusion and Filippov solution. Through nonsmooth Lyapunov analysis, the convergence result and the avoidance of Zeno behavior are established. Finally, two engineering examples are provided to demonstrate the validity of the theoretical results.

It poses technical difficulty to achieve distributed consensus tracking control with input quantizations and deception attacks for nonlinear multi-agent systems subject to mismatched parametric uncertainties via backstepping design. The underlying problem becomes even more complicated because i) the system contains mismatched uncertainties; ii) the output becomes unavailable after attacks, making the conventional recursive control design strategy using traditional error surfaces unsuitable; iii) since only the compromised output signal is available, the impacts of nonlinear items related to unknown attack weights become difficult to be explicitly addressed in the existing available output feedback control results. In this paper, we present a solution to circumvent these obstacles by constructing a set of new K-filters using compromised output only, which, together with a coordinate transformation involving the attacked output and filter variables, allow a new form of backstepping based distributed resilient adaptive control protocol to be developed. Meanwhile, an extra compensation term is incorporated into the real controller to handle the effect of quantization on the system stability. It is shown that, with proper choices of Lyapunov functions, the global uniform boundedness of all the closed-loop signals and the asymptotically output consensus tracking can be achieved. A practice example is provided to verify the benefits of our scheme.

This paper investigates the prescribed-time fully distributed Nash equilibrium seeking (PT-FDNES) problem for nonlinear multi-agent systems (MASs) over weight-unbalanced directed graphs (digraphs). To counterbalance unweighted communication flows caused by the unbalanced network, the temporal transformation technique is first introduced to derive a consensus-based algorithm for calculating the left eigenvector of the Laplacian matrix, based on which a prescribed-time fully distributed estimator with adaptive gains is developed to obtain the NE without requiring any global information. By utilizing this NE estimator to formulate an intermediate control law, the NE seeking problem is then effectively transformed into a local reference-tracking problem. To deal with the non-differentiability issue caused by the NE estimator and ensure the exact tracking, the dynamic gain technique and novel scaling functions are employed to derive a prescribed-time tracking controller which completely compensates for the mismatched uncertainties while reducing the computational burden. The proposed control framework enables the actions of all agents to reach the NE within a prescribed time. In addition, the obtained results are further re-designed to exhibit the robustness by introducing an improved $\sigma$-modification scheme without sacrificing the convergence performance. Numerical examples are provided to demonstrate the validity of the theoretical results.

The opinion evolution problem is studied in this paper for stubborn individuals in cooperation–competition networks, where the individuals’ opinion dynamics is described by the Friedkin–Johnsen model and the competitive relationship between individuals is characterized by negative weights. Then the lifting approach is successfully applied to the Friedkin–Johnsen model to deal with the influence of the negative weights while the path-dependence theory is used to the transition of two arbitrarily adjacent topics. Starting from the weight topology, the relationship between the weight topology and the augmented topology is established, and some sufficient conditions about achieving neutrality, bipartite consensus and convergence for the individuals’ opinions in a sequence of topics are obtained. Interestingly, a necessary and sufficient condition is given to ensure bipartite consensus for the individuals’ opinions under the premise that the weight topology is structurally unbalanced. Furthermore, the Friedkin–Johnsen model with dynamic stubbornness is also considered, and the concept of common topic subsequence is introduced. It is proved that all elements of the topic transfer matrix are positive for the common topic subsequence, and neutrality and bipartite consensus for the individuals’ opinions can be achieved for different types of weight topologies, respectively. Finally, numerical examples are given to support the correctness of the theoretical results.