Dissipativity for Lur’e distributed parameter control systems

AbstractIn this work, dissipativity of Lur’e distributed parameter control systems has been addressed. Delay-dependent sufficient conditions for the dissipativity with respect to the infinite-dimensional version of energy supply rate (Q1,S1,R1) characterized exclusively by unbounded operator Q1 are established in terms of linear operator inequalities (LOIs). Finally, the heat equation illustrates our result

Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.Comment: This is an extended version of our IEEE CDC 2015 paper to appear in Japa

Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System

Many problems with control theory have led to investigations into switched systems. One of the most urgent problems related to the analysis of the dynamics of switched systems is the stability problem. The stability of a switched system can be ensured by a common Lyapunov function for all switching modes under an arbitrary switching law. Finding a common Lyapunov function is still an interesting and challenging problem. The purpose of the present paper is to prove the stability of equilibrium in a certain class of nonlinear switched systems by introducing a common Lyapunov function; the Lyapunov function is based on generalized Kullback–Leibler divergence or Csiszár's I-divergence between the state and equilibrium. The switched system is useful for finding positive solutions to linear algebraic equations, which minimize the I-divergence measure under arbitrary switching. One application of the stability of a given switched system is in developing a new approach to reconstructing tomographic images, but nonetheless, the presented results can be used in numerous other areas

Stability of switched linear differential systems

We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching instants is specified by gluing conditions, i.e. algebraic conditions on the trajectories and their derivatives at the switching instant. We provide sufficient conditions for stability based on LMIs for systems with general gluing conditions. We also analyse the role of positive-realness in providing sufficient polynomial-algebraic conditions for stability of two-modes switched systems with special gluing conditions

Switched Stackelberg game analysis of false data injection attacks on networked control systems

summary:This paper is concerned with a security problem for a discrete-time linear networked control system of switched dynamics. The control sequence generated by a remotely located controller is transmitted over a vulnerable communication network, where the control input may be corrupted by false data injection attacks launched by a malicious adversary. Two partially conflicted cost functions are constructed as the quantitative guidelines for both the controller and the attacker, after which a switched Stackelberg game framework is proposed to analyze the interdependent decision-making processes. A receding-horizon switched Stackelberg strategy for the controller is derived subsequently, which, together with the corresponding best response of the attacker, constitutes the switched Stackelberg equilibrium. Furthermore, the asymptotic stability of the closed-loop system under the switched Stackelberg equilibrium is guaranteed if the switching signal exhibits a certain average dwell time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method in this paper

Group and total dissipativity and stability of multi-equilibria hybrid automata

Complex systems, which consist of different interdependent and interlocking subsystems, typically have multiple equilibrium points associated with different set points of each operation mode. These systems are usually interpreted as switched systems, or in general, as hybrid systems. Surprisingly, the consideration of multiple equilibria is not common in hybrid systems’ literature, being typically focused on the study of stability and dissipativity properties for switched systems whose subsystems share the same equilibrium point. This paper will expand the discussion to the case of having multiple co-existing equilibrium points for hybrid systems modelled as hybrid automata, which are more general than switched systems. A classification of equilibria for hybrid automata is offered, and some stability related properties are shown for them. Moreover, some dissipativity-related properties are studied. The chief idea of our approach is to identify stable and dissipative components as group of discrete locations within the hybrid automaton. Two examples are used to illustrate our conclusions