Sontag's ‘input to state stability condition’ and global stabilization using state detection

This paper deals with the global stabilization problem for nonlinear system using state detection. Sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included. These conditions are based to a version of a Lyapunov-like condition proposed by Sontag, which guarantees ‘input to state stability’.     

A new critical theorem for adaptive nonlinear stabilization

It is fairly well known that there are fundamental differences between adaptive control of continuous-time and discrete-time nonlinear systems. In fact, even for the seemingly simple single-input single-output control system y_t+1=θ₁f(y_t)+u_t+w_t+1 with a scalar unknown parameter θ₁ and noise disturbance {w_t}, and with a known function f(⋅) having possible nonlinear growth rate characterized by |f(x)|=Θ(|x|^b) with b≥1, the necessary and sufficient condition for the system to be globally stabilizable by adaptive feedback is b<4. This was first found and proved by Guo (1997) for the Gaussian white noise case, and then proved by Li and Xie (2006) for the bounded noise case. Subsequently, a number of other types of “critical values” and “impossibility theorems” on the maximum capability of adaptive feedback were also found, mainly for systems with known control parameter as in the above model. In this paper, we will study the above basic model again but with additional unknown control parameter θ₂, i.e., u_t is replaced by θ₂u_t in the above model. Interestingly, it turns out that the system is globally stabilizable if and only ifb<3. This is a new critical theorem for adaptive nonlinear stabilization, which has meaningful implications for the control of more general uncertain nonlinear systems.     

Stabilizability by state feedback implies stabilizability by encoded state feedback

Encoded state feedback is a term which refers to the situation in which the state feedback signal is sampled every T units of time and converted (encoded) into a binary representation. In this note stabilization of nonlinear systems by encoded state feedback is studied. It is shown that any nonlinear control system which can be globally asymptotically stabilized by “standard” (i.e. with no encoding) state feedback can also be globally asymptotically stabilized by encoded state feedback, provided that the number of bits used to encode the samples is not less than an explicitly determined lower bound. By means of this bound, we are able to establish a direct relationship between the size of the expected region of attraction and the data rate, under the stabilizability assumption only, a result which—to the best of our knowledge—does not have any precedent in the literature.     

A converse Lyapunov theorem for almost sure stabilizability

We prove a converse Lyapunov theorem for almost sure stabilizability and almost sure asymptotic stabilizability of controlled diffusions: given a stochastic system a.s. stochastic open-loop stabilizable at the origin, we construct a lower semicontinuous positive definite function whose level sets form a local basis of viable neighborhoods of the equilibrium. This result provides, with the direct Lyapunov theorems proved in a companion paper, a complete Lyapunov-like characterization of the a.s. stabilizability.     

基于FPGA的多特征融合司机疲劳状态检测系统设计

驾驶员的疲劳驾驶是造成交通事故的重要因素,为了实时有效地检测驾驶员的驾驶状态,设计了一种融合多种疲劳特征进行疲劳状态判定的检测算法,并构建了车载的基于现场可编程门阵列(FPGA)的嵌入式检测平台。该多检测算法融合了眼睛和嘴巴的疲劳特征,当某一特征的检测受到影响时可以使用另外的特征进行疲劳状态的判定,较传统的单一特征疲劳检测算法拥有更高的检测效率。实验结果表明:系统的算法简单、可靠、实时性强。     

A generalization of Rosenbrock's theorem

This note presents the simple generalization of Rosenbroek's theorem, concerning the limits of linear state variable feedback in modifying the dynamics of constant linear multivariable systems.     

基于状态权的小波边缘检测算法

提出了一种基于小波变换和各向异性扩散的图像多尺度边缘检测方法。对噪声图像进行小波变换,得到高频和低频小波系数。对高频小波系数归一化后进行各向异性扩散得到状态权,把该权值作用在原高频小波系数上,得到了既去除噪声又保持结构不变的小波系数。对低频小波系数直接用小波阈值方法去噪,利用小波系数模极大值法对去噪后的高频和低频小波系数进行边缘检测,得到最终的边缘图像。实验结果表明,该边缘检测方法由于结合了小波和各向异性扩散方法,从而有效地抑制了噪声,得到了连续、清晰的边缘。     

Periodic stabilizability of switched linear control systems

Stabilizability via direct/observer-based state feedback control for discrete-time switched linear control systems (SLCSs) is investigated in this paper. For an SLCS, the control factors are not only the control input but also the switching signal, and they need to be designed in order to stabilize the system. As a result, stabilization design for SLCSs is more complicated than that for non-switched ones. Differently from the existing approaches, a periodic switching signal and piecewise constant linear state feedback control are adopted to achieve periodic stabilizability for such systems. It is highlighted that multiple feedback controllers need to be designed for one subsystem. For discrete-time SLCSs, it is proved that reachability implies periodic stabilizability via state feedback. A necessary and sufficient criterion for periodic stabilizability is also established. Two stabilization design algorithms are presented for real application. Moreover, it is proved that reachability and observability imply periodic stabilizability via observer-based feedback for discrete-time SLCSs. Periodic detectability, as the dual concept of periodic stabilizability, is discussed and the stabilization design algorithms via observer-based feedback are presented as well.     

A generalization of the Lin-Zhao theorem

The theorem on loop formulas due to Fangzhen Lin and Yuting Zhao shows how to turn a logic program into a propositional formula that describes the program’s stable models. In this paper we simplify and generalize the statement of this theorem. The simplification is achieved by modifying the definition of a loop in such a way that a program is turned into the corresponding propositional formula by adding loop formulas directly to the conjunction of its rules, without the intermediate step of forming the program’s completion. The generalization makes the idea of a loop formula applicable to stable models in the sense of a very general definition that covers disjunctive programs, programs with nested expressions, and more.     

Bounded-input—bounded-output stabilization of nonlinear systems using state detectors

This paper is devoted to the study of relations between Lyapunov stabilization and bounded-input—bounded-output (BIBO) stabilization of nonlinear systems when the state is not available for measurement and various state detectors are employed for implementing feedback control. It is found that with some constraints imposed on the detectors, Lyapunov stabilization implies BIBO stabilization. A feedback control scheme for achieving BIBO stability is presented.     

Asymptotic controllability and observability imply semiglobal practical asymptotic stabilizability by sampled-data output feedback

It is shown, for general nonlinear systems, that asymptotic controllability and observability are sufficient for semiglobal practical asymptotic stabilization by output feedback. Indeed, as previously shown in the literature, asymptotic controllability implies the existence of a (discontinuous in general) state feedback that, when implemented by sample and hold, is semiglobally practically stabilizing and robust to measurement disturbance; moreover, a weak form of observability allows reconstruction of the state with arbitrary precision in an arbitrarily short amount of time. So, we can build an output feedback that operates periodically in two modes: an initial, small fraction of a sampling period is used to estimate the state, and the remainder of the sampling period is used to implement the state feedback control using the state estimate. Our stabilization results are presented not only for compact target sets (e.g., the origin) but also for noncompact target sets.     

Reverse reachability analysis: A new technique for deadlock detection on communicating finite state machines

The communicating finite state machines can exchange messages over bounded FIFO channels. In this paper, a new technique, called reverse reachability analysis, is proposed to detect deadlocks on the communication between the communicating finite state machines. The technique is based on finding reverse reachable paths starting from possible deadlock states. If a reverse reachable path can reach the initial global state, then deadlock occurs. Otherwise the communication is deadlock-free. The effectiveness of the technique has been verified by some real protocols such as a specification of X.25 call establishment/clear protocol and Bartlet's alternating bit protocol.     

Robust fault detection in linear systems based on full-order state observers

A parametric approach to robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order state observers （FSO）. Based on an analytical solution to a type of Sylvester matrix equations, the parameterization of the observer gain matrix is given. In terms of the design degrees of freedom provided by the parametric observer design and a group of introduced parameter vectors, a sufficient and necessary condition for fullorder state observer design with disturbance decoupling is then established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance on the residual signal is also decoupled, and a simple algorithm is developed. The presented approach offers all the degrees of design freedom. Finally, a numerical example illustrates the effect of the proposed approach.     

On a fallacious conjecture about the stabilizability properties of solutions of the Riccati difference equation

In [1], among other results, some conjectures concerning the monotonicity and stabilizing properties of solutions of the difference Riccati equation were proven to be fallacious by means of suitable counterexamples. Moreover, a ‘possibly fallacious conjecture’ was formulated for which no counterexample had been found. In this letter, such a counterexample is provided together with an interpretation of the somewhat counterintuitive behaviour of the Riccati equation.     

Robust strong stabilizability of interval plants: It suffices to check two vertices

It is shown that a proper interval plant is strongly stabilizable if and only if all members are free from unstable pole-zero cancellations and two specially selected vertex plants are strongly stabilizable.     

基于Snort规则库的冲突检测

为了解决Snort入侵检测系统中由于规则库存在冲突而可能导致的漏报和误报问题,提出了检测规则冲突的方法.定义了规则之间的关系;通过单根结构的策略树简单有效的表示规则,并揭示规则之间的关系;由规则之间的关系和相对顺序定义了冲突的类型,并通过冲突状态转换图反映冲突发现的过程,在此基础上进一步提出冲突检测算法;最后对Snort规则库的一部分进行检测,结果表明这种方法可以有效发现冲突.     

A survey on cyber attacks against nonlinear state estimation in power systems of ubiquitous cities

It is well-known that critical infrastructures would be targets for cyber attacks. In this paper, we focus on the power systems (i.e. smart grids) in ubiquitous cities, where every meter is linked to an information network through wireless networking. In a smart grid system, information from smart meters would be used to perform a state estimation in real time to maintain the stability of the system. A wrong estimation may lead to disastrous consequences (e.g. suspension of electricity supply or a big financial loss). Unfortunately, quite a number of recent results showed that attacks on this estimation process are feasible by manipulating readings of only a few meters. In this paper, we focus on nonlinear state estimation which is a more realistic model and widely employed in a real power grid environment. We category cyber attacks against nonlinear state estimation, and review the mechanisms behind. State-of-the-art security measures to detect these attacks are discussed via sensor protection. Hope that the community would be able to come up with a secure system architecture for ubiquitous cities.     

Linear stabilizability of planar nonlinear systems

This paper considers scalar-input two-dimensional nonlinear systems for which the linearization, has a simple zero uncontrollable eigenvalue. The existence of linear stabilizing feedback laws is investigated, using center manifold techniques. This work was partially supported by the Ministero della Pubblica Istruzione, Italia (Progetti di ricerca, di interesse nazionale).