Stabilizing composite control for a class of linear systems modeled by singularly perturbed Ito differential equations

In this paper, the problem of robust H_∞ control is investigated for sampled-data systems with probabilistic sampling. The parameter uncertainties are time-varying norm-bounded and appear in both the state and input matrices. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input delay approach, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters in the system matrices. By linear matrix inequality (LMI) approach, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an H_∞ performance. Moreover, an H_∞ controller design procedure is then proposed. An illustrative example is included to demonstrate the effectiveness of the proposed techniques.     

Attainability of the minimum data rate for stabilization of linear systems via logarithmic quantization

This paper investigates the attainability of the minimum average data rate for stabilization of linear systems via logarithmic quantization. It is shown that a finite-level logarithmic quantizer suffices to approach the well-known minimum average data rate for stabilizing an unstable linear discrete-time system under two basic network configurations. In particular, we derive explicit finite-level logarithmic quantizers and the corresponding controllers to approach the minimum average data rate.     

On event design in event-triggered feedback systems

This paper studies event design in event-triggered feedback systems. A novel event-triggering scheme is presented to ensure exponential stability of the resulting sampled-data system. The scheme postpones the triggering of events over previously proposed methods and therefore enlarges the intersampling period. The resulting intersampling periods and deadlines are bounded strictly away from zero when the continuous time system is input-to-state stable with respect to measurement errors.     

On the performance of high-gain observers with gain adaptation under measurement noise

We address the problem of state observation for a system whose dynamics may involve poorly known, perhaps even nonlocally Lipschitz functions and whose output measurement may be corrupted by noise. It is known that one way to cope with all these uncertainties and noise is to use a high-gain observer with a gain adapted on-line. The proposed method, while presented for a particular case, relies on a “generic” analysis tool based on the study of differential inequalities involving quadratic functions of the error system in two coordinate frames plus the gain adaptation law. We establish that, for bounded system solutions, the estimated state and the gain are bounded. Moreover, we provide an upper bound for the mean value of the error signals as a function of the observer parameters. Since due to perturbations the gain adaptation law may drive the observer/plant interconnection to nearby boundary of its stability region, oscillatory behavior may emerge. To overcome this issue, we suggest an adaptive procedure based on a space averaging technique involving several copies of the observer.     

A constructive speed observer design for general Euler–Lagrange systems

Astolfi, Ortega, and Venkatraman (2010) recently proved the existence of a globally exponentially convergent speed observer for general Euler–Lagrange systems. Key to their result, is a function defined by certain integrals which cannot be solved a priori, and may not have explicit analytic solutions. In this paper, this obstacle to a constructive design is removed and equations that solve the speed observer problem are given in closed form. The design is further simplified by removing up to one third of the observer states used in Astolfi et al. (2010). With the significant reduction in complexity, the new observer is easily applied to estimate the angular velocities in a Furuta pendulum example.     

Partial-realization theory for linear switched systems —A formal power series approach

The paper presents partial-realization theory and a realization algorithm for linear switched systems. The results are similar to partial-realization theory of linear and bilinear systems. Our main tool is the theory of rational formal power series.     

An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range

In this paper, we present an automatic C-code generation strategy for real-time nonlinear model predictive control (NMPC), which is designed for applications with kilohertz sample rates. The corresponding code export module has been implemented within the software package ACADO Toolkit. It is capable of exporting fixed step-size integrators together with their sensitivities as well as a real-time Gauss–Newton method. Here, we employ the symbolic representation of optimal control problems in ACADO in order to auto-generate plain C-code which is optimized for final production. The exported code has been tested for model predictive control scenarios comprising constrained nonlinear dynamic systems with four states and a control horizon of ten samples. The numerical simulations show a promising performance of the exported code being able to provide feedback in much less than a millisecond.     

Controlled linear perturbation

We present an algorithmic solution to the robustness problem in computational geometry, called controlled linear perturbation, and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Approximate computation in floating point arithmetic is efficient but can assign incorrect signs to geometric predicates, which can cause combinatorial errors in the algorithm output. We make approximate computation accurate by performing small input perturbations, which we compute using differential calculus. This strategy supports fast, accurate Minkowski sum computation. The only prior robust implementation uses a less efficient algorithm, requires exact algebraic computation, and is far slower based on our extensive testing.     

Fuzzy identity based signature with applications to biometric authentication

We introduce a new cryptographic primitive which is the signature analog of fuzzy identity based encryption (FIBE). We call it fuzzy identity based signature (FIBS). It possesses similar error-tolerance property as FIBE that allows a user with the private key for identity ω to decrypt a ciphertext encrypted for identity ω′ if and only if ω and ω′ are within a certain distance judged by some metric. We give the definition and security model of FIBS and present the first practical FIBS scheme. We prove that our scheme is existentially unforgeable against adaptively chosen message attack in the standard model. To our best knowledge, this primitive was never considered in the identity based signature before. FIBS is of particular value for biometric authentication, where biometric identifiers such as fingerprints, iris, voice and gait are used in human identification. We demonstrate the applicability of our construction to secure biometric authentication.