Biblio

This brief presents a methodology to develop recursive filters in reproducing kernel Hilbert spaces. Unlike previous approaches that exploit the kernel trick on filtered and then mapped samples, we explicitly define the model recursivity in the Hilbert space. For that, we exploit some properties of functional analysis and recursive computation of dot products without the need of preimaging or a training dataset. We illustrate the feasibility of the methodology in the particular case of the γ-filter, which is an infinite impulse response filter with controlled stability and memory depth. Different algorithmic formulations emerge from the signal model. Experiments in chaotic and electroencephalographic time series prediction, complex nonlinear system identification, and adaptive antenna array processing demonstrate the potential of the approach for scenarios where recursivity and nonlinearity have to be readily combined.

The gradient-descent total least-squares (GD-TLS) algorithm is a stochastic-gradient adaptive filtering algorithm that compensates for error in both input and output data. We study the local convergence of the GD-TLS algoritlun and find bounds for its step-size that ensure its stability. We also analyze the steady-state performance of the GD-TLS algorithm and calculate its steady-state mean-square deviation. Our steady-state analysis is inspired by the energy-conservation-based approach to the performance analysis of adaptive filters. The results predicted by the analysis show good agreement with the simulation experiments.

This paper develops an opposition-based learning harmony search algorithm with mutation (OLHS-M) for solving global continuous optimization problems. The proposed method is different from the original harmony search (HS) in three aspects. Firstly, opposition-based learning technique is incorporated to the process of improvisation to enlarge the algorithm search space. Then, a new modified mutation strategy is instead of the original pitch adjustment operation of HS to further improve the search ability of HS. Effective self-adaptive strategy is presented to fine-tune the key control parameters (e.g. harmony memory consideration rate HMCR, and pitch adjustment rate PAR) to balance the local and global search in the evolution of the search process. Numerical results demonstrate that the proposed algorithm performs much better than the existing improved HS variants that reported in recent literature in terms of the solution quality and the stability.

Distributed optimization is an emerging research topic. Agents in the network solve the problem by exchanging information which depicts people's consideration on a optimization problem in real lives. In this paper, we introduce two algorithms in continuous-time to solve distributed optimization problems with equality constraints where the cost function is expressed as a sum of functions and where each function is associated to an agent. We firstly construct a continuous dynamic system by utilizing the Lagrangian function and then show that the algorithm is locally convergent and globally stable under certain conditions. Then, we modify the Lagrangian function and re-construct the dynamic system to prove that the new algorithm will be convergent under more relaxed conditions. At last, we present some simulations to prove our theoretical results.

The vast majority of today's critical infrastructure is supported by numerous feedback control loops and an attack on these control loops can have disastrous consequences. This is a major concern since modern control systems are becoming large and decentralized and thus more vulnerable to attacks. This paper is concerned with the estimation and control of linear systems when some of the sensors or actuators are corrupted by an attacker. We give a new simple characterization of the maximum number of attacks that can be detected and corrected as a function of the pair (A,C) of the system and we show in particular that it is impossible to accurately reconstruct the state of a system if more than half the sensors are attacked. In addition, we show how the design of a secure local control loop can improve the resilience of the system. When the number of attacks is smaller than a threshold, we propose an efficient algorithm inspired from techniques in compressed sensing to estimate the state of the plant despite attacks. We give a theoretical characterization of the performance of this algorithm and we show on numerical simulations that the method is promising and allows to reconstruct the state accurately despite attacks. Finally, we consider the problem of designing output-feedback controllers that stabilize the system despite sensor attacks. We show that a principle of separation between estimation and control holds and that the design of resilient output feedback controllers can be reduced to the design of resilient state estimators.