A modified GADIA-based upper-bound to the capacity of Gaussian general N-relay networks

In this paper, we present a general Gaussian N-relay network by allowing relays to communicate to each other and allowing a direct channel between source and destination as compared to the standard diamond network in Nazaroğlu et al. (IEEE Trans Inf Theory 60:6329–6341, 2014) at the cost of extra channel uses. Our main focus is to examine the min-cut bound capacities of the relay network. Very recently, the results in Uykan (IEEE Trans Neural Netw Learn Syst 31:3294–3304, 2020) imply that the GADIA in Babadi and Tarokh (IEEE Trans Inf Theory 56:6228–6252, 2010), a pioneering algorithm in the interference avoidance literature, actually performs max-cut of a given power-domain (nonnegative) link gain matrix in the 2-channel case. Using the results of the diamond network in Nazaroğlu et al. (2014) and the results in Uykan (2020), in this paper, we (i) turn the mutual information maximization problem in the Gaussian N-relay network into an upper bound minimization problem, (ii) propose a modified GADIA-based algorithm to find the min-cut capacity bound and (iii) present an upper and a lower bound to its min-cut capacity bound using the modified GADIA as applied to the defined “squared channel gain matrix/graph”. Some advantages of the proposed modified GADIA-based simple algorithm are as follows: (1) The Gaussian N-relay network can determine the relay clusters in a distributed fashion and (2) the presented upper bound gives an insight into whether allowing the relays to communicate to each other pays off the extra channel uses or not as far as the min-cut capacity bound is concerned. The simulation results confirm the findings. Furthermore, the min-cut upper bound found by the proposed modified-GADIA is verified by the cut-set bounds found by the spectral clustering based solutions as well.

Global Stability and Exponential Decay of Processes in Nonlinear Feedback Systems with Different Fractional Orders

The global stability of continuous-time multi-input multi-output nonlinear feedback systems with different fractional orders and interval matrices of positive linear parts is investigated. New sufficient conditions for the global stability of this class of positive nonlinear systems are established. Sufficient conditions for the exponential decay of processes in fractional nonlinear systems are given. Procedures for computation of a gain matrix characterizing the class of nonlinear elements are proposed and illustrated by examples.

System Characterization and Adaptive Tracking Control of Quadrotors under Multiple Operating Conditions

This paper presents an adaptive controller design framework with input compensation for quadrotor systems, which deals with different system operating conditions with a uniform update law for the controller parameters. The motivation of the work is to handle the situation that existing adaptive control schemes are either restricted to the system equilibrium as the hover condition or unable to deal with the diverse system uncertainties which cause system interactor matrix and high-frequency gain matrix to change. An adaptive control scheme equipped with an input compensator is constructed to make the system to have a uniform interactor matrix and a consistent pattern of the gain matrix signs over different operating conditions, which are key prior design conditions for model reference adaptive control applied to quadrotor systems. To deal with the uncertain system high-frequency gain matrix, a gain matrix decomposition technique is employed to parametrize an error system model in terms of the gain parameters and tracking errors, for the design of an adaptive parameter update law with reduced system knowledge. It is ensured that all closed-loop system signals are bounded, and the system output tracks a reference output asymptotically despite the system parameter uncertainties and the uncertain offsets at non-equilibrium operating conditions. The proposed scheme expands the capacity of adaptive control for quadrotors to operate at multiple operating conditions in the presence of system uncertainties. Simulation results of a quadrotor with the proposed adaptive control scheme are presented to show the desired system performance.

Fuzzy Adaptive Control of Uncertain MIMO Chaotic Systems with Unknown Control Direction

This paper presents an adaptive controller for MIMO chaotic systems with system uncertainties and unknown control direction. In the controller design, the matrix decomposition theory is used, and we decompose the control gain matrix into a positive matrix, a diagonal matrix whose diagonal entries are +1 or −1, and a unity upper triangular matrix. To handle the unknown control direction (i.e., the unknown sign of the control gain matrix), we use the Nussbaum-type function. In addition, we propose an adaptation law named proportional integral (PI) law to update the parameters of the fuzzy system. The stability of the controlled system is proven strictly. Finally, simulation results are presented.

Low-Speed Stability Optimization of Full-Order Observer for Induction Motor

In terms of the instability of the full-order observer for the induction motor in the low-speed regenerative mode, the low-speed unstable region which leads to the extension of the commissioning cycle cannot be eliminated by the traditional adaptive law which aims at good system performance. It is proposed that the feedback gain matrix can control both the unstable region and the system performance both. To make a trade-off between the stability and performance by designing the feedback gain matrix is still an open problem. To solve this problem, first we analyze the cause of instability and derive constraints to ensure system stability by establishing a transfer function of the adaptive observing system for the speed. Then, with the derived constraints as the design criteria for the feedback gain matrix, a control strategy combining the weighted adaptive law with the improved feedback gain matrix is proposed to improve the stability at low speed. Finally, by comparing the traditional control strategy with the proposed control strategy through simulations and experiments, we show that the proposed control strategy achieves better performance with higher stability.

Guaranteed Cost Formation Tracking Control for Swarm Systems with Intermittent Communications

The current paper studies guaranteed cost time-varying formation tracking design and analysis problems of high-order swarm systems subject to intermittent communications. Different from the existing work of the time-varying formation control, the time-varying formation tracking can be achieved while certain performance can be guaranteed, and the impacts of the intermittent communications and switching topologies are considered. First, a new intermittent time-varying formation tracking control protocol with a global performance index is proposed, where not only the formation regulation performances but also the control energy expenditures are involved. The codesign of the gain matrix with the performance index is achieved to compromise the formation regulation performances against control energy expenditures, and the guaranteed cost is determined to restrain the upper bound of the performance index. Then, guaranteed cost time-varying formation tracking design and analysis criteria are given, where the matrix variable of the linear matrix inequality conditions is used to design the gain matrix and to determine the guaranteed cost. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results.